scholarly journals Dynamics of turbulent western-boundary currents at low latitude in a shallow-water model

Ocean Science ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 471-481 ◽  
Author(s):  
C. Q. C. Akuetevi ◽  
A. Wirth
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Numerical Models ◽  
Water Model ◽  
Western Boundary ◽  
Advective Transport ◽  
Shallow Water Model ◽  
Low Latitude ◽  
Western Boundary Currents ◽  
Boundary Currents

Abstract. The dynamics of low latitude turbulent western-boundary currents (WBCs) crossing the Equator are considered using numerical results from integrations of a reduced-gravity shallow-water model. For viscosity values of 1000 m2 s−1 and greater, the boundary layer dynamics compares well to the analytical Munk-layer solution. When the viscosity is reduced, the boundary layer becomes turbulent and coherent structures in the form of anticyclonic eddies, bursts (violent detachments of the viscous sub-layer, VSL) and dipoles appear. Three distinct boundary layers emerge, the VSL, the advective boundary layer and the extended boundary layer. The first is characterized by a dominant vorticity balance between the viscous transport and the advective transport of vorticity; the second by a balance between the advection of planetary vorticity and the advective transport of relative vorticity. The extended boundary layer is the area to which turbulent motion from the boundary extends. The scaling of the three boundary layer thicknesses with viscosity is evaluated. Characteristic scales of the dynamics and dissipation are determined. A pragmatic approach to determine the eddy viscosity diagnostically for coarse-resolution numerical models is proposed.

scholarly journals Dynamics of turbulent western boundary currents at low latitude in a shallow water model

2014 ◽  
Vol 11 (6) ◽  
pp. 2461-2493
Author(s):  
C. Q. C. Akuetevi ◽  
A. Wirth
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Numerical Models ◽  
Water Model ◽  
Western Boundary ◽  
Advective Transport ◽  
Shallow Water Model ◽  
Low Latitude ◽  
Western Boundary Currents ◽  
Boundary Currents

Abstract. The dynamics of low latitude turbulent western boundary currents crossing the equator is considered using numerical results from integrations of a reduced gravity shallow-water model. For viscosity values of 1000 m2 s−1 and more, the boundary layer dynamics compares well to the analytical Munk-layer solution. When the viscosity is reduced, the boundary layer becomes turbulent and coherent structures in form of anticyclonic eddies, bursts (violent detachments of the viscous sub-layer) and dipoles appear. Three distinct boundary layers emerge, the viscous sub-layer, the advective boundary layer and the extended boundary layer. The first is characterized by a dominant vorticity balance between the viscous transport and the advective transport of vorticity. The second by a balance between the advection of planetary vorticity and the advective transport of relative vorticity. The extended boundary layer is the area to which turbulent motion from the boundary extends. The scaling of the three boundary layer thicknesses with viscosity is evaluated. Characteristic scales of the dynamics and dissipation are determined. A pragmatic approach to determine the eddy viscosity diagnostically for coarse resolution numerical models is proposed.

scholarly journals Dynamics of turbulent western boundary currents at low latitude in a shallow water model

2014 ◽  
Vol 11 (2) ◽  
pp. 753-788 ◽  
Author(s):  
C. Q. C. Akuetevi ◽  
A. Wirth
Keyword(s):  
Boundary Layer ◽  
Shallow Water ◽  
Water Model ◽  
Trade Wind ◽  
Western Boundary ◽  
Advective Transport ◽  
Shallow Water Model ◽  
Low Latitude ◽  
Western Boundary Currents ◽  
Boundary Currents

