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The buoyancy-driven thermogravitational Rayleigh–Benard convection (RBC) occurs in a 1–3 cm-deep layer of normal He-I in a wide experimental cell heated from above at temperatures below the liquid 4He density maximum T

Vortex thinning is one of the main mechanisms of two-dimensional turbulence. By direct numerical simulation to the two-dimensional Navier–Stokes equations with small-scale forcing and large-scale damping, Xiao et al (2009 J. Fluid Mech. 619 1–44) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. On the other hand, Alexakis and Doering (2006 Phys. Lett. A 359 652–657) calculated the upper bound of the bulk averaged enstrophy dissipation rate of the steady-state two dimensional turbulence. In this paper, we show that vortex thinning induces enhanced dissipation with strictly slower vanishing order of the enstrophy dissipation than Re−1.

We investigate the effect of the secondary baroclinic vorticity (SBV) on the energy cascade in the mixing induced by the multi-mode Richtmyer–Meshkov instability (RMI). With the aid of vorticity-based simplified models and the vortex-surface field, we find that the effect of the SBV peaks at a critical time when the vortex reconnection widely occurs in the mixing zone. Before the critical time, spikes and bubbles evolve almost independently, and we demonstrate that the variation of the kinetic energy spectrum induced by the SBV has the $-1$ scaling law at intermediate wavenumbers using the model of vortex rings. This SBV effect causes the slope of the total energy spectrum at intermediate wavenumbers to evolve towards $-3/2$ at the critical time. Subsequently, the SBV effect diminishes and the energy spectrum decays to the $-5/3$ law. Inspired by the vortex dynamics, we develop a model for estimating the mixing width and validate the model using numerical simulations of the multi-mode RMI with various modes of initial perturbations. This model captures the nonlinear growth of the mixing width before the self-similar growth stage.

The fluid mechanics of hurricanes strongly depends on boundary layer energetics due to the warm-core nature of the system with peak velocities located at lower levels. One barrier that has inhibited a more complete characterization of energy transfer in the boundary layer is a lack of observations that resolve large, turbulent eddies. In particular, the occurrence and structure of upscale energy transfer (backscatter) in the hurricane boundary layer as well as the effects of backscatter on the vortex intensity are unknown. The analysis presented here of very high-resolution, three-dimensional wind observations from Hurricane Rita (2005) at peak intensity reveals large regions of organized backscatter in the boundary layer associated with coherent, turbulent eddies. Strong forwardscatter is also found next to the backscatter regions due to the interaction between adjacent eddies. Two components of the stress tensor are primarily responsible for this alternating scatter structure, as shown by large correlation coefficients between the fields: the radial–vertical component () with average correlations of 79 % and 49 %, respectively. The Leonard, Reynolds and cross-term stress components are also provided. The impact of the sub-filter-scale energy transfer is estimated by computing the kinetic energy budget for the resolved-scale and eddy-scale motions. The results show that the sub-filter-scale energy transfer term is of the same order as the other terms in the eddy-scale budgets, contributing between 16 % and 40 % to the local time tendency with an average contribution of approximately 30 %. These results indicate that the coherent turbulent eddies can affect the vortex dynamics through wave–wave nonlinear interactions, which can subsequently influence the wave–mean flow interactions. This is the first study to examine the full sub-filter-scale energy transfer and its impact on the kinetic energy budget in the hurricane boundary layer. These findings emphasize the importance of coherent turbulence in the energy cascade and have the potential to improve turbulence closure schemes used in numerical simulations.

The present paper’s main goal is to investigate the turbulence structures and combustion characteristics in a model wall jet can combustor (WJCC) employing the large eddy simulation (LES) approach. The laminar flamelet combustion and discrete ordinates radiation models are applied in an Eulerian–Lagrangian approach to simulate a reactive spray flow. The results illustrate that LES together with an appropriate mesh and a suitable time step could properly capture the coherent vortical structures, including vortex tube, streamwise and hairpin vortices throughout the model WJCC. Also, the energy cascade from the largest turbulence length scale (integral length scale) at lower frequency of the spectrum to the smallest one along with the recirculation zones is revealed suitably. At the beginning of WJCC, immediately after the swirler, a region of dense coherent structures is formed that can influence the sharp fluctuations of the droplet. In the primary and intermediate zones the hairpin vortices and in the dilutions zone the streamwise vortices are observed more. A significant temperature reduction and a maximum scalar dissipation rate are detected in the head of hairpins. Results also indicate that the strain rate and flow temperature have an inverse relationship. The greatest strain rate is visible at the center of the collision of the primary jets and the main stream, where there is minimum temperature. The largest values of temperature are detected in the intermediate zone under the influence of the largest reverse flow.

The decay of the developed energy cascade of vortex motion on the water surface excited by perpendicular standing waves at a frequency of 6 Hz is investigated experimentally. It is shown that after the pumping is switched off, the relaxation process begins from the large wave vectors k and occurs in the quasi-adiabatic mode: the Kolmogorov energy distribution proportional to k−5/3 is maintained for a long time due to the nonlinear interaction of vortices.

