Chaotic advection induced by a topographic vortex in baroclinic ocean (original) (raw)
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Slow oscillations in an ocean of varying depth Part 1. Abrupt topography
Journal of Fluid Mechanics, 1969
This paper is part of a study of quasigeostrophic waves, which depend on the topography of the ocean floor and the curvature of the earth.In a homogeneous, β-plane ocean, motion of the fluid across contours of constant f/h releases relative vorticity (f is the Coriolis parameter and h the depth). This well-known effect provides a restoring tendency for either Rossby waves (with h constant) or topographic waves over a slope. The long waves in general obey an elliptic partial differential equation in two space variables. Because the equation has been integrated in the vertical direction, the exact inviscid bottom boundary condition appears in variable coefficients.When the depth varies in only one direction the equation is separable at the lowest order in ω, the frequency upon f. With a simple slope, |[xdtri ]h/h| = constant, the transition from Rossby to topographic waves occurs at |[xdtri ]h| ∼ h/Re, where Re is the radius of the earth. Isolated topographic features are considered i...
Chaotic advection in the ocean
Physics-Uspekhi, 2006
The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. K V Koshel, S V Prants Il'ichev Pacific Oceanological Institute, Far-Eastern Branch of the Russian Academy
Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model
Journal of Fluid Mechanics, 2001
We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallowwater dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-timescale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f −1 0 and (f 0 Ro) −1 respectively, where f 0 is the Coriolis parameter. The slow component is not influenced by the fast one and remains close to the geostrophic balance. The algorithm of its initialization readily follows by construction. The scenario of adjustment depends on the characteristic scale and/or initial relative elevation of the free surface ∆H/H 0 , where ∆H and H 0 are typical values of the initial elevation and the mean depth, respectively. For small relative elevations (∆H/H 0 = O(Ro)) the evolution of the slow motion is governed by the well-known quasigeostrophic potential vorticity equation for times t 6 (f 0 Ro) −1. We find modifications to this equation for longer times t 6 (f 0 Ro 2) −1. The fast component consists mainly of linear inertia-gravity waves rapidly propagating outward from the initial disturbance. For large relative elevations (∆H/H 0 Ro) the slow field is governed by the frontal geostrophic dynamics equation. The fast component in this case is a spatially localized packet of inertial oscillations coupled to the slow component of the flow. Its envelope experiences slow modulation and obeys a Schrödinger-type modulation equation describing advection and dispersion of the packet. A case of intermediate elevation is also considered.
Russian Journal of Mathematical Modelling, 2003
We consider a barotropic inviscid model of chaotic advection in a unidirectionalpulsating background ow over a seamount of an elliptic form. We numerically study the process of passive tracer transport from the vortex area to the ow-through area, and in particular we give the dependence of evolution of the corresponding Poincaré maps on the frequency and amplitude of incident ow pulsations. We propose an approach to the study of the mechanism and parameters of chaotic advection in open systems with nite trajectories lifetime. It is based on studying the time it takes for tracers to be carried out from the vortex area to the ow-through area. We show the essential impact of the seamount orientation with respect to an incident ow on the rate and scenario of tracers transport from the vortex area.
Influence of topography on the dynamics of baroclinic oceanic eddies
1994
In this work we study motion of a baroclinic upper-ocean eddy over a large-scale topography which simulates a continental slope. We use a quasigeostrophic f-plane approximation with continuous stratification. To study this problem we develop a new numerical technique which we call "semi-lagrangian contour dynamics". This technique resembles the traditional 2-D contour dynamics method but differs significantly from it in the numerical algorithm. In addition to "Lagrangian" moving contours it includes an underlying "Eulerian" regular grid to which vorticity or density fields are interpolated. To study topographic interactions in a continuously stratified model we use density contours at the bottom in a similar manner as vorticity contours are used in the standard contour dynamics. For the case of a localized upper-ocean vortex moving over a sloping bottom the problem becomes computationally 2-dimensional (we need to follow only bottom density contours and the position of the vortex itself) although the physical domain is still 3-dimensional.
Journal of Fluid Mechanics, 1993
Solutions for inviscid rotating flow over a right circular cylinder of finite height are studied, and comparisons are made to quasi-geostrophic solutions. To study the combined effects of finite topography and the variation of the Coriolis parameter with latitude a steady inviscid model is used. The analytical solution consists of one part which is similar to the quasi-geostrophic solution that is driven by the potential vorticity anomaly over the topography, and another, similar to the solution of potential flow around a cylinder, that is driven by the matching conditions on the edge of the topography. When the characteristic Rossby wave speed is much larger than the background flow velocity, the transport over the topography is enhanced as the streamlines follow lines of constant background potential vorticity. For eastward flow, the Rossby wave drag can be very much larger than that predicted by quasi-geostrophic theory. The combined effects of finite height topography and time-d...