Abstract. The dynamics of low latitude turbulent western boundary currents, subject to two different types of idealized wind forcing, Monsoon Wind and Trade Wind, is considered using numerical results from integrations of a reduced gravity shallow-water model. For viscosity values of 1000 m2 s−1 and above, the boundary layer dynamics compares well to the analytical solutions of the Munk-layer and the inertial-layer, derived from quasigeostrophic theory. Modifications due to variations in the layer thickness (vortex stretching) are only important close to the boundary. When the viscosity is reduced the boundary layer becomes turbulent and coherent structures in form of anticyclonic eddies, bursts (violent detachments of the viscous sub-layer) and dipoles appear. Three distinct boundary layers emerge, the viscous sub-layer, the advective boundary layer and the extended boundary layer. The first is characterized by a dominant vorticity balance between the viscous transport and the advective transport of vorticity. The second by a balance between the advection of planetary vorticity and the advective transport of relative vorticity. The extended boundary layer is the area to which turbulent motion from the boundary extends. The scaling of the three boundary layer thicknesses with viscosity is evaluated. A pragmatic approach to determine the eddy viscosity diagnostically for coarse resolution numerical models is proposed.

scholarly journals Kelvin wave hydraulic control induced by interactions between vortices and topography

2011 ◽  
Vol 687 ◽  
pp. 194-208 ◽  
Author(s):  
Andrew McC. Hogg ◽  
William K. Dewar ◽  
Pavel Berloff ◽  
Marshall L. Ward
Keyword(s):  
Shallow Water ◽  
Analytical Solutions ◽  
Critical Condition ◽  
Numerical Models ◽  
Kelvin Waves ◽  
Water Model ◽  
Hydraulic Jumps ◽  
Hydraulic Control ◽  
Kelvin Wave ◽  
Shallow Water Model

AbstractThe interaction of a dipolar vortex with topography is examined using a combination of analytical solutions and idealized numerical models. It is shown that an anticyclonic vortex may generate along-topography flow with sufficient speeds to excite hydraulic control with respect to local Kelvin waves. A critical condition for Kelvin wave hydraulic control is found for the simplest case of a 1.5-layer shallow water model. It is proposed that in the continuously stratified case this mechanism may allow an interaction between low mode vortices and higher mode Kelvin waves, thereby generating rapidly converging isopycnals and hydraulic jumps. Thus, Kelvin wave hydraulic control may contribute to the flux of energy from mesoscale to smaller, unbalanced, scales of motion in the ocean.

scholarly journals A Laboratory Study of the Zonal Structure of Western Boundary Currents

2008 ◽  
Vol 38 (5) ◽  
pp. 1073-1090 ◽  
Author(s):  
Stefano Pierini ◽  
Vincenzo Malvestuto ◽  
Giuseppe Siena ◽  
Thomas A. McClimans ◽  
Stig M. Løvås
Keyword(s):  
Boundary Layer ◽  
Western Boundary ◽  
Zonal Structure ◽  
Viscous Boundary Layer ◽  
Western Boundary Currents ◽  
Boundary Currents ◽  
Meridional Velocity ◽  
Beta Effect ◽  
Piston Speed ◽  
Viscous Boundary

Abstract The zonal structure of strongly nonlinear inertial western boundary currents (WBCs) is studied experimentally along a straight “meridional” coast in a 5-m-diameter rotating basin by analyzing the “zonal” profile of the meridional velocity field as a function of transport intensity and other dynamical parameters. The return flow that is generated by the surface wind stress curl in the oceanic interior is forced in the rotating basin by the motion of a piston, in the absence of any surface stress. The laboratory setup consists of two parallel rectangular channels separated by an island and linked by two curved connections: in the first channel, a piston is forced at a constant speed up ranging from 0.5 to 3 cm s−1 over a distance of 2.5 m, producing a virtually unsheared current at the entrance of the second channel. In the latter, a linear reduction of the water depth provides the topographic beta effect that is necessary for the development of the westward intensification. Nearly steady currents are obtained and measured photogrammetrically over a region of about 1 m2. In all of the experiments performed, an appropriate horizontal Reynolds number (Re = ɛ/E, where ɛ and E are dimensionless numbers measuring the importance of nonlinearity and lateral friction, respectively) is Re ≫ 1. The zonal profile of the meridional velocity is always found to have (away from the viscous boundary layer) a nearly exponential structure typical of inertial WBCs, whose width agrees well with the classical inertial boundary layer length scale δI. A control experiment (with up = 1 cm s−1) is analyzed in detail: it has the same ɛ as the Gulf Stream (GS) but a much smaller E. This implies that the laboratory flow is expected to be geometrically similar to the GS outside the viscous boundary layer, but to differ within it. To assess the effect of such a departure from dynamic similarity, a mathematical model is used that numerically simulates a flow that is fully dynamically similar to the GS. The comparison between the profile thus obtained numerically and the one obtained experimentally shows that they are, indeed, virtually coincident outside the viscous boundary layer, except for a small offset that tends to vanish as Re → ∞. Moreover, additional sensitivity experiments in which the piston speed, the rotation rate of the basin, the topographic beta effect, and the width of the main channel are varied provide further information on the zonal structure of WBCs.