We extend the vortex-surface field (VSF), whose isosurface is a vortex surface consisting of vortex lines, to identify vortex tubes and sheets in homogeneous isotropic turbulence. The VSF at a time instant is constructed by solving a pseudo-transport equation. This equation is convected by a given instantaneous vorticity obtained from direct numerical simulation. In each pseudo-time step, we develop a novel local optimization algorithm to minimize a hybrid VSF constraint, balancing the accuracy and smoothness of VSF solutions. This key improvement makes the numerical construction of VSFs feasible for arbitrarily complex flow fields, as a general flow diagnostic tool. In the visualization of VSF isosurfaces in decaying homogeneous isotropic turbulence, the initial curved vortex sheets first evolve into vortex tubes, and then the vortex tubes are stretched and tangled, constituting a complex network. Some vortex tubes exhibit helical geometry, which suggests the important role of vortex twisting in the generation of small-scale structures in energy cascade.

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

In Richardson’s cascade description of turbulence, large vortices break up to form smaller ones, transferring the kinetic energy of the flow from large to small scales. This energy is dissipated at the smallest scales due to viscosity. We study energy cascade in a phenomenological model of vortex breakdown. The model is a binary tree of spring-connected masses, with dampers acting on the lowest level. The masses and stiffnesses between levels change according to a power law. The different levels represent different scales, enabling the definition of “mass wavenumbers.” The eigenvalue distribution of the model exhibits a devil’s staircase self-similarity. The energy spectrum of the model (defined as the energy distribution among the different mass wavenumbers) is derived in the asymptotic limit. A decimation procedure is applied to replace the model with an equivalent chain oscillator. For a significant range of the stiffness decay parameter, the energy spectrum is qualitatively similar to the Kolmogorov spectrum of 3D homogeneous, isotropic turbulence and we find the stiffness parameter for which the energy spectrum has the well-known $$-\,5/3$$ scaling exponent.

Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo an inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived analytically by Galtier (Galtier S., Phys. Rev. E, 68 (2003) 015301), thus offering numerical proof of the relevance of wave turbulence theory for three-dimensional, anisotropic waves. Lastly, we show that the same forcing leads to either geostrophic or wave turbulence depending on the initial conditions. Our results thus bring further evidence for bi-stability in rotating turbulent flows at low Rossby numbers.

The tendency of turbulent flows to produce fine-scale motions from large-scale energy injection is often viewed as a scale-wise cascade of kinetic energy driven by vorticity stretching. This has been recently evaluated by an exact, spatially local relationship (Johnson, P.L. Phys. Rev. Lett., vol. 124, 2020, p. 104501), which also highlights the contribution of strain self-amplification. In this paper, the role of these two mechanisms is explored in more detail. Vorticity stretching and strain amplification interactions between velocity gradients filtered at the same scale account for approximately half of the energy cascade rate, directly connecting the restricted Euler dynamics to the energy cascade. Multiscale strain amplification and vorticity stretching are equally important, however, and more closely resemble eddy viscosity physics. Moreover, ensuing evidence of a power-law decay of energy transfer contributions from disparate scales supports the notion of an energy cascade, albeit a ‘leaky’ one. Besides vorticity stretching and strain self-amplification, a third mechanism of energy transfer is introduced and related to the vortex thinning mechanism important for the inverse cascade in two dimensions. Simulation results indicate this mechanism also provides a net source of backscatter in three-dimensional turbulence, in the range of scales associated with the bottleneck effect. Taken together, these results provide a rich set of implications for large-eddy simulation modelling.

For high-Mach-number turbulent flows, the Kolmogorov length scale can be comparable to the gas-molecule mean-free path, which could introduce noncontinuum molecular-level effects into the turbulent energy cascade. To investigate this issue, compressible Taylor-Green vortex flow is simulated using both noncontinuum molecular gas dynamics and continuum computational fluid dynamics. Although the energy-decay rates are the same, molecular-level fluctuations break the flow symmetries and thereby produce different but statistically similar routes from the initial nonturbulent flow to the long-time turbulent flow.

The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the mean are fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascade is shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. Finally, the QL model is shown to generate anisotropic turbulence throughout the entire wavenumber space and inhibit the nonlinear regeneration of streamwise vortices in the self-sustaining process.

We investigate incompressible, inviscid vorticity dynamics on a rotating unit sphere using a discrete exterior calculus scheme. For a prescribed initial vorticity distribution, we vary the rotation rate of the sphere from zero [non-rotating case, which corresponds to infinite Rossby number (Ro)] to 320 (which corresponds to Ro = 1.30×10−3) and investigate the evolution with time of the vorticity field. For the non-rotating case, the vortices evolve into thin filaments due to so-called forward/direct enstrophy cascade. The energy cascades to the larger scales due to the inverse energy cascade, and at late times, an oscillating quadrupolar vortical field emerges. Rotation diminishes the forward cascade of enstrophy (and hence the inverse cascade of energy) and tends to align the vortical structures in the azimuthal/zonal direction. Our investigation reveals that, for the initial vorticity field comprising intermediate-wavenumber spherical harmonics, the zonalization of the vortical structures is not monotonic with ever decreasing Rossby numbers, and the structures revert back to a non-zonal state below a certain Rossby number. On the other hand, for the initial vorticity field comprising intermediate to large-wavenumber spherical harmonics, the zonalization is monotonic with decreasing Rossby number. Although rotation diminishes the forward cascade of enstrophy, it does not completely cease/arrest the cascade for the parameter values employed in the present work.

