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Kloosterziel, RC, Carnevale GF, Orlandi P.  2017.  Equatorial inertial instability with full Coriolis force. Journal of Fluid Mechanics. 825:69-108.   10.1017/jfm.2017.377   AbstractWebsite

The zonally symmetric inertial instability of oceanic near-equatorial flows is studied through high-resolution numerical simulations. In homogeneous upper layers, the instability of surface-confined westward currents implies potentially fast downward mixing of momentum with a predictable final equilibrium. With increasing Reynolds number, latitudinal scales along the surface associated with the instability become ever smaller and initially the motions are ever more concentrated underneath the surface. The results suggest that even if the upper layer is stratified, it may still be necessary to include the full Coriolis force in the dynamics rather than use the traditional beta-plane approximation.

Kloosterziel, RC, Orlandi P, Carnevale GF.  2015.  Saturation of equatorial inertial instability. Journal of Fluid Mechanics. 767:562-594.   10.1017/jfm.2015.63   AbstractWebsite

Inertial instability in parallel shear flows and circular vorwes in a uniformly rotating system (f-plane) redistributes absolute linear momentum or absolute angular momentum in such a way as to neutralize the instability. In previous studies we showed that, in the absence of other instabilities, at high Reynolds numbers the final equilibrium can be predicted with a simple construction based on conservation of total momentum. In this paper we continue this line of research with a study of barotropic shear flows on the equatorial /3-plane, Through numerical simulations the evolution of the instability is studied in select illuminating cases: a westward flowing Gaussian jet With the flow axis exactly on the equator, a uniform shear flow and eastward and Wes t w ard flowing jets that have their flow axis shifted away from the equator. In the numerical simulations it is assumed that there are no along -stream variations. 'fins suppresses equatorial Rossby W a ve s and barotropic shear instabilities and allows only inertial instability to develop. We investigate whether for these flow S the equatorial t-plane the final equilibrated flow can be predicted as was possible for flows on the f-plane. For the Gaussian jet centred on the equator the prediction of the equilibrated flow is obvious by mere inspection of the initial momentum distribution and by assuming that momentum is mixed and homogenized to render the equilibrated flow inertially stable. For the uniform shear flow, however, due to the peculiar nature of the initial momentum distribution and the fact that the Coriolis parameter f varies with latitude, it appears that, unlike in our earlier studies of flows on the f-plane, additional constraints need to be considered to correctly predict the outcome of the highly nonlinear evolution of the instability, The mixing range of the linear shear flow and the value of the mixed momentum is determined numerically and this is used to predict the equilibrated flow that emerges from an eastward flowing jet that is shifted a small distance away from the equator. For shifts large enough to induce no shcar at the equator the equilibrium flow can be well predicted using the simple rccipe used in our carlicr studies of parallel shear flows on the f-plane. For thc westward flowing jet shifted a very small distance from the equator, no prcdiction appears feasible. For modcstly small shifts a prediction is possiblc by combining the empirical prcdiction for thc linear shear flow with a prediction similar to what we used in our previous studies for flows on the f-plane.

Carnevale, GF, Kloosterziel RC, Orlandi P.  2013.  Inertial and barotropic instabilities of a free current in three-dimensional rotating flow. Journal of Fluid Mechanics. 725:117-151.   10.1017/jfm.2013.191   AbstractWebsite

A current in a homogeneous rotating fluid is subject to simultaneous inertial and barotropic instabilities. Inertial instability causes rapid mixing of streamwise absolute linear momentum and alters the vertically averaged velocity profile of the current. The resulting profile can be predicted by a construction based on absolute-momentum conservation. The alteration of the mean velocity profile strongly affects how barotropic instability will subsequently change the flow. If a current with a symmetric distribution of cyclonic and anticyclonic vorticity undergoes only barotropic instability, the result will be cyclones and anticyclones of the same shape and amplitude. Inertial instability breaks this symmetry. The combined effect of inertial and barotropic instability produces anticyclones that are broader and weaker than the cyclones. A two-step scheme for predicting the result of the combined inertial and barotropic instabilities is proposed and tested. This scheme uses the construction for the redistribution of streamwise absolute linear momentum to predict the mean current that results from inertial instability and then uses this equilibrated current as the initial condition for a two- dimensional simulation that predicts the result of the subsequent barotropic instability. Predictions are made for the evolution of a Gaussian jet and are compared with three-dimensional simulations for a range of Rossby numbers. It is demonstrated that the actual redistribution of absolute momentum in the three-dimensional simulations is well predicted by the construction used here. Predictions are also made for the final number and size of vortices that result from the combined inertial and barotropic instabilities.