Meridional dynamics of grounded abyssal water masses on a sloping bottom in a mid-latitude -plane

2018 ◽  
Vol 841 ◽  
pp. 674-701 ◽  
Author(s):  
Gordon E. Swaters
Keyword(s):  
Baroclinic Instability ◽  
Volume Transport ◽  
Finite Amplitude ◽  
Meridional Flow ◽  
Water Masses ◽  
Time Dependent ◽  
Meridional Transport ◽  
Initial Current ◽  
Abyssal Current ◽  
Parallel Shear Flow

Observations, numerical simulations and theoretical scaling arguments suggest that in mid-latitudes, away from the source regions and the equator, the meridional transport of abyssal water masses along a continental slope corresponds to planetary geostrophic flows that are gravity- or density-driven and topographically steered. We investigate these dynamics using a nonlinear reduced-gravity model that can describe grounded abyssal meridional flow over sloping topography that crosses the planetary vorticity gradient. Exact nonlinear steady and time-dependent solutions are obtained. The general steady theory is illustrated for a non-parallel equatorward flow that possesses a single along-slope grounding along the upslope flank of the current (complementing previous work). Four specific nonlinear time-dependent solutions are described. Two initial-value problems are solved exactly. The first initial configuration corresponds to an equatorward abyssal flow that has no cross-slope shear in the along-slope velocity and possesses a single grounding along the upslope flank of the current. The nonlinear time-dependent evolution of this initial current into a non-parallel shear flow is described. The second initial condition corresponds to an isolated radially symmetric grounded abyssal pool or dome. The nonlinear time-dependent evolution of this abyssal dome, which propagates equatorward with unsteady along- and cross-slope velocities while deforming into an elliptically shaped abyssal dome with $\unicode[STIX]{x1D6FD}$-induced diminishing height, is described. Finally, the nonlinear time-dependent boundary-value problem can be solved exactly in which the in-flow boundary condition on the poleward boundary of the mid-latitude domain corresponds to a time-dependent abyssal current with both an upslope and downslope grounding. Two specific time-dependent boundary conditions are examined. The first corresponds to a time-limited surge in the equatorward volume transport in the abyssal current along the poleward boundary. The second configuration corresponds to the nonlinear evolution of a finite-amplitude downslope plume or loop that forms in the abyssal current that is reminiscent of those seen in baroclinic instability simulations.

Finite-Amplitude Baroclinic Instability of Time-Varying Abyssal Currents

2006 ◽  
Vol 36 (1) ◽  
pp. 122-139 ◽  
Author(s):  
Seung-Ji Ha ◽  
Gordon E. Swaters
Keyword(s):  
Baroclinic Instability ◽  
Soliton Solutions ◽  
Zonal Flow ◽  
Finite Amplitude ◽  
Marginal Stability ◽  
Time Variability ◽  
Time Varying ◽  
Weakly Nonlinear ◽  
Abyssal Current ◽  
The Stability

Abstract The weakly nonlinear baroclinic instability characteristics of time-varying grounded abyssal flow on sloping topography with dissipation are described. Specifically, the finite-amplitude evolution of marginally unstable or stable abyssal flow both at and removed from the point of marginal stability (i.e., the minimum shear required for instability) is determined. The equations governing the evolution of time-varying dissipative abyssal flow not at the point of marginal stability are identical to those previously obtained for the Phillips model for zonal flow on a β plane. The stability problem at the point of marginally stability is fully nonlinear at leading order. A wave packet model is introduced to examine the role of dissipation and time variability in the background abyssal current. This model is a generalization of one introduced for the baroclinic instability of zonal flow on a β plane. A spectral decomposition and truncation leads, in the absence of time variability in the background flow and dissipation, to the sine–Gordon solitary wave equation that has grounded abyssal soliton solutions. The modulation characteristics of the soliton are determined when the underlying abyssal current is marginally stable or unstable and possesses time variability and/or dissipation. The theory is illustrated with examples.

