Baroclinic Instability of Frontal Geostrophic Currents over a Slope

2005 ◽  
Vol 35 (5) ◽  
pp. 911-918 ◽  
Author(s):  
Marc Pavec ◽  
Xavier Carton ◽  
Gordon Swaters
Keyword(s):  
Steady Flow ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Mathieu Equation ◽  
Relative Vorticity ◽  
Stability Study ◽  
Mean Flow ◽  
Low Frequencies ◽  
Layer Flow ◽  
Quasigeostrophic Model

Abstract The Phillips problem of baroclinic instability is generalized in a frontal geostrophic model. The configuration used here is a two-layer flow (with quasigeostrophic upper-layer current) over a sloping bottom. Baroclinic instability in the frontal model has a single unstable mode, corresponding to isobaths and isopycnals sloping in the same direction, contrary to the quasigeostrophic model, which has two unstable modes. In physical terms, this is explained by the absence of relative vorticity in the lower (frontal) layer. Indeed, the frontal geostrophic model can be related to the quasigeostrophic model in the limit of very small thickness of the lower layer, implying that potential vorticity reduces to vortex stretching in this layer. This stability study is then extended to unsteady flows. In the frontal geostrophic model, a mean flow oscillation can stabilize an unstable steady flow; it can destabilize a stable steady flow only for a discrete spectrum of low frequencies. In this case, the model equations reduce to the Mathieu equation, the properties of which are well known.

Evolution of solitary marginal disturbances in baroclinic frontal geostrophic dynamics with dissipation and time-varying background flow

2007 ◽  
Vol 463 (2083) ◽  
pp. 1749-1769 ◽  
Author(s):  
Mattea R Turnbull ◽  
Gordon E Swaters
Keyword(s):  
Lower Layer ◽  
Baroclinic Instability ◽  
Variable Coefficients ◽  
Time Variability ◽  
Perturbation Approach ◽  
Dynamical Regime ◽  
Time Varying ◽  
Mean Flow ◽  
Background Flow ◽  
Frontal Geostrophic Dynamics

A two-layer frontal geostrophic flow corresponds to a dynamical regime that describes the low-frequency evolution of baroclinic ocean currents with large amplitude deflections of the interface between the layers on length-scales longer than the internal deformation radius within the context of a thin upper layer overlying a dynamically active lower layer. The finite-amplitude evolution of solitary disturbances in baroclinic frontal geostrophic dynamics in the presence of time-varying background flow and dissipation is shown to be governed by a two-equation extension of the unstable nonlinear Schrödinger (UNS) equation with variable coefficients and forcing. The soliton solution of the unperturbed UNS equation corresponds to a saturated isolated coherent anomaly in the baroclinic instability of surface-intensified oceanographic fronts and currents. The adiabatic evolution of the propagating soliton and the uniformly valid first-order perturbation fields are determined using a direct perturbation approach together with phase-averaged conservation relations when both dissipation and time variability are present. It is shown that the soliton amplitude parameter decays exponentially due to the presence of the dissipation but is unaffected by the time variability in the background flow. On the other hand, the soliton translation velocity is unaffected by the dissipation and evolves only in response to the time variability in the background flow. The adiabatic solution for the induced mean flow exhibits a dissipation-generated ‘shelf region’ in the far field behind the soliton, which is removed by solving the initial-value problem.

Equilibration of Baroclinic Turbulence in Primitive Equations and Quasigeostrophic Models

2009 ◽  
Vol 66 (4) ◽  
pp. 837-863 ◽  
Author(s):  
Pablo Zurita-Gotor ◽  
Geoffrey K. Vallis
Keyword(s):  
Baroclinic Instability ◽  
Quantitative Agreement ◽  
Equation Model ◽  
Turbulence Theory ◽  
Mean Flow ◽  
Primitive Equation ◽  
Primitive Equation Model ◽  
Barotropic Flow ◽  
Quasigeostrophic Model ◽  
Parameter Ranges

Abstract This paper investigates the equilibration of baroclinic turbulence in an idealized, primitive equation, two-level model, focusing on the relation with the phenomenology of quasigeostrophic turbulence theory. Simulations with a comparable two-layer quasigeostrophic model are presented for comparison, with the deformation radius in the quasigeostrophic model being set using the stratification from the primitive equation model. Over a fairly broad parameter range, the primitive equation and quasigeostrophic results are in qualitative and, to some degree, quantitative agreement and are consistent with the phenomenology of geostrophic turbulence. The scale, amplitude, and baroclinicity of the eddies and the degree of baroclinic instability of the mean flow all vary fairly smoothly with the imposed parameters; both models are able, in some parameter ranges, to produce supercritical flows. The criticality in the primitive equation model, which does not have any convective parameterization scheme, is fairly sensitive to the external parameters, most notably the planet size (i.e., the f /β ratio), the forcing time scale, and the factors influencing the stratification. In some parameter settings of the models, although not those that are most realistic for the earth’s atmosphere, it is possible to produce eddies that are considerably larger than the deformation scales and an inverse cascade in the barotropic flow with a −5/3 spectrum. The vertical flux of heat is found to be related to the isentropic slope.

