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Bach Lien Hua

Abstract

Data from the Tourbillon Experiment Intensive Period in the northeast Atlantic presented evidence of a vertical phase shift with time of the main eddy, interpreted as an occurrence of internal barotropic instability. In order to justify this: (i) the idealized case of an isolated eddy immersed in a stratified environment, whose characteristics correspond to the Tourbillon site (see Part I) and (ii) the realistic case using the full three-dimensional data from the experiment as initial conditions (Part II) are modeled. Both studies use a quasi-geostrophic periodic spectral model with six vertical normal modes and a horizontal 128×128 grid. It is demonstrated that a some what realistic “forecast” can be obtained for an integration time of up to one month.

While a linear instability analysis revealed that the Tourbillon eddy is very slowly unstable (Part I), its encounter with a Mediterranean Water tongue caused a large-amplitude baroclinic perturbation, triggering a nonlinear destabilization of the eddy, and hence the observed tilting of its vertical axis with time. One failure of the model concerns the final fate of the eddy: at the end of the intensive measurement period, the eddy is observed to remain a single entity, while the quasi-geostrophic modeling predicts its fragmentation into two vertically smaller structures by the strong instability.

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Bach Lien Hua

Abstract

Gent and McWilliams have identified the mechanism of internal barotropic instability for axisymmetric vortices which are purely barotropic, but are immersed in a stratified environment. The energy source is the kinetic energy of the barotropic vortex, which can be converted into baroclinic energy by growing oscillations of finite vertical scale. This occurs when the eddy is too tall and thin. The present paper deals with the generalized instability problem of surface-intensified eddies, presenting a complex vertical structure. We first consider the class of eddies whose horizontal size is either close to (or smaller than) the first radius of deformation. On an f-plane, such eddies are more stable than their purely barotropic counterpart to internal barotropic instability, all the more so that they are fat. This result, which is fond through the identification of the linearly unstable normal modes, is also confirmed through direct numerical simulations. The β-effect acts asymmetrically with regard to internal barotropic instability between purely barotropic and surface-intensified eddies: it stabilizes purely barotropic vortices, wile it enhances the instability of surface-intensified ones. Nonlinear destabilization of vortices can also occur when they undergo finite-amplitude perturbations, for instance, through their interaction with other structures. The Tourbillon eddy is shown to be weakly unstable to linear barotropic instability, but can be destabilized nonlinearly by finite-amplitude perturbations. Finally, eddies whose horizontal size is at least twice as large as the radius of deformation are shown to be primarily unstable to baroclinic instability.

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Bach Lien Hua

Abstract

The purpose of this note is to investigate the use of Lagrangian potential vorticity conservation as a numerically independent method for checking a posteriori the dynamical consistency of an eddy-resolving GCM simulation. This is performed for a series of simulations with increasing horizontal and vertical resolution. The result that higher vertical modes play a catalytic role in the largest scales of eddy-driven flows is independently confirmed through this Lagrangian test.

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Bach-Lien Hua and Francois Thomasset

Abstract

An attempt is made to explain the fixed locations of coastal upwelling centers in the Gulf of Lions as a function of the coastline geometry alone. The semi-implicit numerical model, based on two-layer shallow water equations, uses a spatial discretization with triangular finite elements. Vertical mixing is shown to play an important role in determining the final shape of the upwelling centers. It is conjectured that an observed upwelling filament results from the straining and stretching of a coastal upwelling center by the observed anticyclonic circulation farther offshore.