The Meridional Flow of Source-Driven Abyssal Currents in a Stratified Basin with Topography. Part I: Model Development and Dynamical Properties

2006 ◽  
Vol 36 (3) ◽  
pp. 335-355 ◽  
Author(s):  
Gordon E. Swaters
Keyword(s):  
Baroclinic Instability ◽  
Model Development ◽  
Finite Amplitude ◽  
Meridional Flow ◽  
Gravity Models ◽  
Western Boundary ◽  
Reduced Gravity ◽  
The Stability ◽  
Abyssal Currents ◽  
Variable Topography

Abstract The equatorward flow of source-driven grounded deep western boundary currents within a stratified basin with variable topography is examined. The model is the two-layer quasigeostrophic (QG) equations, describing the overlying ocean, coupled to the finite-amplitude planetary geostrophic (PG) equations, describing the abyssal layer, on a midlatitude β plane. The model retains subapproximations such as classical Stommel–Arons theory, the Nof abyssal dynamical balance, the so-called planetary shock wave balance (describing the finite-amplitude β-induced westward propagation of abyssal anomalies), and baroclinic instability. The abyssal height field can possess groundings. In the reduced gravity limit, a new nonlinear steady-state balance is identified that connects source-driven equatorward abyssal flow (as predicted by Stommel–Arons theory) and the inertial topographically steered deep flow described by Nof dynamics. This model is solved explicitly, and the meridional structure of the predicted grounded abyssal flow is described. In the fully baroclinic limit, a variational principle is established and is exploited to obtain general stability conditions for meridional abyssal flow over variable topography on a β plane. The baroclinic coupling of the PG abyssal layer with the QG overlying ocean eliminates the ultraviolet catastrophe known to occur in inviscid PG reduced gravity models. The baroclinic instability problem for a constant-velocity meridional abyssal current flowing over sloping topography with β present is solved and the stability characteristics are described.

Parameterization of Mixed Layer Eddies. Part I: Theory and Diagnosis

2008 ◽  
Vol 38 (6) ◽  
pp. 1145-1165 ◽  
Author(s):  
Baylor Fox-Kemper ◽  
Raffaele Ferrari ◽  
Robert Hallberg
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Climate Impacts ◽  
Surface Mixed Layer ◽  
Rotation Rates ◽  
Wide Range ◽  
Horizontal Density Gradient ◽  
Mixed Layers

Abstract Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.

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 The Effect of Lower Stratospheric Shear on Baroclinic Instability

2007 ◽  
Vol 64 (2) ◽  
pp. 479-496 ◽  
Author(s):  
Matthew A. H. Wittman ◽  
Andrew J. Charlton ◽  
Lorenzo M. Polvani
Keyword(s):  
Growth Rate ◽  
Lower Stratosphere ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Finite Amplitude ◽  
Reanalysis Data ◽  
Life Cycles ◽  
Vertical Shear ◽  
Northern Annular Mode ◽  
Jet Structure

Abstract Using a hierarchy of models, and observations, the effect of vertical shear in the lower stratosphere on baroclinic instability in the tropospheric midlatitude jet is examined. It is found that increasing stratospheric shear increases the phase speed of growing baroclinic waves, increases the growth rate of modes with low synoptic wavenumbers, and decreases the growth rate of modes with higher wavenumbers. The meridional structure of the linear modes, and their acceleration of the zonal mean jet, changes with increasing stratospheric shear, but in a way that apparently contradicts the observed stratosphere–troposphere northern annular mode (NAM) connection. This contradiction is resolved at finite amplitude. In nonlinear life cycle experiments it is found that increasing stratospheric shear, without changing the jet structure in the troposphere, produces a transition from anticyclonic (LC1) to cyclonic (LC2) behavior at wavenumber 7. All life cycles with wavenumbers lower than 7 are LC1, and all with wavenumber greater than 7 are LC2. For the LC1 life cycles, the effect of increasing stratospheric shear is to increase the poleward displacement of the zonal mean jet by the eddies, which is consistent with the observed stratosphere–troposphere NAM connection. Finally, it is found that the connection between high stratospheric shear and high-tropospheric NAM is present by NCEP–NCAR reanalysis data.

scholarly journals Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

2012 ◽  
Vol 708 ◽  
pp. 149-196 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Shear Flow ◽  
Growth Process ◽  
Close Association ◽  
Nonlinear Dynamical System ◽  
Finite Amplitude ◽  
Time Dependent ◽  
Minimal Realization ◽  
Reynolds Stresses ◽  
Perturbation Field ◽  
Dependent State

