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Necessary conditions for radiative–dynamical instability of quasigeostrophic waves induced by trace shortwave radiative absorbers are derived. The analysis pivots on a pseudomomentum conservation equation that is obtained by combining conservation equations for quasigeostrophic potential vorticity, thermodynamic energy, and trace absorber mixing ratio. Under the assumptions that the absorber-induced diabatic heating rate is small and the zonal-mean basic state is hydrodynamically neutral, a perturbation analysis of the pseudomomentum equation yields the conditions for instability. The conditions, which only require knowledge of the zonally averaged background distributions of wind and absorber, expose the physical processes involved in destabilization—processes not exposed in previous analytical and modeling studies of trace absorber-induced instabilities. The simplicity of instability conditions underscores their utility as a tool that is both interpretive and predictive. The conditions for instability, which have broad application to synoptic-scale waves in Earth's and other planetary atmospheres, are discussed in light of previous instability studies involving stratospheric ozone and Saharan mineral dust aerosols. [ABSTRACT FROM AUTHOR]

As a mode-1 internal tide (IT) propagates across a geostrophic current V(x, z), we have investigated the amount of IT energy reflected from the current and the impact of the current on the transmitted wave field. These are quantified by considering the reflection coefficient R and the linear modal energy conversion Pn, where n is the modal number. Here, a linear theory built upon idealized barotropic currents is presented. Fully nonlinear numerical simulations are used for the baroclinic currents. We conclude that the reflection is determined by the horizontal shear of the current Vx through varying the effective frequency feff. The modal energy conversion Pn is determined by the vertical shear of the current Vz, i.e., the horizontal variation of the density ρx as a result of the thermal wind relation. The current can increase R up to around 50%. However, Pn is less than 6% among all our simulations. This indicates that IT can propagate through the current without losing much of its structure and the interaction is mostly linear. [ABSTRACT FROM AUTHOR]

Although geostrophically balanced mesoscale vortices and unbalanced small-scale turbulence have been well studied, the link between them is not entirely clear, especially in the vertical dimension. The inertia–gravity wave (IGW) spiral plays an important role in the energy and enstrophy cascades between the geostrophic vortex and the small-scale turbulence. Since the vertical velocity cannot be measured in practice, the slowly varying IGW spiral formula in a vortex is used to distinguish the direction of vertical velocity. The vertical deformation of the vortex with IGW spirals results in a vertical semi-circulating cycle of the energy cascades: the energy cascades forward from the geostrophic vortex scale to small scales in the IGW spiral at one depth, flows along the IGW spiral, and then inversely cascades to the geostrophic vortex scale at another depth. Some small-scale energy at one depth eventually reaches large scales at another depth, which can prevent some energy from falling into small-scale dissipation, allowing the geostrophic vortex to continue for months in the ocean. A vertical full-circulating cycle is formed by connecting every IGW spiral in different geostrophic vortices and jets, similar to the energy exchange in the capillaries of the human body. The vertical closed zero-flux line of enstrophy cascades caused by the IGW spiral in a geostrophic vortex isolates the enstrophy at different scales to reduce the dissipation. Due to the IGW spiral, the energy and enstrophy spectra in the geostrophic vortex are −1 and 1 at small scales, respectively. [ABSTRACT FROM AUTHOR]

Random forcing of geostrophic motion is a common approach in idealized simulations of rotating stratified turbulence. Such forcing represents the injection of energy into large-scale balanced motion, and the resulting breakdown of quasi-geostrophic turbulence into inertia-gravity waves and stratified turbulence can shed light on the turbulent cascade processes of the atmospheric mesoscale. White noise forcing is commonly employed, which excites all frequencies equally, including frequencies much higher than the natural frequencies of large-scale vortices. In this paper, the effects of these high frequencies in the forcing are investigated. Geostrophic motion is randomly forced with red noise over a range of decorrelation time scales τ, from a few time steps to twice the large-scale vortex time scale. It is found that short τ (i.e., nearly white noise) results in about 46% more gravity wave energy than longer τ, despite the fact that waves are not directly forced. We argue that this effect is due to wave-vortex interactions, through which the high frequencies in the forcing are able to excite waves at their natural frequencies. It is concluded that white noise forcing should be avoided, even if it is only applied to the geostrophic motion, when a careful investigation of spontaneous wave generation is needed. [ABSTRACT FROM AUTHOR]