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Bach Lien Hua, Frédéric Marin, and Richard Schopp

Abstract

A fully three-dimensional primitive equation simulation is performed to “reunite” the local equatorial dynamics of the subsurface countercurrents (SCCs) and thermostad with the large-scale tropical ventilated ocean dynamics. It captures (i) the main characteristics of the equatorial thermostad, the SCCs' location and their eastward evolution, and the potential vorticity budget with its equatorial homogenization to zero values and (ii) the large-scale meridional shoaling of the thermocline equatorward. It supports the idea that the two-dimensional Hadley cell mechanism proposed by Marin et al. is a candidate able to operate in a fully three-dimensional ocean. The main difference between the 2D Hadley cell mechanism and the oceanic 3D case is that for the 3D case the large-scale meridional velocity at zeroth order is geostrophic, while the cell mechanism is a next-order, small-scale mechanism. A detailed budget of the zonal momentum equation is provided for the ageostrophic dynamics at work in the SCCs. The mean meridional advection and the Coriolis term dominate, discounting the possibility that lateral eddies play a major role for the SCCs' creation. A 3½-layer idealized ventilation model, calibrated to the three-dimensional simulation parameters, is able not only to capture the tropical density structure, but also to isolate the main controlling factors leading to the triggering of the equatorial secondary cells with its associated jet and thermostad, namely, the shoaling of the equatorial thermocline because of low potential vorticity injection at distant subduction latitudes. It is also shown that equatorial recirculation gyres play a quantitative role that may be of the same order of magnitude as ventilation from higher latitudes.

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Frédéric Marin, Bach Lien Hua, and Richard Schopp

Abstract

From a numerical simulation of the Atlantic Ocean, Jochum and Malanotte-Rizzoli provide evidence that the equatorial subsurface countercurrents can be triggered by tropical instability waves through eddy–mean flow interactions in a low-Rossby-number regime. Adapting the transformed Eulerian mean formalism to a shoaling jet, they propose eddy heat fluxes to be the driving mechanism for the subsurface countercurrents. Here it is shown that such a formalism relying on the existence of a residual meridional streamfunction cannot be applied to a shoaling jet, so that the eddy heat fluxes term in the zonal momentum equation cannot be rigorously justified. Moreover, the role of the zonal pressure gradient that was dropped in their study needs to be reassessed. Despite this mathematical questioning of Jochum and Malanotte-Rizzoli’s framework, the authors agree with them that eddy heat fluxes may contribute to the dynamics of the subsurface countercurrents.

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Frédéric Marin, Richard Schopp, and Bach Lien Hua

Abstract

Sensitivity tests are performed to assess the respective influences of the large-scale ventilation and of the near-equatorial winds on the dynamics of the the subsurface countercurrents (SCCs) and thermostad. They show that the intensity of the inertial jets is a function of the potential vorticity (PV) values at subduction and that stronger jets are favored by low PV injection, forced in the authors' framework either by a deep mixed layer at subduction and/or by an injection of PV at lower latitudes. Such circumstances lead to a strong meridional shoaling of the thermocline near the equator. The resulting inertial jets occur at about 3°N in the western part of the basin and are the poleward limit of a near-0 PV region and of an equatorial thermostad. A necessary condition for the existence of inertial jets is that the equatorial wind fetch is large enough, otherwise only weak time-mean eastward currents are produced by a nonlinear rectification of instability waves farther away from the equator. The presence of a North Equatorial Countercurrent does not constitute a barrier for equatorward motions within the lower thermocline, and inertial jets are still controlled by the meridional slope of the SSCs' layer setup through the establishment of tropical PV pools predicted by ventilation theory.

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Anne Marie Treguier and Bach Lien Hua

Abstract

The quasi-geostrophic response to stochastic wind fluctuations is calculated using a doubly periodic nonlinear model, with a vertical resolution of three modes in most cases. The influence of various parameters on the response is investigated: space and time scale of the forcing, stratification, bottom friction and β-effect. One aim of this study is to understand the influence of nonlinear transfer, and therefore, most simulations are situated in a parameter range where nonlinearities are important. The model “pseudodispersion relation” clearly shows two regimes: a linear regime made of resonant Rossby waves for the barotropic large scales and a nonlinear regime that is dynamically similar, for example, to quasi-geostrophic turbulence forced by baroclinic instability. The forcing time scale and β-effect have little influence on the response. The most important parameter is found to be the ratio R = κ1/Kmin of the largest forced wavelength to the wavelength of the first baroclinic mode Rossby radius. When R grows, the amount of energy in the linear regime grows, and the kinetic energy becomes essentially barotrophic (currents are then depth-independent). For our model, R must be of order 5 in order to obtain a realistic vertical structure, while observations show that R is larger than 10. From this discrepancy we conclude that other physical mechanisms have to be taken into account to reproduce the vertical structure of the oceanic response, although our results confirm that wind fluctuations can effectively generate eddy energy in the ocean.

