Effects of weak planetary rotation on the stability and dynamics of internal stratified jets

Abstract

This study explores the stability characteristics and nonlinear evolution of internal jets in rotating stratified fluids using a combination of direct numerical simulations and linear instability analyses. Our ultimate goal is the assessment of the potential impact of the Earth’s rotation on relatively small-scale structures, exemplified by turbulent wakes generated by propagating bluff objects in the ocean. We question the popular notion that ascribes a secondary role to the Coriolis effects in large Rossby number (Ro) systems. It is shown that the Earth’s rotation can substantially influence circulation patterns with Rossby numbers as high as Ro ∼ 103. Therefore, such effects must be taken into account in the numerical and theoretical models of finescale (∼10–100 m) processes in the ocean. We present a series of examples in which planetary rotation controls flows with large but finite values of Ro through centrifugal destabilization. These calculations reveal that centrifugal instabilities can affect fluid motion either directly, by modifying the basic state, or indirectly, by preferentially eliminating anticyclonic coherent vortices that form in the course of dynamic destabilization of jets. The results of this study have potentially significant geophysical implications in terms of elucidating mechanisms of energy cascade to progressively smaller scales. In the naval context, we anticipate that our investigation could influence the development of algorithms for detection and analysis of late wakes, generated by propagating submersibles in the ocean.