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A detailed energetics analysis of the Gulf Stream (GS) and associated eddies is performed using a high-resolution multidecadal regional ocean model simulation. The energy equations for the time-mean and time-varying flows are derived as a theoretical framework for the analysis. The eddy–mean flow energy components and their conversions show complex spatial distributions. In the along-coast region, the cross-stream and cross-bump variations are seen in the eddy–mean flow energy conversions, whereas in the off-coast region, a mixed positive–negative conversion pattern is observed. The local variations of the eddy–mean flow interaction are influenced by the varying bottom topography. When considering the domain-averaged energetics, the eddy–mean flow interaction shows significant along-stream variability. Upstream of Cape Hatteras, the energy is mainly transferred from the mean flow to the eddy field through barotropic and baroclinic instabilities. Upon separating from the coast, the GS becomes highly unstable and both energy conversions intensify. When the GS flows into the off-coast region, an inverse conversion from the eddy field to the mean flow dominates the power transfer. For the entire GS region, the mean current is intrinsically unstable and transfers 28.26 GW of kinetic energy and 26.80 GW of available potential energy to the eddy field. The mesoscale eddy kinetic energy is generated by mixed barotropic and baroclinic instabilities, contributing 28.26 and 9.15 GW, respectively. Beyond directly supplying the barotropic pathway, mean kinetic energy also provides 11.55 GW of power to mean available potential energy and subsequently facilitates the baroclinic instability pathway.

This study explores the dynamics of intense coherent vortices in large-scale vertically sheared flows. We develop an analytical theory for vortex propagation and validate it by a series of numerical simulations. Simulations are conducted using both stable and baroclinically unstable zonal background flows. We find that vortices in stable westward currents tend to adjust to an equilibrium state characterized by quasi-uniform zonal propagation. These vortices persist for long periods, during which they propagate thousands of kilometers from their points of origin. The adjustment tendency is realized to a much lesser extent in eastward background flows. These findings may help to explain the longevity of the observed oceanic vortices embedded in predominantly westward flows. Finally, we examine the influence of background mesoscale variability induced by baroclinic instability of large-scale flows on the propagation and persistence of isolated vortices.

We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasigeostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

Baroclinic instabilities are ubiquitous in many types of geostrophic flow; however, they are seldom observed in river plumes despite strong lateral density gradients within the plume front. Supported by results from a realistic numerical simulation of the Mississippi–Atchafalaya River plume, idealized numerical simulations of buoyancy-driven flow are used to investigate baroclinic instabilities in buoyancy-driven flow over a sloping bottom. The parameter space is defined by the slope Burger number S = Nf −1 α , where N is the buoyancy frequency, f is the Coriolis parameter, and α is the bottom slope, and the Richardson number Ri = N 2 f 2 M −4 , where M 2 = |∇ H b | is the magnitude of the lateral buoyancy gradients. Instabilities only form in a subset of the simulations, with the criterion that S H ≡ S Ri −1/2 = Uf −1 W −1 = M 2 f −2 α 0.2, where U is a horizontal velocity scale and S H is a new parameter named the horizontal slope Burger number. Suppression of instability formation for certain flow conditions contrasts linear stability theory, which predicts that all flow configurations will be subject to instabilities. The instability growth rate estimated in the nonlinear 3D model is proportional to ω I max S −1/2 , where ω I max is the dimensional growth rate predicted by linear instability theory, indicating that bottom slope inhibits instability growth beyond that predicted by linear theory. The constraint S H 0.2 implies a relationship between the inertial radius L i = Uf −1 and the plume width W . Instabilities may not form when 5 L i > W ; that is, the plume is too narrow for the eddies to fit.

The baroclinic and barotropic components of atmospheric dynamics are usually viewed as interlinked through the baroclinic life cycle, with baroclinic growth of eddies connected to heat fluxes, barotropic decay connected to momentum fluxes, and the two eddy fluxes connected through the Eliassen–Palm wave activity. However, recent observational studies have suggested that these two components of the dynamics are largely decoupled in their variability, with variations in the zonal mean flow associated mainly with the momentum fluxes, variations in the baroclinic wave activity associated mainly with the heat fluxes, and essentially no correlation between the two. These relationships are examined in a dry dynamical core model under different configurations and in Southern Hemisphere observations, considering different frequency bands to account for the different time scales of atmospheric variability. It is shown that at intermediate periods longer than 10 days, the decoupling of the baroclinic and barotropic modes of variability can indeed occur as the eddy kinetic energy at those time scales is only affected by the heat fluxes and not the momentum fluxes. The baroclinic variability includes the oscillator model with periods of 20–30 days. At both the synoptic time scale and the quasi-steady limit, the baroclinic and barotropic modes of variability are linked, consistent with baroclinic life cycles and the positive baroclinic feedback mechanism, respectively. In the quasi-steady limit, the pulsating modes of variability and their correlations depend sensitively on the model climatology.

