Circulation Induced by Isolated Dense Water Formation over Closed Topographic Contours

The problem of localized dense water formation over a sloping bottom is considered for the general case in which the topography forms a closed contour. This class of problems is motivated by topography around islands or shallow shoals in which convection resulting from brine rejection or surface heat loss reaches the bottom. The focus of this study is on the large-scale circulation that is forced far from the region of surface forcing. The authors find that a cyclonic current is generated around the topography, in the opposite sense to the propagation of the dense water plume. In physical terms, this current results from the propagation of low sea surface height from the region of dense water formation anticyclonically along the topographic contours back to the formation region. This pressure gradient is then balanced by a cyclonic geostrophic flow. This basic structure is well predicted by a linear quasigeostrophic theory, a primitive equation model, and in rotating tank experiments. For sufficiently strong forcing, the anticyclonic circulation of the dense plume meets this cyclonic circulation to produce a sharp front and offshore advection of dense water at the bottom and buoyant water at the surface. This nonlinear limit is demonstrated in both the primitive equation model and in the tank experiments.

Ensemble Simulations and Pullback Attractors of a Periodically Forced Double-Gyre System

A primitive equation ocean model has recently reproduced with reasonable realism the synchronization between the North Pacific Oscillation and the last two Kuroshio Extension decadal cycles observed from altimetry. However, the timing of the cycles is imperfect: could a different model initialization improve this fundamental aspect of the phenomenon? Ensemble simulations stemming from many initial conditions should be carried out to answer this question, but doing that with a primitive equation model is highly computationally expensive. A preliminary analysis is therefore performed here with a nonlinear low-order ocean model, which identifies a significant paradigm of intrinsic oceanic double-gyre low-frequency variability. The chaotic pullback attractors of the periodically forced model are first recognized to be periodic and cycloergodic. Two parameters are then introduced to analyze the topological structure of the pullback attractors as a function of the forcing period; their joint use allows one to identify four forms of sensitivity to initialization corresponding to different system behaviors. The model response under periodic forcing turns out to be, in most cases, very sensitive to initialization. Implications concerning the primitive equation model are finally discussed.

On Imbalance Generated by Vortical Flows in a Two-Layer Spherical Boussinesq Primitive Equation Model

The spontaneous adjustment emission of inertia–gravity waves is investigated by examining the amount of imbalance generated during the evolution of unstable jets in an isentropic two-layer primitive equation model on the sphere. To determine the balance and thus the imbalance, potential vorticity (PV) inversion by means of the first-, second-, and third-order plain-δδ, plain-δγ, and plain-γγ balance relations, as well as the Bolin–Charney balance relations, is applied. Five sets of experiments are carried out by (i) changing the upper-layer potential temperature with a fixed initial jet speed and (ii) changing the initial jet speed with a fixed upper-layer potential temperature. For each set, the relation between the optimal measure of imbalance with the corresponding measure of balanced vortical flow is sought at the peak of instability. The minimal imbalance obtained by 1 of the above 10 PV inversion procedures is considered as the optimal. The focus herein is on the magnitude of imbalance and its scaling with various measures of balanced flow. It is shown that for the magnitude of imbalance it is always possible to find the proper measure with an exponentially small scaling. For the imbalance-to-balance ratio, however, a power law is obtained when either the jet or the stratification is weak. The latter difference in scaling behavior of the imbalance and imbalance-to-balance ratio may be an artifact of the inevitable numerical errors whose effects are felt more strongly when the signature of vortical flow is weak.