Baroclinic instability of large-amplitude geostrophic flows

1993 ◽  
Vol 251 ◽  
pp. 501-514 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Large Amplitude ◽  
Large Scale ◽  
Hamiltonian Structure ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Vertical Shear ◽  
Governing Equations ◽  
Zonal Flows ◽  
Wave Disturbances ◽  
Geostrophic Flows

This paper examines the large-scale dynamics of a layer of stratified fluid on the β-plane. A three-dimensional asymptotic system is derived which governs geostrophic flows with large displacement of isopycnal surfaces. This is then reduced to a two-dimensional set of equations which describe the interaction of a baroclinic ‘quasi-mode’ with arbitrary vertical profile and barotrophic motion. The baroclinic instability of large-amplitude zonal flows with vertical shear is studied within the framework of these equations. In the case where the displacement of isopycnal surfaces is small, the results obtained should overlap with the ‘traditional’ baroclinic instability of quasi-geostrophic (small-amplitude) flows. In order to compare the two types of instability, the quasi-geostrophic boundary-value problem is solved asymptotically for the case of long-wave disturbances and weak β-effect (the latter limit of quasi-geostrophic theory has not been considered previously). The instability that is found is linked to the Hamiltonian structure of the governing equations. The equations derived are generalized for the case of more than one baroclinic quasi-mode.

scholarly journals Nonlinear evolution of a baroclinic wave and imbalanced dissipation

2014 ◽  
Vol 756 ◽  
pp. 965-1006 ◽  
Author(s):  
Balasubramanya T. Nadiga
Keyword(s):  
Large Scale ◽  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Base Flow ◽  
Vertical Shear ◽  
Baroclinic Wave ◽  
Set Up ◽  
Secondary Instabilities

AbstractWe consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere: a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic (QG) equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. That is, analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales whereas the bulk of the energy is confined to large balanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These two processes acting together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall slowly when frontogenesis slows down; eventually balanced and imbalanced modes decouple. A measurement of the dissipation of balanced energy by imbalanced processes reveals that it scales exponentially with Rossby number of the base flow. We expect that this scaling will hold more generally than for the specific set-up we consider given the fundamental nature of the dynamics involved. In other results, (a) a break is seen in the total energy (TE) spectrum at small scales: while a steep $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}k^{-3}$ geostrophic scaling (where $k$ is the three-dimensional wavenumber) is seen at intermediate scales, the smaller scales display a shallower $k^{-5/3}$ scaling, reminiscent of the atmospheric spectra of Nastrom & Gage and (b) at the higher of the Rossby numbers considered a minimum is seen in the vertical shear spectrum, reminiscent of similar spectra obtained using in situ measurements.

scholarly journals Properties of Steady Geostrophic Turbulence with Isopycnal Outcropping

2012 ◽  
Vol 42 (1) ◽  
pp. 18-38 ◽  
Author(s):  
G. Roullet ◽  
J. C. McWilliams ◽  
X. Capet ◽  
M. J. Molemaker
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Mechanical Energy ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Primary Source ◽  
Eddy Diffusivity ◽  
Energy Cycle ◽  
Geostrophic Turbulence ◽  
Pv Gradient

Abstract High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

scholarly journals NUMERICAL SIMULATION OF THREE-DIMENSIONAL FLOW AROUND HARBOR DUE TO TSUNAMI USING FAVOR METHOD AND WENO SCHEME

2018 ◽  
pp. 71
Author(s):  
Yuki Kajikawa ◽  
Masamitsu Kuroiwa ◽  
Naohiro Otani
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Weno Scheme ◽  
Scale Model ◽  
Governing Equations ◽  
3D Flow ◽  
Complex Boundaries ◽  
Cartesian Coordinate ◽  
Fifth Order

In this paper, a three-dimensional (3D) tsunami flow model was proposed in order to predict a 3D flow field around a harbor accurately when tsunami strikes. In the proposed numerical model, the Cartesian coordinate system was adopted, and the Fractional Area/Volume Obstacle Representation (FAVOR) method, which has the ability to impose boundary conditions smoothly at complex boundaries, was introduced into the governing equations in consideration of applying the estimation to actual harbors with complex shape in the future. Moreover, the fifth-order Weighted Essentially Non- Oscillatory (WENO) scheme, which is a technique for achieving high accuracy even if the calculation mesh is coarse, was applied to discretization of the convection terms of the governing equations. In order to verify the validity of the model, it was applied to a large-scale laboratory experiment with a scale model of harbor. Comparisons between the simulated and experimental results showed that the model was able to reproduce the time variation of the flow field with sufficient accuracy. Moreover, the simulated results showed that a complex 3D flow field with some vertical vortex flows was generated around a harbor when tsunami struck.