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the meanare fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascadeis shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. It is also found that the streamwise wave number spectra of turbulent transport, obtained with the classical Reynolds decomposition, statistically characterizes the instability of the linearised fluctuation equations. Further supporting evidence of this claim is presented by carrying out a numerical experiment, in which the QL model with single streamwise Fourier mode is found to generate the strongest turbulence for Lx/Lz= 1∼3, consistent with previous findings (Lx and Lz are the streamwise and spanwise computational domains, respectively). Finally, the QL model is shown to completely ignore the role of slow pressure in the fluctuations, resulting in a significant damage of pressure-strain transport at all length scales. This explains the anisotropic turbulence of the QL model throughout the entire wavenumber space as well as the inhibited nonlinear regeneration of streamwise vortices in the self-sustaining process.

In recent years, the H-rotor vertical-axis turbine has attracted considerable attention in the field of wind and tidal power generation. After a series of complex spatiotemporal evolutions, the vortex shed from turbine blades forms a turbulent wake with a multi-scale coherent structure. An analysis of the wake characteristics of twin turbines forms the basis of array optimisation. This study aimed to examine the instability characteristics of a twin-turbine wake with two rotational configurations. The dynamic evolution characteristics of coherent structures with different scales in the wake were analysed via wavelet analysis. The results show that an inverse energy cascade process occurs after the high-frequency small-scale coherent structures induced by rotation lose their coherence. This self-organising characteristic is more apparent in the quasi two-dimensional wake of a forward-moving counter-rotating turbine (Array 1) than in that of a backward-moving counter-rotating turbine (Array 2). With greater organisation and coherence, the wake of Array 1 exhibits low-frequency instability characteristics dominated by a large-scale coherent structure. In addition, the signals reconstructed using wavelet transform show that asymmetric modes exist between low-frequency large-scale coherent structures. The experimental results provide a new perspective on the instability mechanism of twin-turbine wakes, as well as important data for numerical modelling.

The turbulence in a fast rotating fluid becomes effectively two-dimensional. The inverse energy cascade leads to formation of coherent columnar vortices. An analytical theory describing interaction of such a vortex with turbulent pulsations is developed. The radial velocity profile of the vortex is established.

Inertia-gravity waves (IGWs) play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when propagating upwards. An open question is to which extent IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes $k^{-3}$ for the large scales and $k^{-5/3}$ for the small scales. By separating the spectra into the vortex and the wave component, it emerges that at the large-scale end of the mesoscale the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs., Comment: 18 pages, 6 figures

The kinetic energy spectrum in the atmospheric mesoscale has a - 5/3 slope, which suggests an energy cascade. But the underlying dynamics of this cascade is still not fully understood. Is it driven by inertia–gravity waves, vortices or something else? To answer these questions, it is necessary to decompose the spectrum into contributions from waves and vortices. Linear decompositions are straightforward, but can lead to ambiguous results. A recent paper by Wang & Buhler (J. Fluid Mech., vol. 882, 2020, A16) addresses this problem by presenting a nonlinear decomposition of the energy spectrum into waves and vortices using the omega equation. They adapt this method for one-dimensional aircraft data and apply it to two datasets. In the lower stratosphere, the results show a mesoscale spectrum dominated by waves. The situation in the upper troposphere is different: here vortices are just as important, or possibly more than important, as waves, although the limitations of the one-dimensional data preclude a definitive answer.

The development of instability of gravity-capillary waves on the surface of water excited by two perpendicular plungers has been experimentally observed. As a result of a four-wave process, waves with a frequency of 8 Hz scatter in pairs into waves with frequencies of 3.92 and 4.08 Hz, as well as 11.98 and 12.02 Hz. The amplitude of low-frequency waves increases exponentially with a characteristic time of about 90 s which exceeds the time of viscous wave damping almost by an order of magnitude. Along with the main pumping mode, the appeared low-frequency harmonics, propagating on the surface of water at an angle of 15° to each other, form large-scale vortex flows on the surface of water. The wave energy is transferred from the pumping region directly to vortices with a size comparable to the length of a bath wall. In a vortex system, a direct energy cascade with the energy distribution close to E(k) ~ k–5/3 is formed from the region of low wave vectors.

The generation of a vortex flow by waves on a water surface, which simulate an energy cascade in a system of gravity waves at frequencies of 3, 4, 5, and 6 Hz, has been studied experimentally. It has been found that pumping is accompanied by the propagation of waves on the surface at different angles to the fundamental mode and by a nonlinear interaction between waves resulting in the generation of new harmonics. It has been shown that large-scale flows are formed by modes of the lowest frequency of 3 Hz intersecting at acute angles. The energy distribution of the vortex motion can be described by a power-law function of the wavenumber and is independent of the energy distribution in a system of surface waves. The energy coming to large-scale vortex flows directly from the wave system is transferred to small scales. A direct rather than inverse energy flux is established in the system of vortices.