We numerically investigate single-layer shallow-water beta-plane quasi-geostrophic turbulence in a doubly periodic domain with emphasis onwavenumber-frequency spectra.We conduct a broad parameter sweep, varying the deformation radius (Ld ), the narrow-band forcing wavenumber (kf), and the meridional gradient of the Coriolis parameter (β). Out of 54 simulations we present ten in detail spanning slowly propagating vortices to strong jets.We define a nondimensional parameter γβ in terms of β, Ld, and the energy injection rate. The moderately low γβ case is characterized by westward propagating coherent vortices and zonal wavenumber-frequency spectra dominated by a nondispersive line (NDL) corresponding to uniform propagation at or near the long-wave Rossby speed. The moderately high γβ case is characterized by jets, and the NDL persists even when there are no coherent vortices. The jets have large meridional excursions (meanders) that propagate westward nearly uniformly at a speed slower than the long-wave Rossby speed. Also at moderately high γβ, a second dispersion relation appears, roughly corresponding to linear waves on a zonal potential vorticity (PV) staircase. At very high γβ, during the slow evolution to a PV staircase, the structure of the linear waves is altered by the small perturbations to a constant potential vorticity gradient. A simple model treating the small perturbation as a sinusoid accurately predicts the meridional wavenumber-frequency spectra in the very high γβ simulations. [ABSTRACT FROM AUTHOR]

In this paper, we first generalize a new energy approach, developed by Guo and Wang [Commun. Partial Differ. Equations 37, 2165-2208 (2012)] in the framework of homogeneous Besov spaces for proving the optimal temporal decay rates of solutions to the fractional power dissipative equation, then we apply this approach to the critical and supercritical surface quasi-geostrophic equation and the critical Keller-Segel system.We show that certain weighted negative Besov norm of solutions is preserved along time evolution and obtain the optimal temporal decay rates of the spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques. [ABSTRACT FROM AUTHOR]

The so-called carousel tripoles are constructed and characterized in the framework of two-layer quasi-geostrophic contour dynamics, and their stability is examined. Such a tripole is a steadily rotating doubly symmetric ensemble of three collinear vortices, or more specifically, uniform-potential-vorticity patches, with the central, core vortex, located in the upper layer, and the two remaining, satellite vortices, in the lower layer, or vice versa. The carousel tripole solutions are obtained with the use of a numerical iterative procedure. A tripole with zero total potential vorticity can be generally identified by a point in the plane spanned by two parameters, namely, the typical size of the patches relative to the Rossby deformation radius, and some shape parameter. We consider two kinds of the parameter plane by taking as the second parameter either the distance d between the centroids of the core and one of the satellites (termed also separation) or, alternatively, the minimal distance h between the core centroid and the satellite contour, measured along the symmetry axis that passes through the centroids of the core and satellites. Accordingly, to capture the stationary tripoles, we use two alternative numerical procedures, which are based on fixing the first or the second pair of parameters. This is done because the areas of convergence of the two procedures differ somewhat from each other. The areas of convergence are plotted in the parameter planes, and in each of the planes, two branches of solutions are found bifurcating from some segments of the lines bounding the convergence areas. Stability is tested in numerical simulations with the numerical noise taken as a perturbation factor. Stability/instability of a tripole is determined by examining the oscillations in the perimeter of one of the vortex satellites. For each tripole size, both stable and unstable solutions exist. The stability bounds coincide with the bifurcation lines, so that one branch of the solutions is stable while the other is not. As a whole, tripoles with considerable separation behave stably. [ABSTRACT FROM AUTHOR]

The effect of mean shear flows on zonal flow formation is considered in the contexts of plasma drift wave turbulence and quasi-geostrophic turbulence models. The generation of zonal flows by modulational instability in the presence of large-scale mean shear flows is studied using the method of characteristics as applied to the wave kinetic equation. It is shown that mean shear flows reduce the modulational instability growth rate by shortening the coherency time of the wave spectrum with the zonal shear. The scalings of zonal flow growth rate and turbulent vorticity flux with mean shear are determined in the strong shear limit. [ABSTRACT FROM AUTHOR]

