Timour Radko

Residual-Mean Solutions for the Antarctic Circumpolar Current and Its Associated Overturning Circulation

Abstract Residual-mean theory is applied to the streamwise-averaged Antarctic Circumpolar Current to arrive at a concise description of the processes that set up its stratification and meridional overturning circulation on an f plane. Simple solutions are found in which transfer by geostrophic eddies colludes with applied winds and buoyancy fluxes to determine the depth and stratification of the thermocline and the pattern of associated (residual) meridional overturning circulation.

A mechanism for layer formation in a double-diffusive fluid

The dynamics of layer formation by salt fingers from the uniform temperature and salinity gradients is studied by direct numerical simulations of the two-dimensional Navier–Stokes equations. It is shown that formation of steps in the model is caused by the parametric variation of the flux ratio (

Salt fingers in an unbounded thermocline

\gamma\,{=}\,{\overline{wT}}/{\overline{wS}}

Eddy-Induced Diapycnal Fluxes and Their Role in the Maintenance of the Thermocline

) as a function of the density ratio (

What determines the thickness of layers in a thermohaline staircase

R

The Antarctic Circumpolar Current in Three Dimensions

), which leads to an instability of equilibrium with uniform stratification. These unstable large-scale perturbations continuously grow in time until well-defined layers are formed. Subsequent evolution of the numerical staircases is explained by considering the secondary instabilities of a series of salt finger interfaces.

Salt fingers in three dimensions

Numerical solutions for salt e ngers in an unbounded thermocline with uniform overall vertical temperature-salinity gradients are obtained from the Navier-Stokes-Boussinesq equations in a e nite computational domain with periodic boundary conditions on the velocity. First we extend previous two-dimensional (2D) heat-salt calculations [Prandtl number Pr 5 n/k T 5 7 and molecular diffusivity ratio t 5 k S/k T 5 0.01] for density ratio R 5 2; as R decreases we show that the average heat and salt e uxes increase rapidly. Then three-dimensional (3D) calculations for R 5 2.0, Pr 5 7, and the numerically “ accessible” values of t 5 1/6, 1/12 show that the ratio of these 3D e uxes to the corresponding 2D values [at the same ( t, R, Pr)] is approximately two. This ratio is then extrapolated to t 5 0.01 and multiplied by the directly computed 2D e uxes to obtain a e rst estimate for the 3D heat-salt e uxes, and for the eddy salt diffusivity (dee ned in terms of the overall vertical salinity gradient). Since these calculations are for relatively “ small domains” [ O(10) e nger pairs], we then consider much larger scales, such as will include a slowly varying internal gravity wave. An analytic theory which assumes that the e nger e ux is given parametrically by the small domain e ux laws shows that if a critical number A is exceeded, the wave-strain modulates the e nger e ux divergence in a way which amplie es the wave. This linear theoretical result is cone rmed, and the e nite amplitude of the wave is obtained, in a 2D numerical calculation which resolves both waves and e ngers. For highly supercritical A (small R) it is shown that the temporally increasing wave shear does not reduce the e uxes until the wave Richardson number drops to ;0.5, whereupon the wave starts to overturn. The onset of density inversions suggests that at later time (not calculated), and in a sufe ciently large 3D domain, strong convective turbulence will occur in patches.

Semi-Adiabatic Model of the Deep Stratification and Meridional Overturning

High-resolution numerical experiments are diagnosed to study the integral effects of geostrophic eddy fluxes on the large-scale ocean circulation. Three characteristic large-scale flows are considered: 1) an anticyclonic single gyre, 2) a double gyre, and 3) an unblocked zonal flow, a simple analog of the Antarctic Circumpolar Current. It is found that buoyancy and potential vorticity budgets in the presence of eddies are dominated by a balance between vertical advection into the control volume by Ekman pumping and eddy transfer across the density surfaces achieved by diapycnal eddy fluxes, with small-scale mixing making only a minor contribution. Possible oceanographic implications of the results are discussed. In this paper we discuss the role of time-dependent geostrophic eddy motions in the buoyancy and potential vorticity budgets diagnosed from numerical models of large-scale ocean flows. The ocean is full of energetic eddies that, as suggested by the numerical experiments herein, may be very effective in balancing global buoyancy and potential vorticity budgets. The possible role of eddies in this manner has been discussed in highly idealized laboratory and numerical studies by Marshall et al. (2002), Karsten et al. (2002), and Radko and Marshall (2003)—see also the discussion in Hughes (2002). Radko and Marshall (2003) considered an idealized abstraction of a subtrobical ocean gyre: the equilibration of a warm-pumped lens on a b plane. By construction, geostrophic eddies play a central role in the volume budget of the lens: warm fluid pumped down from the surface is fluxed away laterally by geostrophic eddies formed as a result of the baroclinic instability of a large-scale current in the region of western intensification. Here we consider more complex and perhaps more realistic configurations in which the downward flux of buoyancy from the Ekman layer could either be balanced by eddies, explicit dissipation, or by advective fluxes. Three-dimensional eddy-resolving numerical experiments of ocean gyres are diagnosed to quantify the roles of eddy buoyancy, momentum, and potential vorticity transfer. While many previous eddy-resolving studies have focused on the properties of isopycnal

Mechanics of merging events for a series of layers in a stratified turbulent fluid

The article of record as published may be found at http://dx.doi.org/10.1017/S0022112004002290

The Self-Propagating Quasi-Monopolar Vortex

A simple theory is developed for the large-scale three-dimensional structure of the Antarctic Circumpolar Current and the upper cell of its overturning circulation. The model is based on a perturbation expansion about the zonal-average residual-mean model developed previously by Marshall and Radko. The problem is solved using the method of characteristics for idealized patterns of wind and buoyancy forcing constructed from observations. The equilibrium solutions found represent a balance between the Eulerian meridional overturning, eddy-induced circulation, and downstream advection by the mean flow. Depth and stratification of the model thermocline increase in the Atlantic–Indian Oceans sector where the mean wind stress is large. Residual circulation in the model is characterized by intensification of the overturning circulation in the Atlantic–Indian sector and reduction in strength in the Pacific Ocean region. Predicted three-dimensional patterns of stratification and residual circulation in the interior of the ACC are compared with observations.