We study how the properties of forcing and dissipation affect the scaling behaviour of the vortex population in the two-dimensional turbulent inverse energy cascade. When the flow is forced at scales intermediate between the domain and dissipation scales, the growth rates of the largest vortex area and the spectral peak length scale are robust to all simulation parameters. For white-in-time forcing the number density distribution of vortex areas follows the scaling theory predictions of Burgess & Scott (J. Fluid Mech., vol. 811, 2017, pp. 742–756) and shows little sensitivity either to the forcing bandwidth or to the nature of the small-scale dissipation: both narrowband and broadband forcing generate nearly identical vortex populations, as do Laplacian diffusion and hyperdiffusion. The greatest differences arise in comparing simulations with correlated forcing to those with white-in-time forcing: in flows with correlated forcing the intermediate range in the vortex number density steepens significantly past the predicted scale-invariant $A^{-1}$ scaling. We also study the impact of the forcing Reynolds number $Re_{f}$, a measure of the relative importance of nonlinear terms and dissipation at the forcing scale, on vortex formation and the scaling of the number density. As $Re_{f}$ decreases, the flow changes from one dominated by intense circular vortices surrounded by filaments to a less structured flow in which vortex formation becomes progressively more suppressed and the filamentary nature of the surrounding vorticity field is lost. However, even at very small $Re_{f}$, and in the absence of intense coherent vortex formation, regions of anomalously high vorticity merge and grow in area as predicted by the scaling theory, generating a three-part number density similar to that found at higher $Re_{f}$. At late enough stages the aggregation process results in the formation of long-lived circular vortices, demonstrating a strong tendency to vortex formation, and via a route distinct from the axisymmetrization of forcing extrema seen at higher $Re_{f}$. Our results establish coherent vortices as a robust feature of the two-dimensional inverse energy cascade, and provide clues as to the dynamical mechanisms shaping their statistics.

The increase of computational capabilities led recent studies to implement very high-resolution simulations that gave access to new scale interaction processes, particularly those associated with the transfer of energy from the oceanic mesoscales to smaller scales through an interior route to dissipation, which is still underexplored. In this context, we study spindown simulations of a mesoscale interior vortex, unstable to a mixed baroclinic–barotropic instability. Even though the global energy is almost conserved, some energy is transferred down to dissipation scales during the development of instabilities. However, in our parameter regime, there is no substantial forward energy cascade sustained by unbalanced dynamics. Rather than exploring the physical parameter range, we clarify numerical discretization issues that can be detrimental to the physical solutions and our interpretation of finescale dynamics. Special care is given to determining the effective resolution of the different simulations. We improve it by a factor of 2 in our primitive equation (PE) finite-difference Coastal and Regional Ocean Community (CROCO) model by implementing a fifth-order accurate horizontal advection scheme. We also explore a range of grid aspect ratios dx/dz and find that energy spectra converge for aspect ratios that are close to N/f, the ratio of the stratification N over the Coriolis parameter f. However, convergence is not reached in the PE model when using a fourth-order centered scheme for vertical tracer advection (standard in ROMS-family codes). The scheme produces dispersion errors that trigger baroclinic instabilities and generate spurious submesoscale horizontal features. This spurious instability shows great impact on submesoscale production and energy cascade, emphasizing the significance of numerical settings in oceanic turbulence studies.

The understanding of turbulent flow and the turbulent energy cascade is a main unresolved problem in physics. To model the energy cascade (which refers to the energy transfer among the different scales of vortices), we introduce a mechanistic turbulence model which is a binary tree of masses and springs, in which the bottom masses are connected to the ground with dampers. The eigenvalue distribution of the system is a devil’s staircase type distribution. The discrete energy spectrum of the mechanistic model is defined and calculated for various mass and stiffness distributions. We find parameters for which the energy spectrum shares the features of the Kolmogorov-spectrum of turbulence.

The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using${\sim}10^{10}$grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width,${\approx}100~\text{m}$, primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.

The evolution of a vortex flow excited by an electromagnetic technique in a thin layer of a conducting liquid was studied experimentally. Small-scale vortices, excited at the pumping scale, merge with time due to the nonlinear interaction and produce large-scale structures—the inverse energy cascade is formed. The dependence of the energy spectrum in the developed inverse cascade is well described by the Kraichnan law k–5/3. At large scales, the inverse cascade is limited by cell sizes, and a large-scale coherent vortex flow is formed, which occupies almost the entire area of the experimental cell. The radial profile of the azimuthal velocity of the coherent vortex immediately after the pumping was switched off has been established for the first time. Inside the vortex core, the azimuthal velocity grows linearly along a radius and reaches a constant value outside the core, which agrees well with the theoretical prediction.

In the presence of strong background rotation, the velocity field tends to become quasi-two-dimensional, which leads to the inverse energy cascade. If the damping is small enough, then the energy is accumulated at the largest scales of the system, forming coherent columnar vortex structures known as condensates. Recently, it was found that the radial velocity profiles of axisymmetric cyclones and anticyclones are described by the dependence UGφ(r)=±ϵ/ν r ln (R/r), where ϵ is statistically stationary turbulent forcing power per unit mass, ν is the kinematic viscosity of a fluid, and R is the transverse size of the vortex. However, the corresponding theory did not take into account the boundary effects and, therefore, was mainly applicable to numerical simulations with periodic boundary conditions. Here, we demonstrate that for typical experimental conditions, the damping of the condensate far enough from the symmetry axis is determined by the linear Ekman friction α=2Ω0E1/2 associated with the no-slip conditions at the lower and upper boundaries of the system, where Ω0 is the angular velocity of the background rotation and E is the Ekman number. In this case, the azimuthal velocity of the coherent vortex does not depend on the distance to the vortex center and is determined by the expression UGφ=±3ϵ/α. We discuss the structure of the coherent vortex in this case and compare the results with velocity profiles of condensates in two-dimensional systems.

