scholarly journals Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

2014 ◽  
Vol 44 (7) ◽  
pp. 1919-1940 ◽  
Author(s):  
T. Radko ◽  
D. Peixoto de Carvalho ◽  
J. Flanagan
Keyword(s):  
Numerical Simulations ◽  
Large Scale ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Vertical Shear ◽  
Balance Model ◽  
Mesoscale Variability ◽  
Beta Effect ◽  
Eddy Transport ◽  
Secondary Instabilities

Abstract A theoretical model is developed, which attempts to predict the lateral transport by mesoscale variability, generated and maintained by baroclinic instability of large-scale flows. The authors are particularly concerned by the role of secondary instabilities of primary baroclinically unstable modes in the saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for evaluating the equilibrium magnitude of mesoscale eddies as a function of the background parameters: vertical shear, stratification, beta effect, and bottom drag. The proposed technique is applied to two classical models of baroclinic instability—the Phillips two-layer model and the linearly stratified Eady model. Theory predicts that the eddy-driven lateral mixing rapidly intensifies with increasing shear and weakens when the beta effect is increased. The eddy transport is also sensitive to the stratification pattern, decreasing as the ratio of upper/lower layer depths in the Phillips model is decreased below unity. Theory is successfully tested by a series of direct numerical simulations that span a wide parameter range relevant for typical large-scale currents in the ocean. The spontaneous emergence of large-scale patterns induced by mesoscale variability, and their role in the cross-flow eddy transport, is examined using a suite of numerical simulations.

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>

scholarly journals Seasonal and mesoscale variability of oceanic transport of anthropogenic CO<sub>2</sub>

2009 ◽  
Vol 6 (11) ◽  
pp. 2509-2523 ◽  
Author(s):  
Z. Lachkar ◽  
J. C. Orr ◽  
J.-C. Dutay
Keyword(s):  
Southern Ocean ◽  
North Atlantic ◽  
Large Scale ◽  
Vertical Shear ◽  
Ekman Transport ◽  
Mesoscale Variability ◽  
Meridional Transport ◽  
Anthropogenic Co2 ◽  
Eddy Transport ◽  
The Tropics

Abstract. Estimates of the ocean's large-scale transport of anthropogenic CO2 are based on one-time hydrographic sections, but the temporal variability of this transport has not been investigated. The aim of this study is to evaluate how the seasonal and mesoscale variability affect data-based estimates of anthropogenic CO2 transport. To diagnose this variability, we made a global anthropogenic CO2 simulation using an eddy-permitting version of the coupled ocean sea-ice model ORCA-LIM. As for heat transport, the seasonally varying transport of anthropogenic CO2 is largest within 20° of the equator and shows secondary maxima in the subtropics. Ekman transport generally drives most of the seasonal variability, but the contribution of the vertical shear becomes important near the equator and in the Southern Ocean. Mesoscale variabilty contributes to the annual-mean transport of both heat and anthropogenic CO2 with strong poleward transport in the Southern Ocean and equatorward transport in the tropics. This "rectified" eddy transport is largely baroclinic in the tropics and barotropic in the Southern Ocean due to a larger contribution from standing eddies. Our analysis revealed that most previous hydrographic estimates of meridional transport of anthropogenic CO2 are severely biased because they neglect temporal fluctuations due to non-Ekman velocity variations. In each of the three major ocean basins, this bias is largest near the equator and in the high southern latitudes. In the subtropical North Atlantic, where most of the hydrographic-based estimates have been focused, this uncertainty represents up to 20% and 30% of total meridional transport of heat and CO2. Generally though, outside the tropics and Southern Ocean, there are only small variations in meridional transport due to seasonal variations in tracer fields and time variations in eddy transport. For the North Atlantic, eddy variability accounts for up to 10% and 15% of the total transport of heat and CO2. This component is not accounted for in coarse-resolution hydrographic surveys.

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 The Loop Current: Observations of Deep Eddies and Topographic Waves

2019 ◽  
Vol 49 (6) ◽  
pp. 1463-1483 ◽  
Author(s):  
Peter Hamilton ◽  
Amy Bower ◽  
Heather Furey ◽  
Robert Leben ◽  
Paula Pérez-Brunius
Keyword(s):  
Large Scale ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Short Interval ◽  
Loop Current ◽  
Boundary Current ◽  
The West ◽  
Eastern Basin ◽  
Topographic Rossby Waves ◽  
Deep Eddies