Dynamics of Gap-leaping Western Boundary Currents with Throughflow Forcing

2021 ◽  
Author(s):  
Charles W. McMahon ◽  
Joseph J. Kuehl ◽  
Vitalii A. Sheremet
Keyword(s):  
Particle Tracking Velocimetry ◽  
Numerical Models ◽  
Western Boundary ◽  
Loop Current ◽  
Western Boundary Currents ◽  
Nonlinear Dynamical ◽  
Boundary Currents ◽  
Lab Experiments ◽  
Experimental Apparatus ◽  
The Kuroshio

AbstractThe dynamics of gap-leaping western boundary currents (e.g. the Kuroshio intrusion, the Loop Current) are explored through rotating table experiments and a numerical model designed to replicate the experimental apparatus. Simplified experimental and numerical models of gap-leaping systems are known to exhibit two dominant states (leaping or penetrating into the gap) as the inertia of the current competes with vorticity constraints (in this case the β-effect). These systems are also known to admit multiple states with hysteresis. To advance towards more realistic oceanographic scenarios, recent studies have explored the effects of islands, mesoscale eddies, and variable baroclinic deformation radii on the dynamical system. Here, the effect of throughflow forcing is considered, with particle tracking velocimetry (PTV) used in the lab experiments. Mean transport in or out of the gap is found to significantly shift the hysteresis range as well as change its width. Because of these transformations, changes in throughflow can induce transitions in the gap-leaping system when near a critical state (leaping-to-penetrating/ penetrating-to-leaping). Results from the study are interpreted within a nonlinear dynamical framework and various properties of the system are explored.

scholarly journals Elongation and Contraction of the Western Boundary Current Extension in a Shallow-Water Model: A Bifurcation Analysis

2008 ◽  
Vol 38 (7) ◽  
pp. 1469-1485 ◽  
Author(s):  
François Primeau ◽  
David Newman
Keyword(s):  
Shallow Water ◽  
Bifurcation Analysis ◽  
Low Frequency ◽  
Water Model ◽  
Western Boundary ◽  
Stress Profile ◽  
Shallow Water Model ◽  
Low Frequency Variability ◽  
Eigenmode Analysis ◽  
Recirculation Gyres

Abstract The double-gyre circulation, formulated in terms of the quasigeostrophic equations, has a symmetry about the basin midlatitude (y → −y, ψ → −ψ), which is absent in a formulation based on the shallow-water equations. As a result, the shallow-water model does not have the pitchfork bifurcation structures that, in the case of the quasigeostrophic model, connect together multiple solution branches with elongated and contracted recirculation gyres. For the shallow-water model, solution branches with elongated recirculation gyres are disconnected, and a one-parameter bifurcation analysis is unable to detect their existence. The deeply penetrating jet solution branches do, however, continue to exist, and can be found using a bifurcation analysis couched in terms of two parameters. An effective pair of parameters is the viscosity and a parameter controlling the symmetry of the wind stress profile. A bifurcation analysis with these parameters reveals the existence of new solution branches that were not found in previous bifurcation analyses of the shallow-water model. The new solutions have a jet extension that penetrates farther eastward and that is more stable than the jet-up and jet-down solutions found in previous studies. Furthermore, the origin of the low-frequency variability at low viscosities is associated with a sequence of bifurcations originating from one of the new steady-state solution branches. In particular, the eigenmode analysis of the new branch reveals that a so-called gyre mode is at the origin of the model’s low-frequency variability at decadal time scales.