Collision of two vortex rings (VR) initially arranged in axis-offset and orthogonal configurations at Reynolds numbers ( ReΓ) in the range of 5000–200 000 was simulated to investigate turbulent energy cascade associated with their reconnection. Two elliptical VRs are generated by joining each part of the first VR with another part of the second VR for the axis-offset collision, while two VRs associate to form a double U-shaped vortex, and this vortex reconnects itself at two points to form three elliptical VRs linked by the vortex filaments for the orthogonal collision. Many vortex structures in various scales and shapes, including small-scale VRs and horseshoe vortices, are observed in connection regions for both cases. As ReΓ increases, the energy of formed small vortices raises and their wavenumber (k) range enlarges. The flow energy spectrum approaches a k−5/3 slope of the Kolmogorov hypotheses at low wavenumbers. For the axis-offset collision, the energy spectrum at medium wavenumbers continuously changes from k−3.0 at ReΓ= 5000 to k−1.8 at ReΓ= 200 000, and the exponent (α) of the wavenumber is determined by a function as α=0.3304 ln(ReΓ)−5.6538. Meanwhile, the energy spectrum at two medium-wavenumber subranges for the orthogonal collision with ReΓ≥ 20 000 approaches the slopes of k−3.0 and k−2.6. Turbulent mixing performance due to the axis-offset collision of two vortex rings is better than that with the orthogonal one.

The formation of vortex motion by nonlinear gravity waves on the surface of water is studied experimentally in a bath with dimensions of 70 × 70 cm. Gravity waves are excited by two plungers installed perpendicularly to each other at a distance of 1 cm from the bath walls. The pumping frequency is 4 Hz, and the excitation wavelength is 9.6 cm. The liquid flow is visualized by polyamide decorating particles. After pumping is switched on, the traveling waves propagate over the surface and, at first, form a system of bores, which then transforms into a vortex lattice when a standing wave is formed on the surface. The ideal vortex lattice is broken down by intense vortex interaction with time. The energy distribution over the wave vector can be described by a power function with the variable subscript n, E ~ k-n, 1.5 < n < 3. The scale of the vortex with the maximum size is close to the size of the bath. It is assumed that a forward energy cascade is formed in the system of vortices; however, the nonlinear interaction of vortices is weak. After the pumping of waves is switched off and the waves are damped on the surface, vortex motion in a viscous sublayer produced by nonlinear waves remains. The smaller scale vortices damp more rapidly with time, and one or two large vortices remain on the surface and are dominant.

International audience; Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded flows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel flow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy flow structures embedded in the fully turbulent flow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal flow configuration reproduces well the spatial spectra as well as the probability density function typical of turbulent flows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.

PA acknowledges funding from his STFC Ernest Rutherford Fellowship (No. ST/R004285/1). TVD was funded by GOA-2015-014 (KU Leuven). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 724326). The inhomogeneous solar corona is continuously disturbed by transverse MHD waves. In the inhomogeneous environment of coronal flux tubes, these waves are subject to resonant absorption, a physical mechanism of mode conversion in which the wave energy is transferred to the transition boundary layers at the edge between these flux tubes and the ambient corona. Recently, transverse MHD waves have also been shown to trigger the Kelvin-Helmholtz instability (KHI) due to the velocity shear flows across the boundary layer. Also, continuous driving of kink modes in loops has been shown to lead to fully turbulent loops. It has been speculated that resonant absorption fuels the instability by amplifying the shear flows. In this work, we show that this is indeed the case by performing simulations of impulsively triggered transverse MHD waves in loops with and without an initially present boundary layer, and with and without enhanced viscosity that prevents the onset of KHI. In the absence of the boundary layer, the first unstable modes have high azimuthal wavenumber. A boundary layer is generated relatively late due to the mixing process of KHI vortices, which allows the late onset of resonant absorption. As the resonance grows, lower azimuthal wavenumbers become unstable, in what appears as an inverse energy cascade. Regardless of the thickness of the initial boundary layer, the velocity shear from the resonance also triggers higher order azimuthal unstable modes radially inwards inside the loop and a self-inducing process of KHI vortices occurs gradually deeper at a steady rate until basically all the loop is covered by small-scale vortices. We can therefore make the generalisation that all loops with transverse MHD waves become fully turbulent and that resonant absorption plays a key role in energising and spreading the transverse wave-induced KHI rolls all over the loop. Publisher PDF

Self-organization and anomalous transport in gradient-drift driven turbulence in partially magnetized plasmas with crossed electric and magnetic fields is demonstrated in two-dimensional fluid simulations. The development of large scale structures and flows is shown to occur as a result of the inverse energy cascade from short wavelength instabilities. The turbulence shows complex interaction of small scale modes with large scale zonal flow modes, vortices, and streamers resulting in strongly intermittent anomalous transport that significantly exceeds the classical collisional values. The turbulence driven secondary instabilities and large scale structures are shown to dominate the anomalous electron current. Such anomalous transport and structures are consistent with a number of experimental observations in laboratory plasmas.