Developing Innovative Deep Water Pipeline Construction Techniques with Physical Models

2004 ◽  
Vol 129 (1) ◽  
pp. 56-60 ◽  
Author(s):  
R. J. Brown ◽  
Andrew Palmer
Keyword(s):  
Deep Water ◽  
Large Scale ◽  
Three Dimensional ◽  
Physical Models ◽  
Governing Equations ◽  
Pipeline Construction ◽  
Construction Techniques ◽  
Construction Risk ◽  
Water Pipeline ◽  
Model Technique

On the large scale of deep-water construction, marine pipelines are extremely flexible. Construction procedures can exploit that flexibility to connect pipelines and risers to floaters, manifolds, wellheads, buoys, and platforms. The paper describes a three-dimensional physical model technique. It helps the engineer to think imaginatively and rapidly to explore different options, with the objective of minimizing construction risk and creating procedures that can be accomplished by the equipment available. The relevant governing equations are derived, and from them come the conditions required for the model to obey the correct mechanical similarity conditions. The model is exact, and can be used to derive forces and stresses; it is much more than just a picture. The paper describes a series of applications to two- and three-dimensional pipeline construction problems, most recently an application to the current Thunder Horse project.

scholarly journals Deep rotating convection generates the polar hexagon on Saturn

2020 ◽  
Vol 117 (25) ◽  
pp. 13991-13996 ◽  
Author(s):  
Rakesh K. Yadav ◽  
Jeremy Bloxham
Keyword(s):  
Flow Pattern ◽  
High Latitude ◽  
Large Scale ◽  
Three Dimensional ◽  
Giant Planets ◽  
Zonal Flows ◽  
Self Organized ◽  
Consistent Model ◽  
Self Consistent ◽  
Polygonal Pattern

Numerous land- and space-based observations have established that Saturn has a persistent hexagonal flow pattern near its north pole. While observations abound, the physics behind its formation is still uncertain. Although several phenomenological models have been able to reproduce this feature, a self-consistent model for how such a large-scale polygonal jet forms in the highly turbulent atmosphere of Saturn is lacking. Here, we present a three-dimensional (3D) fully nonlinear anelastic simulation of deep thermal convection in the outer layers of gas giant planets that spontaneously generates giant polar cyclones, fierce alternating zonal flows, and a high-latitude eastward jet with a polygonal pattern. The analysis of the simulation suggests that self-organized turbulence in the form of giant vortices pinches the eastward jet, forming polygonal shapes. We argue that a similar mechanism is responsible for exciting Saturn’s hexagonal flow pattern.

scholarly journals Baroclinic Waves with Parameterized Effects of Moisture Interpreted Using Rossby Wave Components

2010 ◽  
Vol 67 (9) ◽  
pp. 2766-2784 ◽  
Author(s):  
Hylke de Vries ◽  
John Methven ◽  
Thomas H. A. Frame ◽  
Brian J. Hoskins
Keyword(s):  
Rossby Wave ◽  
Large Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Lower Boundary ◽  
Vertical Shear ◽  
Zonal Flows ◽  
Baroclinic Waves ◽  
Strength Of Interaction ◽  
Type C

Abstract A theoretical framework is developed for the evolution of baroclinic waves with latent heat release parameterized in terms of vertical velocity. Both wave–conditional instability of the second kind (CISK) and large-scale rain approaches are included. The new quasigeostrophic framework covers evolution from general initial conditions on zonal flows with vertical shear, planetary vorticity gradient, a lower boundary, and a tropopause. The formulation is given completely in terms of potential vorticity, enabling the partition of perturbations into Rossby wave components, just as for the dry problem. Both modal and nonmodal development can be understood to a good approximation in terms of propagation and interaction between these components alone. The key change with moisture is that growing normal modes are described in terms of four counterpropagating Rossby wave (CRW) components rather than two. Moist CRWs exist above and below the maximum in latent heating, in addition to the upper- and lower-level CRWs of dry theory. Four classifications of baroclinic development are defined by quantifying the strength of interaction between the four components and identifying the dominant pairs, which range from essentially dry instability to instability in the limit of strong heating far from boundaries, with type-C cyclogenesis and diabatic Rossby waves being intermediate types. General initial conditions must also include passively advected residual PV, as in the dry problem.

scholarly journals Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

2015 ◽  
Vol 785 ◽  
pp. 1-30 ◽  
Author(s):  
Jean N. Reinaud ◽  
Xavier Carton
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Steady States ◽  
Point Vortices ◽  
Velocity Shear ◽  
Vertical Shear ◽  
Finite Area ◽  
Geostrophic Flows ◽  
Vertically Aligned ◽  
Baroclinic Vortices

Hetons are baroclinic vortices able to transport tracers or species, which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. First, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-of-eight shaped) upper cores. In the case of vertically distant upper and lower cores, the latter can nearly join near the centre of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.