The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech., 744, 2014, pp. 329–351). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic-wave mode of characteristic (small) amplitude $\\unicode[STIX]{x1D716}$ and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at $O(\\unicode[STIX]{x1D716})$ rather than at $O(\\unicode[STIX]{x1D716}^{2})$ . Consequently, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce $O(1)$ rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel Wentzel–Kramers–Brillouin–Jeffreys analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Analytical solutions of the reduced system are derived for weak wave forcing and are shown to reproduce results from prior direct numerical simulations (DNS) of the compressible Navier–Stokes and heat equations with remarkable accuracy. Moreover, numerical simulations of the reduced system are performed in the regime of strong wave/mean-flow coupling for a fraction of the computational cost of the corresponding DNS. These simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer.

The dynamics of a fluid flow in a differentially heated square container is investigated numerically. Two opposite conducting walls are maintained at constant temperatures, one hot and the other cold, and the other two walls are insulated. When the conducting walls are horizontal with the lower one cold, the static linearly stratified state is stable. When the container is tilted, the static equilibrium ceases to exist and the fluid flows due to the baroclinic torque arising from the bending of isotherms near the tilted insulated walls. This flow is found to be steady for tilt angles less than$45^{\\circ }$, regardless of the relative balance between buoyancy and viscous effects (quantified by a buoyancy number$R_{N}$). For tilt angles above$45^{\\circ }$, the flow becomes unsteady above a critical$R_{N}$with localized boundary layer undulations at the conducting walls, at the heights of the horizontally opposite corners. From these corners emanate horizontal shear layers, which become thinner and more intense with increasing$R_{N}$. As the tilt angle approaches$90^{\\circ }$, the nature of the instability changes, corresponding to that of the well-studied laterally heated cavity flow.

This paper investigates the effects of baroclinic pressure gradients on mean flow and turbulence in the diabatic atmospheric boundary layer (ABL). Large-eddy simulations are conducted where the direction of the baroclinicity, its strength, and the surface buoyancy flux are systematically varied to examine their interacting effects. The thermal wind vector, which represents the vertical change in the geostrophic wind vector resulting from horizontal temperature gradients, significantly influences the velocity profiles, the Ekman turning, and the strength and location of the low-level jet (LLJ). For instance, cold advection and positive (negative) geostrophic shear increased (decreased) friction velocity and changed the LLJ elevation. Given the baroclinicity strength and direction under neutral conditions, a simple reduced model is proposed and validated here to predict the general trends of baroclinic mean winds. The baroclinic effects on turbulence intensity and structure are even more intricate, with turbulent kinetic energy (TKE) profiles displaying an increase of TKE magnitude with height for some cases. When a fixed destabilizing surface heat flux is added, a positive geostrophic shear favors streamwise aligned roll-type structures, which are typical of neutral ABLs. Conversely, a negative geostrophic shear promotes cell-type structures, which are typical of strongly unstable ABLs. Furthermore, baroclinicity increases shear in the outer ABL and tends to make the outer flow more neutral by decreasing the Richardson flux number. These findings are consequential for meteorological measurements and the wind-energy industry, among others: baroclinicity alters the mean wind profiles, the TKE, coherent structures, and the stability of the ABL, and its effects need to be considered.

This contribution seeks to understand the vertical structure of linearized quasigeostrophic baroclinic modes when they are modified by the presence of a baroclinic mean flow and associated potential vorticity gradients. It is found that even modest, O (0.05 m s −1 ), mean flows can give rise to very substantial changes in modal structures, often in the sense of increased surface intensification. The extent to which stable modes are modified depends strongly on the direction of Rossby wave propagation. Further, baroclinically unstable solutions can appear, and a meaningful inviscid critical-layer solution can occur at the transition to instability when the horizontal gradient of potential vorticity changes sign at some depth within the water column. In addition, the gravest, n = 0, vertical stable mode is no longer strictly barotropic, but rather it can carry density variability at frequencies much higher than those possible for baroclinic (higher) Rossby wave modes. This finding appears to be consistent with oceanic current-meter observations that suggest temperature variability propagation even when the frequency is too high for traditional baroclinic Rossby waves to exist.

We study the convective patterns that arise in a nearly semicylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semicircular boundary at the bottom, and infinitely extended in the third direction. While this configuration is relevant to continuous casting processes that are significantly more complex, we focus on the flow patterns associated with the particular form of mixed convection that arises in it. Linear stability analysis (LSA) and direct numerical simulations (DNS) are conducted, using the spectral-element method to identify observable states. The nature of the bifurcations is determined through Stuart–Landau analysis for completeness. The base flow consists of two counter-rotating rolls driven by the baroclinic imbalance due to the curved isothermal boundary. These are, however, suppressed by the through-flow, which is found to have a stabilising influence as soon as the Reynolds number$Re$based on the through-flow exceeds 25. For a sufficiently high Rayleigh number, this base flow is linearly unstable to three different modes, depending on$Re$. For$Re\\leqslant 75$, the rolls destabilise through a supercritical bifurcation into a travelling wave. For$100\\leqslant Re\\leqslant 110$, a subcritical bifurcation leads to a standing oscillatory mode, whereas for$Re\\geqslant 150$, the unstable mode is non-oscillatory and grows out of a supercritical bifurcation. The DNS confirm that in all cases the dominant mode returned by the LSA precisely matches the topology and evolution of the flow patterns that arise out of the fully nonlinear dynamics.