Turbulent shallow flows are characterized by the presence of horizontal large-scale vortices, caused by local variations of the velocity field. Apart from these 2D large vortices, small scale 3D turbulence, mainly produced by the interaction of the flowing water with the solid boundaries, is also present. The energy spectrum of turbulent shallow flows shows the presence of a 2D energy cascade at low wave numbers and a 3D energy cascade at high wave numbers, with a well-defined separation region between them. Horizontal flow movements (e.g. 2D large-scale vortical structures) at low wave numbers mostly determine the hydrodynamic behavior of these flows. Moreover, the generation of standing waves often occurs closely associated to the interaction of 2D horizontal flows with lateral boundaries, this is the case of seiches. To adequately reproduce these phenomena, a mathematical and numerical model able to resolve 2D turbulence is required. We herein show that depth-averaged (DA) unsteady Reynolds averaged Navier Stokes (URANS) models based on the Shallow Water Equations (SWE) are a suitable choice for the resolution of turbulent shallow flows with sufficient accuracy in an affordable computational time. The 3D small-scale vortices are modeled by means of diffusion terms, whereas the 2D large-scales are resolved. A high order numerical scheme is required for the resolution of 2D large eddies. In this work, we design a DA-URANS model based on a high order augmented WENO-ADER scheme. The mathematical model and numerical scheme are validated against observation of complex experiments in an open channel with lateral cavities that involve the presence of resonant phenomena (seiching). The numerical results evidence that the model accurately reproduces both longitudinal and transversal resonant waves and provides an accurate description of the flow field. The high order WENO-ADER scheme combined with a SWE model allows to obtain a powerful, reliable and efficient URANS simulation tool., The present work has been partially funded by Gobierno de Aragón through the Fondo Social Europeo (T32-17R). This research has also been supported by the Research Project CGL2015-66114-R, funded by the Spanish Ministry of Economy and Competitiveness (MINECO).

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2D). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2D turbulence. Using a one-fluid model it was recently shown [M. Linkmann et al., Phys. Rev. Lett 122, 214503 (2019)10.1103/PhysRevLett.122.214503] that two-dimensional active suspensions support two nonequilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.

The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex shaped as an inverted hairpin followed by an upright hairpin. The asymmetry between the forward and backward cascade arises from the opposite flow circulation within the hairpins, which triggers reversed patterns in the flow., Comment: improved wording, fixed figure labels, some rephrasing

Turbulent flows in a thin layer can develop an inverse energy cascade leading to spectral condensation of energy when the layer height is smaller than a certain threshold. These spectral condensates take the form of large-scale vortices in physical space. Recently, evidence for bistability was found in this system close to the critical height: depending on the initial conditions, the flow is either in a condensate state with most of the energy in the two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow state with most of the energy in the small-scale modes. This bistable regime is characterised by the statistical properties of random and rare transitions between these two locally stable states. Here, we examine these statistical properties in thin-layer turbulent flows, where the energy is injected by either stochastic or deterministic forcing. To this end, by using a large number of direct numerical simulations (DNS), we measure the decay time $\unicode[STIX]{x1D70F}_{d}$ of the 2-D condensate to 3-D flow state and the build-up time $\unicode[STIX]{x1D70F}_{b}$ of the 2-D condensate. We show that both of these times $\unicode[STIX]{x1D70F}_{d},\unicode[STIX]{x1D70F}_{b}$ follow an exponential distribution with mean values increasing faster than exponentially as the layer height approaches the threshold. We further show that the dynamics of large-scale kinetic energy may be modelled by a stochastic Langevin equation. From time-series analysis of DNS data, we determine the effective potential that shows two minima corresponding to the 2-D and 3-D states when the layer height is close to the threshold.

Confined impinging jets (CIJs) are reactors used in processes that require fast mixing. In such equipment two fluids are injected from opposite sides of a chamber, impinging into each other and forming flow structures that enable an effective mixing and reaction. The turbulence analysis shows that the energy is injected from smaller scales, having approximately the injectors width, that feed larger scale structures up to larger vortices that occupy the entire mixing chamber width. This energy distribution has an inverse energy cascade, i. e. it is an inversion of the traditional description of homogeneous 3D turbulence. The typical flow scales of 2D CIJs are clearly shown in this work to be linked to the 2D turbulence energy spectrum and to integral scales of turbulence. Moreover, the turbulence mechanisms in 3D CIJs at transitional flow regimes are shown to be similar to 2D CIJs. This is to our knowledge the first demonstration of 2D turbulence in an industrial mixer/reactor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2335–2347, 2017

We generalize the K − ϵ model of classical turbulence to superfluid helium. In a classical viscous fluid the phenomenological eddy viscosity characterizing the effects of turbulence depends on the turbulent kinetic energy K and the dissipation function ϵ , which are mainly related to the fluctuations of the velocity field and of its gradient. In superfluid helium, instead, we consider the necessary coefficients for describing the effects of classical and quantum turbulence, involving fluctuations of the velocity, the heat flux, and the vortex line density of the quantized vortex lines. By splitting the several fields into a time-average part and a fluctuating part, some expressions involving the second moments of the turbulent fluctuations appear in the evolution equations for the average quantities. As in the K − ϵ model, a practical way of closing such equations is to tentatively express such fluctuating terms as a function of the average quantities. In this context we propose how the turbulent coefficients so introduced could depend on the second moments of the fluctuations of v , q and L (respectively denoted as K , K q and K L ), and on their respective dissipation functions (related to the second moments of their gradients) ϵ , ϵ q and ϵ L .