scholarly journals Nonuniform Upwelling in a Shallow-Water Model of the Antarctic Bottom Water in the Brazil Basin*

2004 ◽  
Vol 34 (11) ◽  
pp. 2492-2513 ◽  
Author(s):  
Olivier Marchal ◽  
Jonas Nycander
Keyword(s):  
Shallow Water ◽  
Bottom Water ◽  
Water Model ◽  
Western Boundary ◽  
Linear Potential ◽  
Antarctic Bottom Water ◽  
Shallow Water Model ◽  
Boundary Current ◽  
Deep Basin ◽  
Brazil Basin

Abstract A numerical model based on the shallow-water equations is developed to represent the flow of Antarctic Bottom Water (AABW) in the Brazil Basin (southwest Atlantic Ocean). The aim is twofold. First, an attempt is made to identify in a model that includes both simplified dynamics and realistic bathymetry (at 1/6° resolution) the impacts of the elevated diapycnal mixing rates near the Mid-Atlantic Ridge (MAR) documented by dissipation data of the Deep Basin Experiment (DBE). To this end, different assumptions regarding the distribution of the velocity across the AABW layer interface (w) are considered. Second, the extent to which the shallow-water model can replicate observations relative to AABW circulation in the basin, in particular the trajectory and velocity of neutrally buoyant floats released in the AABW during the DBE, is examined. The model flows are characterized by small Rossby numbers, except in the northward-flowing western boundary current where kinetic energy is largely concentrated. To interpret the flows, model streamlines are compared with isopleths of linear potential vorticity f/h0 of the shallow-water theory (f is the planetary vorticity and h0 is the layer thickness in the absence of motion). The f/h0 contours are oriented northwest–southeast in the western part of the basin and southwest–northeast in the eastern part, reflecting the bowl-shaped topography of the Southern Hemisphere basin. With a spatially uniform (positive) w, the ubiquitous vortex stretching produces a flow to the southeast, consistent with the Stommel–Arons theory. This flow occurs in most of the basin interior, even in the east where f/h0 contours converge to the northeastern end of the basin. With strongly positive w near the ridge and zero or slightly negative w elsewhere, the flow follows more closely f/h0 contours in the western interior and intersects them near the ridge. The confinement of the diapycnal mass flux near the MAR drastically reduces the southward flow in the interior or even reverses its direction, leading to a circulation quite distinct from that of the Stommel– Arons theory. The model results compare favorably to some (but not all) hydrographic estimates of AABW circulation patterns and rates. On the other hand, the model streamlines and velocities show important differences with, respectively, the trajectory and the velocity of the floats launched in the AABW layer. The prescription of vanishing w in the interior does not systematically improve the fit of the model streamlines to the float trajectories, and the model velocities simulated with spatially uniform w or spatially variable w are on average smaller by one order of magnitude than the float velocities. A variety of mechanisms, which are not included in the numerical experiments, may explain the differences between the model results and the float data.

The instability of vertically curved fronts in a two-layer shallow water model

2020 ◽  
Vol 32 (12) ◽  
pp. 124117
Author(s):  
M. W. Harris ◽  
F. J. Poulin ◽  
K. G. Lamb
Keyword(s):  
Shallow Water ◽  
Water Model ◽  
Shallow Water Model
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