AbstractA set of float trajectories, deployed at 1500- and 2500-m depths throughout the deep Gulf of Mexico from 2011 to 2015, are analyzed for mesoscale processes under the Loop Current (LC). In the eastern basin, December 2012–June 2014 had >40 floats per month, which was of sufficient density to allow capturing detailed flow patterns of deep eddies and topographic Rossby waves (TRWs), while two LC eddies formed and separated. A northward advance of the LC front compresses the lower water column and generates an anticyclone. For an extended LC, baroclinic instability eddies (of both signs) develop under the southward-propagating large-scale meanders of the upper-layer jet, resulting in a transfer of eddy kinetic energy (EKE) to the lower layer. The increase in lower-layer EKE occurs only over a few months during meander activity and LC eddy detachment events, a relatively short interval compared with the LC intrusion cycle. Deep EKE of these eddies is dispersed to the west and northwest through radiating TRWs, of which examples were found to the west of the LC. Because of this radiation of EKE, the lower layer of the eastern basin becomes relatively quiescent, particularly in the northeastern basin, when the LC is retracted and a LC eddy has departed. A mean west-to-east, anticyclone–cyclone dipole flow under a mean LC was directly comparable to similar results from a previous moored LC array and also showed connections to an anticlockwise boundary current in the southeastern basin.

scholarly journals Effects of Environmentally Induced Asymmetries on Hurricane Intensity: A Numerical Study

2004 ◽  
Vol 61 (24) ◽  
pp. 3065-3081 ◽  
Author(s):  
Liguang Wu ◽  
Scott A. Braun
Keyword(s):  
Large Scale ◽  
Numerical Study ◽  
Environmental Influence ◽  
Lower Troposphere ◽  
Vertical Shear ◽  
Hurricane Intensity ◽  
Beta Effect ◽  
The Mean ◽  
Large Scale Flow ◽  
Radial Circulation

Abstract The influence of uniform large-scale flow, the beta effect, and vertical shear of the environmental flow on hurricane intensity is investigated in the context of the induced convective or potential vorticity asymmetries in the core region with a hydrostatic primitive equation hurricane model. In agreement with previous studies, imposition of one of these environmental effects weakens the simulated tropical cyclones. In response to the environmental influence, significant wavenumber-1 asymmetries develop. Asymmetric and symmetric tendencies of the mean radial and azimuthal winds and temperature associated with the environment-induced convective asymmetries are evaluated. The inhibiting effects of environmental influences are closely associated with the resulting eddy momentum fluxes, which tend to decelerate tangential and radial winds in the inflow and outflow layers. The corresponding changes in the symmetric circulation tend to counteract the deceleration effect. The net effect is a moderate weakening of the mean tangential and radial winds. The reduced radial wind can be viewed as an anomalous secondary radial circulation with inflow in the upper troposphere and outflow in the lower troposphere, weakening the mean secondary radial circulation.

scholarly journals On the baroclinic instability of axisymmetric rotating gravity currents with bottom slope

2000 ◽  
Vol 408 ◽  
pp. 149-177 ◽  
Author(s):  
PAUL F. CHOBOTER ◽  
GORDON E. SWATERS
Keyword(s):  
Numerical Simulations ◽  
Linear Stability ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Laboratory Data ◽  
Gravity Current ◽  
Gravity Currents ◽  
Finite Amplitude ◽  
Rotating System ◽  
A Current

The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections of that layer are not small with respect to its scale height. The upper-layer dynamics are quasi-geostrophic, with the Eulerian velocity field principally driven by baroclinic stretching and a background topographic vorticity gradient.Necessary conditions for instability, a semicircle-like theorem for unstable modes, bounds on the growth rate and phase velocity, and a sufficient condition for the existence of a high-wavenumber cutoff are presented. The linear stability equations are solved exactly for the case where the gravity current initially corresponds to an annulus flow with parabolic height profile with two incroppings, i.e. a coupled front. The dispersion relation for such a current is solved numerically, and the characteristics of the unstable modes are described. A distinguishing feature of the spatial structure of the perturbations is that the perturbations to the downslope incropping are preferentially amplified compared to the upslope incropping. Predictions of the model are compared with recent laboratory data, and good agreement is seen in the parameter regime for which the model is valid. Direct numerical simulations of the full model are employed to investigate the nonlinear regime. In the initial stage, the numerical simulations agree closely with the linear stability characteristics. As the instability develops into the finite-amplitude regime, the perturbations to the downslope incropping continue to preferentially amplify and eventually evolve into downslope propagating plumes. These finally reach the deepest part of the topography, at which point no more potential energy can be released.