Turbulent flows at high Reynolds numbers are dominated by vortex filaments and/or sheets with sharp gradients in the vorticity field near the boundaries of the vortical structures. Numerical simulations of high Reynolds number flows are computationally demanding due to the fine grid required to accurately resolve these sharp gradient regions. In this paper, an alternative approach is proposed to improve the computational efficiency of Navier–Stokes solvers by reformulating the momentum equations as a set of equations for the time-dependent evolution of the flexion field. The flexion vector represents the curl of the vorticity field and is better able to resolve nonlinear effects in regions with large vorticity gradients. The improved resolution capabilities of the flexion-based approach are illustrated through the pseudospectral computations of the rollup of a perturbed 2D shear layer and the transition to a turbulence/viscous decay of the three-dimensional (3D) Taylor–Green vortex. The flexion-based formulation also provides further insight into the dynamics of turbulence through the evolution of the mean-square flexion or palinstrophy. Analysis of data from the Taylor–Green vortex simulations shows that the observed rapid growth of small-scale features and palinstrophy in 3D turbulent flows is primarily associated with flexion amplification by the curl of the vortex stretching vector. Consequently, we hypothesize that the primary physical mechanism responsible for energy cascade from large to small scales is the curl of the vortex stretching vector of interacting vortex tubes, as opposed to the stretching of individual vortex tubes.

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for non-equilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in non-planar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of anti-ferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence., 13 pages, supplementary movies available on request; typo in fig 3(b) corrected

Clustering vortices Many-body systems generally become more disordered as more energy is pumped into them. A curious exception to this rule was predicted in the context of turbulent flow by the physical chemist Lars Onsager. He suggested that the entropy of certain two-dimensional (2D) systems can decrease with increasing energy, corresponding to an effective negative temperature. Using 2D Bose-Einstein condensates of atoms, Gauthier et al. and Johnstone et al. put Onsager's theory to the test. They provided energy to the system by perturbing the condensate, creating vortices and antivortices. With increasing energy, the system became more ordered as clusters containing either only vortices or only antivortices emerged. Science , this issue p. 1264 , p. 1267

This study explores the stability characteristics and nonlinear evolution of internal jets in rotating stratified fluids using a combination of direct numerical simulations and linear instability analyses. Our ultimate goal is the assessment of the potential impact of the Earth’s rotation on relatively small-scale structures, exemplified by turbulent wakes generated by propagating bluff objects in the ocean. We question the popular notion that ascribes a secondary role to the Coriolis effects in large Rossby number (Ro) systems. It is shown that the Earth’s rotation can substantially influence circulation patterns with Rossby numbers as high as Ro ∼ 103. Therefore, such effects must be taken into account in the numerical and theoretical models of finescale (∼10–100 m) processes in the ocean. We present a series of examples in which planetary rotation controls flows with large but finite values of Ro through centrifugal destabilization. These calculations reveal that centrifugal instabilities can affect fluid motion either directly, by modifying the basic state, or indirectly, by preferentially eliminating anticyclonic coherent vortices that form in the course of dynamic destabilization of jets. The results of this study have potentially significant geophysical implications in terms of elucidating mechanisms of energy cascade to progressively smaller scales. In the naval context, we anticipate that our investigation could influence the development of algorithms for detection and analysis of late wakes, generated by propagating submersibles in the ocean.This study explores the stability characteristics and nonlinear evolution of internal jets in rotating stratified fluids using a combination of direct numerical simulations and linear instability analyses. Our ultimate goal is the assessment of the potential impact of the Earth’s rotation on relatively small-scale structures, exemplified by turbulent wakes generated by propagating bluff objects in the ocean. We question the popular notion that ascribes a secondary role to the Coriolis effects in large Rossby number (Ro) systems. It is shown that the Earth’s rotation can substantially influence circulation patterns with Rossby numbers as high as Ro ∼ 103. Therefore, such effects must be taken into account in the numerical and theoretical models of finescale (∼10–100 m) processes in ...

