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Flow in the body of gravity currents is typically assumed to be statistically two-dimensional, and cross-stream flow is often neglected (Simpson 1997; Meiburg et al. 2015). Here, we assess the validity of such assumptions using Shake-the-Box particle tracking velocimetry measurements of experimental gravity current flows. The resulting instantaneous, volumetric, whole-field velocity measurements indicate that cross-stream and vertical velocities (and velocity fluctuations) are equivalent in magnitude and thus are key to energy distribution and dissipation within the flow. Further, the presented data highlight the limitations of basing conclusions regarding body structure on a single cross-stream plane (particularly if that plane is central). Spectral analysis and dynamic mode decomposition of the fully three-dimensional, volumetric velocity data suggests internal waves within the current body that are associated with coherent three-dimensional motions in higher Reynolds number flows. Additionally, a potential critical layer at the height of the downstream velocity maximum is identified. [ABSTRACT FROM AUTHOR]

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers 100 ≤ R e ≤ 3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with (R e , S c) = (100 , 10) , (100 , 100) , and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost. [ABSTRACT FROM AUTHOR]

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ($Rm$). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$. [ABSTRACT FROM AUTHOR]

In this paper, we perform direct statistical simulations of a model of two-dimensional flow that exhibits a transition from jets to vortices. The model employs two-scale Kolmogorov forcing, with energy injected directly into the zonal mean of the flow. We compare these results with those from direct numerical simulations. For square domains, the solution takes the form of jets, but as the aspect ratio is increased, a transition to isolated coherent vortices is found. We find that a truncation at second order in the equal-time but nonlocal cumulants that employ zonal averaging (zonal CE2) is capable of capturing the form of the jets for a range of Reynolds numbers as well as the transition to the vortex state but, unsurprisingly, is unable to reproduce the correlations found for the fully nonlinear (non-zonally symmetric) vortex state. This result continues the program of promising advances in statistical theories of turbulence championed by Kraichnan. [ABSTRACT FROM AUTHOR]

We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number (Rm). We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations. [ABSTRACT FROM AUTHOR]

In this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers. [ABSTRACT FROM PUBLISHER]

We investigate the kinematic dynamo properties of interacting vortex tubes. These flows are of great importance in geophysical and astrophysical fluid dynamics: for a large range of systems, turbulence is dominated by such coherent structures. We obtain a dynamically consistent 2 1/2-dimensional velocity field of the form (u(x,y,t),v(x,y,t),w(x,y,t)) by solving the z-independent Navier-Stokes equations in the presence of helical forcing. This system naturally forms vortex tubes via an inverse cascade. It has chaotic Lagrangian properties and is therefore a candidate for fast dynamo action. The kinematic dynamo properties of the flow are calculated by determining the growth rate of a small-scale seed field. The growth rate is found to have a complicated dependence on Reynolds number Rey and magnetic Reynolds number Rem, but the flow continues to act as a dynamo for large Rey and Rem. Moreover the dynamo is still efficient even in the limit Rey gg Rem, providing Rem is large enough, because of the formation of coherent structures. [ABSTRACT FROM AUTHOR]

Astrophysical magnetic fields often display remarkable organization, despite being generated by dynamo action driven by turbulent flows at high conductivity. An example is the eleven-year solar cycle, which shows spatial coherence over the entire solar surface. The difficulty in understanding the emergence of this large-scale organization is that whereas at low conductivity (measured by the magnetic Reynolds number, Rm) dynamo fields are well organized, at high Rm their structure is dominated by rapidly varying small-scale fluctuations. This arises because the smallest scales have the highest rate of strain, and can amplify magnetic field most efficiently. Therefore most of the effort to find flows whose large-scale dynamo properties persist at high Rm has been frustrated. Here we report high-resolution simulations of a dynamo that can generate organized fields at high Rm; indeed, the generation mechanism, which involves the interaction between helical flows and shear, only becomes effective at large Rm. The shear does not enhance generation at large scales, as is commonly thought; instead it reduces generation at small scales. The solution consists of propagating dynamo waves, whose existence was postulated more than 60 years ago and which have since been used to model the solar cycle. [ABSTRACT FROM AUTHOR]