AbstractStreamwise rolls and accompanying streamwise streaks are ubiquitous in wall-bounded shear flows, both in natural settings, such as the atmospheric boundary layer, as well as in controlled settings, such as laboratory experiments and numerical simulations. The streamwise roll and streak structure has been associated with both transition from the laminar to the turbulent state and with maintenance of the turbulent state. This close association of the streamwise roll and streak structure with the transition to and maintenance of turbulence in wall-bounded shear flow has engendered intense theoretical interest in the dynamics of this structure. In this work, stochastic structural stability theory (SSST) is applied to the problem of understanding the dynamics of the streamwise roll and streak structure. The method of analysis used in SSST comprises a stochastic turbulence model (STM) for the dynamics of perturbations from the streamwise-averaged flow coupled to the associated streamwise-averaged flow dynamics. The result is an autonomous, deterministic, nonlinear dynamical system for evolving a second-order statistical mean approximation of the turbulent state. SSST analysis reveals a robust interaction between streamwise roll and streak structures and turbulent perturbations in which the perturbations are systematically organized through their interaction with the streak to produce Reynolds stresses that coherently force the associated streamwise roll structure. If a critical value of perturbation turbulence intensity is exceeded, this feedback results in modal instability of the combined streamwise roll/streak and associated turbulence complex in the SSST system. In this instability, the perturbations producing the destabilizing Reynolds stresses are predicted by the STM to take the form of oblique structures, which is consistent with observations. In the SSST system this instability exists together with the transient growth process. These processes cooperate in determining the structure of growing streamwise roll and streak. For this reason, comparison of SSST predictions with experiments requires accounting for both the amplitude and structure of initial perturbations as well as the influence of the SSST instability. Over a range of supercritical turbulence intensities in Couette flow, this instability equilibrates to form finite amplitude time-independent streamwise roll and streak structures. At sufficiently high levels of forcing of the perturbation field, equilibration of the streamwise roll and streak structure does not occur and the flow transitions to a time-dependent state. This time-dependent state is self-sustaining in the sense that it persists when the forcing is removed. Moreover, this self-sustaining state rapidly evolves toward a minimal representation of wall-bounded shear flow turbulence in which the dynamics is limited to interaction of the streamwise-averaged flow with a perturbation structure at one streamwise wavenumber. In this minimal realization of the self-sustaining process, the time-dependent streamwise roll and streak structure is maintained by perturbation Reynolds stresses, just as is the case of the time-independent streamwise roll and streak equilibria. However, the perturbation field is maintained not by exogenously forced turbulence, but rather by an endogenous and essentially non-modal parametric growth process that is inherent to time-dependent dynamical systems.

First-order effects in time-dependent Petschek-type reconnection

2000 ◽  
Vol 64 (5) ◽  
pp. 547-560 ◽  
Author(s):  
ILYA V. ALEXEEV ◽  
VLADIMIR S. SEMENOV ◽  
HELFRIED K. BIERNAT
Keyword(s):  
Zero Order ◽  
Time Dependent ◽  
Order Effects ◽  
Plasma Velocity ◽  
Plasma Acceleration ◽  
Reconnection Rate ◽  
Initial Current ◽  
First Order ◽  
Potential Trigger ◽  
Outflow Region

The model of time-dependent Petschek-type reconnection is extended to take into account first-order corrections with respect to the reconnection rate. The plasma velocity inside the outflow region turns out to be smaller than the zero-order Alfvén velocity, and therefore strong reconnection is less effective in plasma acceleration. The model is also applied to study the effect of incoming waves on reconnection. We show that incoming waves of Alfvén type, carrying an electric current that is antiparallel to the initial current in the sheet, increase the reconnection rate and cause additional acceleration of the plasma, so that this wave can be considered as a potential trigger.

On the dynamics of finite-amplitude baroclinic waves as a function of supercriticality

1976 ◽  
Vol 78 (3) ◽  
pp. 621-637 ◽  
Author(s):  
Joseph Pedlosky
Keyword(s):  
Steady State ◽  
Baroclinic Instability ◽  
Finite Amplitude ◽  
Steady State Mode ◽  
Final State ◽  
Nonlinear Modes ◽  
Stream Structure ◽  
The Stability ◽  
Amplitude Mode ◽  
Stream Mode

A finite-amplitude model of baroclinic instability is studied in the case where the cross-stream scale is large compared with the Rossby deformation radius and the dissipative and advective time scales are of the same order. A theory is developed that describes the nature of the wave field as the shear supercriticality increases beyond the stability threshold of the most unstable cross-stream mode and penetrates regions of higher supercriticality. The set of possible steady nonlinear modes is found analytically. It is shown that the steady cross-stream structure of each finite-amplitude mode is a function of the supercriticality.Integrations of initial-value problems show, in each case, that the final state realized is the state characterized by the finite-amplitude mode with the largest equilibrium amplitude. The approach to this steady state is oscillatory (nonmonotonic). Further, each steady-state mode is a well-defined mixture of linear cross-stream modes.

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