The role of short-wave instabilities on geostrophic turbulence is studied in a simplified model consisting of three layers in the quasi-geostrophic approximation. The linear stability analysis shows that short-wave instabilities are created by the interplay between the shear in the upper and lower layers. If the stratification is non-uniform, in particular surface intensified, the linear growth rate is larger for short-wave instabilities than for long-wave instabilities and the layers are essentially decoupled, with the small scales growing independently. The fully developed homogeneous turbulence is studied in a number of numerical experiments. Results show that in both the case of equal layer depths and surface intensified stratification an inverse cascade in kinetic energy is observed. The modal kinetic energy spectra for the case with surface intensified stratification show higher energy for higher baroclinic numbers at small scales, due to the decoupling of the layers. As a result, while the case with equal layer depths shows large barotropic instabilities with large scale gradients of potential temperature, the surface intensified stratification is characterized by a transition from surface dynamics, characterized by a patchy distribution of vorticity, to interior dynamics, characterized by vorticity filamentation. The effect of the shortwave instabilities can be seen in the probability distribution functions of the potential vorticity anomaly, which reduces to a Gaussian distribution when the growth rate of the short-wave instabilities is larger than the growth rate for the long-wave instabilities. The surface intensified stratification also alters the vertical structure of the potential vorticity fluxes and shows deviations of the fluxes from a scaling obtained assuming that the turbulence acts as a downgradient diffusion. Experiments with a passive tracer shows a dominance of the coherent structures at large scales, and of filamentation at smaller scales, in the tracer dispersion. [ABSTRACT FROM AUTHOR]

Geostrophic turbulence near horizontal surfaces on which the vertical velocity vanishes exhibits a forward cascade of buoyancy variance, characterized by a shallow energy spectrum, secondary roll-up of filaments, and a fat-tailed vorticity probability distribution. Such surfaces occur at rigid boundaries, but also at discontinuous jumps in stratification. Here we relax this mathematical idealization and investigate geostrophic turbulence near a rapid but smooth jump in stratification, modeled by N(z) = N0[1 + αtanh (z/h)]. The rapidity of change is controlled by the length scale h and the profile approaches a step function as h → 0. The approximated Green's function for the quasigeostrophic potential vorticity (PV) is used to predict the spectral PV-streamfunction relationship, under various assumptions about the distribution of the initial PV. Numerical simulations of freely-evolving quasigeostrophic turbulence in the presence of the model stratification support the predictions and reveal that the jump has two effects: it alters the Green's function in the region of the jump and it produces a peak in PV near the jump, approaching a Dirac delta-function as the jump scale h → 0. When the Green's function is integrated against this sharp PV distribution, contributions far from the jump (|z| > h) are suppressed and the flow in a region |z| <= O(h) exhibits surface effects. This occurs for horizontal scales L >= N0h/f, the deformation scale associated with the jump. These results have implications for geostrophic turbulence near the tropopause in the atmosphere and the base of the mixed layer in the ocean. [ABSTRACT FROM AUTHOR]

The statistical equilibrium state of quasi-geostrophic point vortices is investigated theoretically, based on the maximum entropy theory. We search for the state of maximum Shannon entropy under the constraints of the vertical vorticity distribution P(z), the angular momentum I, and the energy of the vortex system E. Solutions of the mean field equation are obtained by the numerical procedure proposed by Turkington and Whittaker. The most probable state in an infinite fluid domain is axisymmetric, whose radial distribution depends both on the vertical vortex distribution P(z) and the total energy of the vortex system E. At a certain critical energy value Ec, the number of microscopic state of fixed angular momentum becomes largest (zero-inverse temperature state), where the radial distribution is Gaussian at any vertical height. When the energy is smaller (E < Ec: positive temperature), the radial distribution becomes flatter than the Gaussian. In contrast, if the energy is higher (E > Ec: negative temperature), the radial distribution becomes sharper showing tighter concentration near the axis of symmetry. In order to compare with these theoretical results, very long numerical computations are performed using the fast special-purpose computer for molecular dynamics simulations (GRAPE-DR). Quantitative agreements between the theoretical and numerical results are found for any cases considered. [ABSTRACT FROM AUTHOR]

Lock-release laboratory experiments have been performed to examine the collapse of a localized cylindrical mixed patch of fluid in both two-layer and uniformly stratified ambients. The experiments were performed with and without rotation. Unlike bottom propagating gravity currents, non-rotating intrusions typically propagated many lock radii at constant speed, sometimes stopping abruptly due to interactions with internal waves generated by the return flow into the lock. The initial front speeds of the resulting approximately axisymmetric intrusions emanating from locks of comparable depth and radius were found to be 30%-35% less than the predictions of rectilinear theory. Rotation had no impact on the intrusion's initial speed. However, it limited the maximum distance propagated by the intrusion and caused the patch to expand and contract as it approached geostrophic balance. [ABSTRACT FROM AUTHOR]