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Geoffrey K. Vallis and Bach-lien Hua

Abstract

The anticipated potential Vorticity method (APV) is a parameterization of the effects of subgrid or unresolved scales on those explicitly resolved for barotropic, quasi-geostrophic and certain types of primitive equation models. One novelty of the method lies in the fact that it exactly conserves energy, while still dissipating the enstrophy. (Diffusion of potential Vorticity, on the other hand, conserves neither.) We have numerically evaluated the effective eddy diffusivity associated with such parameterizations. Additionally, we have evaluated the effective eddy diffusivity explicitly, i.e., by direct numerical simulation. We find, in accord with closure calculations, that explicit simulations give cusplike behavior near the cut-off wavenumber k max. This is induced by the continuous interaction of scales on both sides of k max, transferring enstrophy to higher wavenumbers. The APV method reproduces this, provided that the lag or anticipation times of the vorticity are suitably (but perhaps arbitrarily) chosen. In particular, it is necessary for the anticipation time to increase rapidly with wavenumber. This in turn necessitates extra boundary conditions at walls. At low wavenumbers, the eddy viscosity produced by the APV method, predicted by closure theory and directly calculated are all negative. The test-field model prescribes a saturation toward a constant negative eddy viscosity for kk max. This is qualitatively verified by explicit simulations. The APV method is consistent for wavenumbers in the inertial range. For the very lowest wavenumber, when the energy at the lowest wavenumbers is small, the method produces large negative values, producing another cusp at the largest scales resolved by the model. Explicit simulations show similar behavior. (Diffusion of potential vorticity, on the other hand, is similar to a constant, positive, eddy viscosity.) Some numerical simulations of baroclinic forced dissipative flows are presented. At medium and high resolutions the APV method is successfully able to produce a fairly “flat” inertial range. At low resolutions, when the maximum wavenumber is in the energy containing range, the APV method either produces unrealistically high energy levels at low wavenumbers, or else the simulation is too energetic at all scales, depending on the strength of the parameterization. An energy conserving parameterization is not necessarily appropriate here. Overall, in terms of eddy viscosities, the APV method performs as well as or better than more conventional schemes using prescribed eddy diffusivities. If the resolution of the model extends into the inertial range, the APV method apparently performs very well, although the effects of a lack of Galilean invariance remain unresolved.

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Guillaume Lapeyre, Patrice Klein, and Bach Lien Hua

Abstract

Potential vorticity (PV) conservation implies a strong constraint on the time evolution of the mean density at a given depth. The authors show that, on an f plane and in the absence of sources and sinks of PV, it only depends on two terms, namely, the time evolution of the product between density anomaly and relative vorticity and the vertical PV flux. This primitive equation result, which applies at any depth, suggests that the ageostrophic dynamics induced by baroclinic eddies strongly affect the mean oceanic stratification profile. This result is illustrated for two simple initial-value simulations of a baroclinic, balanced jet. For initial situations propitious to surface frontogenesis, the simulations show a restratification over the whole water column characterized by the amplification in time of the Brunt–Väisälä frequency in the upper oceanic layers. In the absence of surface frontogenesis, such as when the jet is initialized at the middepth of the water column, the restratification is much weaker and slower. Because both simulations have similar kinetic energy and growth rate of baroclinic instability, the results clearly reveal that the restratification is driven by surface frontogenesis in the first case and by vertical PV flux in the interior in the second case. The authors also point out that the dynamics of the interior PV is tightly related to the surface dynamics because of total mass conservation.

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