Low-Frequency Basin Modes in a Two-Layer Quasigeostrophic Model in the Presence of a Mean Gyre Flow*

2005 ◽  
Vol 35 (11) ◽  
pp. 2167-2186 ◽  
Author(s):  
Mahdi Ben Jelloul ◽  
Thierry Huck
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Multiple Time ◽  
Mean Flow ◽  
Low Frequencies ◽  
Weakly Nonlinear ◽  
Basin Scale ◽  
Rossby Radius Of Deformation ◽  
Quasigeostrophic Model ◽  
Scale Limit

Abstract The spectrum of baroclinic basin modes is investigated in a two-layer wind-driven quasigeostrophic model through weakly nonlinear multiple time-scale expansion in the Burger number. The baroclinic basin modes are mainly advected by a barotropic steady Sverdrup flow. Emphasis is given to the regularizing influence of dispersion rather than to dissipation. In the inviscid large-scale limit, that is, for basin scale considerably larger than the Rossby radius of deformation, all of the basin modes are neutral. Their typology is then numerically examined (with some necessary dissipation), and their frequency and spatial properties are discussed. Three types of modes arise for some wind forcing strong enough to produce a recirculating gyre with closed geostrophic contours: the classical Rossby basin modes deformed by the mean flow (shadow modes), stationary modes, and recirculating pool modes, the two latter being trapped in the closed-contours pool. Focus is made here on the recirculating modes that could have very low frequencies for moderate recirculating gyres. Strong gyres lead to higher frequencies, and recirculating modes resonate with deformed Rossby basin modes.

Transcritical two-layer flow over topography

1987 ◽  
Vol 178 ◽  
pp. 31-52 ◽  
Author(s):  
W. K. Melville ◽  
Karl R. Helfrich
Keyword(s):  
Steady Flow ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Kdv Equation ◽  
Single Layer ◽  
Cubic Nonlinearity ◽  
Arbitrary Length ◽  
Weakly Nonlinear ◽  
Flow Over Topography ◽  
Layer Flow

The evolution of weakly-nonlinear two-layer flow over topography is considered. The governing equations are formulated to consider the effects of quadratic and cubic nonlinearity in the transcritical regime of the internal mode. In the absence of cubic nonlinearity an inhomogeneous Korteweg-de Vries equation describes the interfacial displacement. Numerical solutions of this equation exhibit undular bores or sequences of Boussinesq solitary waves upstream in a transcritical regime. For sufficiently large supercritical Froude numbers, a locally steady flow is attained over the topography. In that regime in which both quadratic and cubic nonlinearity are comparable, the evolution of the interface is described by an inhomogeneous extended Kortewegde Vries (EKdV) equation. This equation displays undular bores upstream in a subcritical regime, but monotonic bores in a transcritical regime. The monotonic bores are solitary wave solutions of the corresponding homogeneous EKdV equation. Again, locally steady flow is attained for sufficiently large supercritical Froude numbers. The predictions of the numerical solutions are compared with laboratory experiments which show good agreement with the solutions of the forced EKdV equation for some range of parameters. It is shown that a recent result of Miles (1986), which predicts an unsteady transcritical regime for single-layer flows, may readily be extended to two-layer flows (described by the forced KdV equation) and is in agreement with the results presented here.Numerical experiments exploiting the symmetry of the homogeneous EKdV equation show that solitary waves of fixed amplitude but arbitrary length may be generated in systems described by the inhomogeneous EKdV equation.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

Eddy-mediated Hadley cell expansion due to axisymmetric angular momentum adjustment to greenhouse gas forcings

2021 ◽  
Author(s):  
Nicholas A. Davis ◽  
Thomas Birner
Keyword(s):  
Angular Momentum ◽  
Greenhouse Gas ◽  
Cell Expansion ◽  
Energy Transport ◽  
Baroclinic Instability ◽  
Temperature Response ◽  
Equilibrium Temperature ◽  
Hadley Cell ◽  
Mean Flow ◽  
Fully Coupled