We give a proof of Lp-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as 'operator splitting methods') and the Bochner-Pollard subordination identities, hence it could be applicable to other equations. [ABSTRACT FROM AUTHOR]

Two-dimensional fluid flow is often approximated in the laboratory with thin electromagnetically forced fluid layers. The faithfulness of such an experimental model must be considered carefully, however, because the physical world is inherently three-dimensional. By adapting an analysis technique developed for oceanographic data, we divide velocity measurements from a thin-layer flow into two components: one that is purely two-dimensional and another that accounts for all out-of-plane flow. We examine the two- and three-dimensional components separately, finding that motion in thin-layer flows is nearly two-dimensional at low Reynolds numbers, but that out-of-plane flow grows quickly above a critical Reynolds number. This onset is likely due to a shear instability. [ABSTRACT FROM AUTHOR]

In the general context of the geostrophic adjustment, we study the formation of coherent structures in a rotating shallow water model on the f-plane starting from localized dipolar configurations. We perform direct numerical simulations with such initial conditions with the help of a well-balanced high-resolution finite-volume numerical scheme. Initializations with geostrophically balanced quasigeostrophic modons with high enough Rossby numbers lead to adjustment toward quasistationary coherent ageostrophic dipoles. Like in laboratory experiments, cyclonic potential vorticity is being detrained from the dipoles and their trajectories bend. Comparisons with recently found exact steady-moving localized dipolar solutions show similarities and differences at the same time. Initializations with unbalanced dipolar initial conditions lead to similar quasistationary configurations at high enough effective Rossby numbers. At low Rossby numbers the classical geostrophic adjustment is observed. Ageostrophic quasistationary dipoles emerging from the simulations are surprisingly robust. They undergo frontal collisions with an exchange of cyclonic partners, which are essentially elastic and do not change their structure. They also keep coherence when encountering a steep topography and ballistically transport passive tracers. [ABSTRACT FROM AUTHOR]

We study the generalised 2D surface quasi-geostrophic (SQG) equation, where the active scalar is given by a fractional power α of Laplacian applied to the stream function. This includes the 2D SQG and Euler equations as special cases. Using Poincaré's successive approximation to higher α-derivatives of the active scalar, we derive a variational equation for describing perturbations in the generalized SQG equation. In particular, in the limit α → 0, an asymptotic equation is derived on a stretched time variable τ = αt, which unifies equations in the family near α = 0. The successive approximation is also discussed at the other extreme of the 2D Euler limit α = 2-0. Numerical experiments are presented for both limits. We consider whether the solution behaves in a more singular fashion, with more effective nonlinearity, when α is increased. Two competing effects are identified: the regularizing effect of a fractional inverse Laplacian (control by conservation) and cancellation by symmetry (nonlinearity depletion). Near α = 0 (complete depletion), the solution behaves in a more singular fashion as α increases. Near α = 2 (maximal control by conservation), the solution behave in a more singular fashion, as α decreases, suggesting that there may be some α in [0, 2] at which the solution behaves in the most singular manner. We also present some numerical results of the family for α = 0.5, 1, and 1.5. On the original time t, the H1 norm of θ generally grows more rapidly with increasing α. However, on the new time τ, this order is reversed. On the other hand, contour patterns for different α appear to be similar at fixed τ, even though the norms are markedly different in magnitude. Finally, point-vortex systems for the generalized SQG family are discussed to shed light on the above problems of time scale. [ABSTRACT FROM AUTHOR]

During the spindown of a unidirectional, geostrophic current in a homogeneous fluid, asymmetry arises in the vertical velocity and vertical relative vorticity fields. A closed-form, time-dependent solution valid to order Rossby number is derived to explore these asymmetries. Momentum advection in the interior and the Ekman layer leads to competing tendencies in the vertical vorticity's evolution. In the interior, momentum advection hastens spindown in cyclonic regions. In the Ekman layer, momentum advection weakens Ekman pumping over Ekman suction and thus tends to slow the spindown of cyclonic vorticity. It is shown that the former effect dominates, and hence cyclonic vorticity decays faster than anticyclonic vorticity. [ABSTRACT FROM AUTHOR]