Steady radiating baroclinic vortices in vertically sheared flows

2021 ◽  
Author(s):  
Georgi Sutyrin ◽  
Jonas Nycander ◽  
Timour Radko
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Vertical Shear ◽  
Alternative Mechanism ◽  
Beta Plane ◽  
Subtropical Oceans ◽  
Baroclinic Vortices ◽  
Favorable Conditions

<p>Baroclinic vortices embedded in a large-scale vertical shear are examined. We describe a new class of steady propagating vortices that radiate Rossby waves but yet do not decay. This is possible since they can extract available potential energy (APE) from a large-scale vertically sheared flow, even though this flow is linearly stable. The vortices generate Rossby waves which induce a meridional vortex drift and an associated heat flux explained by an analysis of pseudomomentum and pseudoenergy. An analytical steady solution is considered for a marginally stable flow in a two-layer model on the beta-plane, where the beta-effect is compensated by the potential vorticity gradient (PVG) associated with the meridional slope of the density interface. The compensation occurs in the upper layer for an upper layer westward flow (an easterly shear) and in the lower layer for an upper layer eastward flow (the westerly shear). The theory is confirmed by numerical simulations indicating that for westward flows in subtropical oceans, the reduced PVG in the upper layer provides favorable conditions for eddy persistence and long-range propagation. The drifting and radiating vortex is an alternative mechanism besides baroclinic instability for converting background APE to mesoscale energy. </p>

Baroclinic instability of quasi-geostrophic flows localized in a thin layer

1995 ◽  
Vol 288 ◽  
pp. 175-199 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Baroclinic Instability ◽  
Vertical Shear ◽  
Layer Model ◽  
Effective Time ◽  
Sufficient Stability ◽  
Geostrophic Flows ◽  
Characteristic Spatial Scale ◽  
Northern Pacific ◽  
Two Layer Model ◽  
Layer I

This paper examines the baroclinic instability of a quasi-geostrophic flow with vertical shear in a continuously stratified fluid. The flow and density stratification are both localized in a thin upper layer. (i) Disturbances whose wavelength is much smaller than the deformation radius (based on the depth of the upper layer) are demonstrated to satisfy an ‘equivalent two-layer model’ with properly chosen parameters. (ii) For disturbances whose wavelength is of the order of, or greater than, the deformation radius we derive a sufficient stability criterion. The above analysis is applied to the subtropical and subarctic frontal currents in the Northern Pacific. The effective time of growth of disturbances (i) is found to be 16–22 days, the characteristic spatial scale is 130–150 km.

The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles

2007 ◽  
Vol 593 ◽  
pp. 359-383 ◽  
Author(s):  
ÁLVARO VIÚDEZ
Keyword(s):  
Wave Packet ◽  
Vertical Velocity ◽  
Large Scale ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Vertical Shear ◽  
Dipole Axis ◽  
Frontal Wave ◽  
Vortex Dipoles ◽  
Vorticity Vector

The origin of the stationary frontal wave packet spontaneously generated in rotating and stably stratified vortex dipoles is investigated through high-resolution three-dimensional numerical simulations of non-hydrostatic volume-preserving flow under the f-plane and Boussinesq approximations. The wave packet is rendered better at mid-depths using ageostrophic quantities like the vertical velocity or the vertical shear of the ageostrophic vertical vorticity. The analysis of the origin of vertical velocity anomalies in shallow layers using the generalized omega-equation reveals that these anomalies are related to the material rate of change of the ageostrophic differential vorticity, which in shallow layers are themselves related to the large-scale ageostrophic flow along the dipole axis, and in particular, to the advective acceleration. It is found that on the anticyclonic side of the dipole axis the combined effect of the speed and centripetal accelerations causes an anticyclonic rotation of the horizontal ageostrophic vorticity vector in a time scale of about one inertial period. These facts support the hypothesis that the origin of the stationary and spontaneously generated frontal wave packet at mid-depths is the large acceleration of the fluid particles as they move along the anticyclonic side of the dipole axis in shallow layers.

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