Compartment temperature estimation of a multiple-layer cable tray fire with different cable arrangements in a closed compartment

2019 ◽  
Vol 37 (4-6) ◽  
pp. 303-319
Author(s):  
Xianjia Huang ◽  
Yuhong Wang ◽  
Wuyong Zeng ◽  
Lan Peng ◽  
Anthony CH Cheng ◽  
...  
Keyword(s):  
Large Scale ◽  
Lower Layer ◽  
Fire Hazard ◽  
Hazard Analysis ◽  
Balance Model ◽  
Vertical Temperature ◽  
Vertical Temperature Profile ◽  
Multiple Layer ◽  
Cable Fire ◽  
Tray Fire

Fire hazard analysis of multiple-layer cable tray is an important part of nuclear safety analysis. Large-scale cable fire experiments with a three-layer horizontal cable tray were conducted in a closed compartment. The vertical temperature profile in the middle of the room was acquired. Distinctive stratification phenomena were found in the vertical temperature distribution. The interface between the upper and lower layer was located at approximately the height of the top cable layer. Heat transfer between the smoke and compartment walls occurred mainly above the smoke interface. A modified non-steady energy balance model in a closed compartment which included the effect of smoke interface height was used to estimate the compartment temperatures. Compared with the experimental results, the modified model for the multiple-layer cable tray fire in a closed compartment provides better estimation than the original model.

scholarly journals Low-frequency electrostatic waves in the ionospheric E-region: a comparison of rocket observations and numerical simulations

2006 ◽  
Vol 24 (11) ◽  
pp. 2959-2979 ◽  
Author(s):  
L. Dyrud ◽  
B. Krane ◽  
M. Oppenheim ◽  
H. L. Pécseli ◽  
K. Schlegel ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Large Scale ◽  
Low Frequency ◽  
Homogeneous Magnetic Field ◽  
Small Scale ◽  
Electrostatic Waves ◽  
Neutral Gas ◽  
E Region ◽  
Locally Homogeneous ◽  
Secondary Instabilities

Abstract. Low frequency electrostatic waves in the lower parts of the ionosphere are studied by a comparison of observations by instrumented rockets and of results from numerical simulations. Particular attention is given to the spectral properties of the waves. On the basis of a good agreement between the observations and the simulations, it can be argued that the most important nonlinear dynamics can be accounted for in a 2-D numerical model, referring to a plane perpendicular to a locally homogeneous magnetic field. It does not seem necessary to take into account turbulent fluctuations or motions in the neutral gas component. The numerical simulations explain the observed strongly intermittent nature of the fluctuations: secondary instabilities develop on the large scale gradients of the largest amplitude waves, and the small scale dynamics is strongly influenced by these secondary instabilities. We compare potential variations obtained at a single position in the numerical simulations with two point potential-difference signals, where the latter is the adequate representation for the data obtained by instrumented rockets. We can demonstrate a significant reduction in the amount of information concerning the plasma turbulence when the latter signal is used for analysis. In particular we show that the bicoherence estimate is strongly affected. The conclusions have implications for studies of low frequency ionospheric fluctuations in the E and F regions by instrumented rockets, and also for other methods relying on difference measurements, using two probes with large separation. The analysis also resolves a long standing controversy concerning the supersonic phase velocities of these cross-field instabilities being observed in laboratory experiments.

Non-geostrophic instabilities of an equilibrium baroclinic state

2013 ◽  
Vol 734 ◽  
pp. 535-566 ◽  
Author(s):  
Alexandre B. Pieri ◽  
F. S. Godeferd ◽  
C. Cambon ◽  
A. Salhi
Keyword(s):  
Numerical Simulations ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Dimensionless Numbers ◽  
Stability Bound ◽  
Simultaneous Existence ◽  
The Stability ◽  
Symmetric Instability

AbstractWe consider non-geostrophic homogeneous baroclinic turbulence without solid boundaries, and we focus on its energetics and dynamics. The homogeneous turbulent flow is therefore submitted to both uniform vertical shear $S$ and stable vertical stratification, parametrized by the Brunt–Väisälä frequency $N$, and placed in a rotating frame with Coriolis frequency $f$. Direct numerical simulations show that the threshold of baroclinic instability growth depends mostly on two dimensionless numbers, the gradient Richardson number $\mathit{Ri}= {N}^{2} / {S}^{2} $ and the Rossby number $\mathit{Ro}= S/ f$, whereas linear theory predicts a threshold that depends only on $\mathit{Ri}$. At high Rossby numbers the nonlinear limit is found to be $\mathit{Ri}= 0. 2$, while in the limit of low $\mathit{Ro}$ the linear stability bound $\mathit{Ri}= 1$ is recovered. We also express the stability results in terms of background potential vorticity, which is an important quantity in baroclinic flows. We show that the linear symmetric instability occurs from the presence of negative background potential vorticity. The possibility of simultaneous existence of symmetric and baroclinic instabilities is also investigated. The dominance of symmetric instability over baroclinic instability for $\mathit{Ri}\ll 1$ is confirmed by our direct numerical simulations, and we provide an improved understanding of the dynamics of the flow by exploring the details of energy transfers for moderate Richardson numbers.

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.

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