In a two-dimensional (2D) classical fluid, a large-scale flow structure emerges out of turbulence, which is known as the inverse energy cascade where energy flows from small to large length scales. An interesting question is whether this phenomenon can occur in a superfluid, which is inviscid and irrotational by nature. Atomic Bose-Einstein condensates (BECs) of highly oblate geometry provide an experimental venue for studying 2D superfluid turbulence, but their full investigation has been hindered due to a lack of the circulation sign information of individual quantum vortices in a turbulent sample. Here, we demonstrate a vortex sign detection method by using Bragg scattering, and we investigate decaying turbulence in a highly oblate BEC at low temperatures, with our lowest being $\sim 0.5 T_c$, where $T_c$ is the superfluid critical temperature. We observe that weak spatial pairing between vortices and antivortices develops in the turbulent BEC, which corresponds to the vortex-dipole gas regime predicted for high dissipation. Our results provide a direct quantitative marker for the survey of various 2D turbulence regimes in the BEC system., Comment: 8 pages, 8 figures

We propose a new similarity theory for the two-dimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that $E\sim t$ yield three length scales, $l_{\unicode[STIX]{x1D714}}$, $l_{E}$ and $l_{\unicode[STIX]{x1D713}}$, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, $t^{1/2}$, $t$ and $t^{3/2}$, respectively. We thus predict that vortex areas grow linearly in time, $A\sim l_{\unicode[STIX]{x1D714}}^{2}\sim t$, while the spectral peak wavenumber $k_{E}\equiv 2\unicode[STIX]{x03C0}l_{E}^{-1}\sim t^{-1}$. We construct a theoretical framework involving a three-part, time-evolving vortex number density distribution, $n(A)\sim t^{\unicode[STIX]{x1D6FC}_{i}}A^{-r_{i}},~i\in 1,2,3$. Just above the forcing scale ($i=1$) there is a forcing-equilibrated scaling range in which the number of vortices at fixed $A$ is constant and vortex ‘self-energy’ $E_{v}^{cm}=(2{\mathcal{D}})^{-1}\int \overline{\unicode[STIX]{x1D714}_{v}^{2}}A^{2}n(A)\,\text{d}A$ is conserved in $A$-space intervals $[\unicode[STIX]{x1D707}A_{0}(t),A_{0}(t)]$ comoving with the growth in vortex area, $A_{0}(t)\sim t$. In this range, $\unicode[STIX]{x1D6FC}_{1}=0$ and $n(A)\sim A^{-3}$. At intermediate scales ($i=2$) sufficiently far from the forcing and the largest vortex, there is a range with a scale-invariant vortex size distribution. We predict that in this range the vortex enstrophy $Z_{v}^{cm}=(2{\mathcal{D}})^{-1}\int \overline{\unicode[STIX]{x1D714}_{v}^{2}}An(A)\,\text{d}A$ is conserved and $n(A)\sim t^{-1}A^{-1}$. The final range ($i=3$), which extends over the largest vortex-containing scales, conserves $\unicode[STIX]{x1D70E}_{v}^{cm}=(2{\mathcal{D}})^{-1}\int \overline{\unicode[STIX]{x1D714}_{v}^{2}}n(A)\,\text{d}A$. If $\overline{\unicode[STIX]{x1D714}_{v}^{2}}$ is constant in time, this is equivalent to conservation of vortex number $N_{v}^{cm}=\int n(A)\,\text{d}A$. This regime represents a ‘front’ of sparse vortices, which are effectively point-like; in this range we predict $n(A)\sim t^{r_{3}-1}A^{-r_{3}}$. Allowing for time-varying $\overline{\unicode[STIX]{x1D714}_{v}^{2}}$ results in a small but significant correction to these temporal dependences. High-resolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum $E(k)$ past the classical $k^{-5/3}$ scaling in the range $k\in [k_{f},k_{v}]$, where $k_{v}$ is the wavenumber associated with the largest vortex, while at larger scales the slope approaches $-5/3$. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.

Geometrical relationships and interactions among hierarchical structures in homogeneous isotropic turbulence are investigated by identifying individual vortices of three different scales in the inertial subrange. Fourier bandpass filters are employed to extract the vortices, and each extracted vortex is replaced by a group of vortex segments with a cylindrical shape. The axes of neighboring vortices tend to be anti-parallel when the distance between them is equivalent to their diameter. Further, results indicate that a vortex is most strongly stretched by vortices twice the scale irrespective of the Reynolds number and the vortex scales. Then, the geometric relationships between the vortices being stretched and those that cause the stretching are analyzed, and the stretching is found to be particularly strong when the two vortices are orthogonal to each other.

In this paper, phenomenological developments are used to explore relative particle dispersion (RPD) in two-dimensional (2D) and quasi-geostrophic (QG) fully-developed turbulence (FDT). The role played by the 2D and QG FDT cascade physics underlying this process is given special attention. Prevalence of spatial intermittency effects in 2D FDT enstrophy cascade, however small, is shown to lead to a structural change in the RPD growth law, more specifically the development of power-law scaling of RPD; this corroborates the difficulty in observing Lin’s (1972) exponential scaling law in laboratory experiments (Jullien (2003)). QG effects are found to lead to an enhanced RPD in the baroclinic regime of the energy cascade, which seems to be traceable to a negative eddy-viscosity characterizing the latter regime. They are also found to lead to particle clumping in the baroclinic regime of the enstrophy cascade (this aspect appears to be associated with the tendency of divorticity sheets to occur near the vortex nulls where particle clumping is known, as per numerical simulations and laboratory experiments, to be favored to occur). These results are developed from the established scaling relations for 2D and QG FDT and are validated further via alternative dimensional/scaling developments for 2D and QG FDT similar to the one given for 3D FDT by Batchelor and Townsend (1956). The feasibility of spatial intermittency effects is underscored via the nonlinear scaling dependence of RPD on the enstrophy (or energy) dissipation rate.