AbstractThe poleward expansion of the Hadley cells is one of the most robust modeled responses to increasing greenhouse gas concentrations. There are many proposed mechanisms for expansion, and most are consistent with modeled changes in thermodynamics, dynamics, and clouds. The adjustment of the eddies and the mean flow to greenhouse gas forcings, and to one another, complicates any effort toward a deeper understanding. Here we modify the Gray Radiation AND Moist Aquaplanet (GRANDMA) model to uncouple the eddy and mean flow responses to forcings. When eddy forcings are held constant, the purely axisymmetric response of the Hadley cell to a greenhouse gas-like forcing is an intensification and poleward tilting of the cell with height in response to an axisymmetric increase in angular momentum in the subtropics. The angular momentum increase drastically alters the circulation response compared to axisymmetric theories, which by nature neglect this adjustment. Model simulations and an eddy diffusivity framework demonstrate that the axisymmetric increase in subtropical angular momentum – the direct manifestation of the radiative-convective equilibrium temperature response – drives a poleward shift of the eddy stresses which leads to Hadley cell expansion. Prescribing the eddy response to the greenhouse gas-like forcing shows that eddies damp, rather than drive, changes in angular momentum, moist static energy transport, and momentum transport. Expansion is not driven by changes in baroclinic instability, as would otherwise be diagnosed from the fully-coupled simulation. These modeling results caution any assessment of mechanisms for circulation change within the fully-coupled wave-mean flow system.

On the Thickness Ratio in the Quasigeostrophic Two-Layer Model of Baroclinic Instability

2013 ◽  
Vol 70 (5) ◽  
pp. 1505-1511 ◽  
Author(s):  
Noboru Nakamura ◽  
Lei Wang
Keyword(s):  
Growth Rate ◽  
Vertical Structure ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Thickness Ratio ◽  
Layer Model ◽  
Optimal Thickness ◽  
Zonal Wavenumber ◽  
The Mean ◽  
Two Layer Model

Abstract It is shown that the classical quasigeostrophic two-layer model of baroclinic instability possesses an optimal ratio of layer thicknesses that maximizes the growth rate, given the basic-state shear (thermal wind), beta, and the mean Rossby radius. This ratio is interpreted as the vertical structure of the most unstable mode. For positive shear and beta, the optimal thickness of the lower layer approaches the midheight of the model in the limit of strong criticality (shear/beta) but it is proportional to criticality in the opposite limit. For a set of parameters typical of the earth’s midlatitudes, the growth rate maximizes at a lower-layer thickness substantially less than the midheight and at a correspondingly larger zonal wavenumber. It is demonstrated that a turbulent baroclinic jet whose statistical steady state is marginally critical when run with equal layer thicknesses can remain highly supercritical when run with a nearly optimal thickness ratio.

scholarly journals Dominant Anomaly Patterns in the Near-Surface Baroclinicity and Accompanying Anomalies in the Atmosphere and Oceans. Part II: North Pacific Basin

2010 ◽  
Vol 23 (24) ◽  
pp. 6445-6467 ◽  
Author(s):  
Mototaka Nakamura ◽  
Shozo Yamane
Keyword(s):  
Heat Flux ◽  
North Pacific ◽  
Spatial Scales ◽  
Baroclinic Instability ◽  
Lower Troposphere ◽  
Pacific Basin ◽  
Mean Flow ◽  
Near Surface ◽  
Eddy Heat Flux ◽  
North Pacific Basin

Abstract Variability in the monthly-mean flow and storm track in the North Pacific basin is examined with a focus on the near-surface baroclinicity. Dominant patterns of anomalous near-surface baroclinicity found from empirical orthogonal function (EOF) analyses generally show mixed patterns of shift and changes in the strength of near-surface baroclinicity. Composited anomalies in the monthly-mean wind at various pressure levels based on the signals in the EOFs show accompanying anomalies in the mean flow up to 50 hPa in the winter and up to 100 hPa in other seasons. Anomalous eddy fields accompanying the anomalous near-surface baroclinicity patterns exhibit, broadly speaking, structures anticipated from simple linear theories of baroclinic instability, and suggest a tendency for anomalous wave fluxes to accelerate–decelerate the surface westerly accordingly. However, the relationship between anomalous eddy fields and anomalous near-surface baroclinicity in the midwinter is not consistent with the simple linear baroclinic instability theories. Composited anomalous sea surface temperature (SST) accompanying anomalous near-surface baroclinicity often exhibits moderate values and large spatial scales in the basin, rather than large values concentrated near the oceanic fronts. In the midsummer and in some cases in cold months, however, large SST anomalies are found around the Kuroshio–Oyashio Extensions. Accompanying anomalies in the net surface heat flux, SST in the preceding and following months, and meridional eddy heat flux in the lower troposphere suggest active roles played by the ocean in generating the concomitant anomalous large-scale atmospheric state in some of these cases.

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.

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