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Stability of stratified downslope flows with an overlying stagnant isolating layer

Published online by Cambridge University Press:  25 November 2016

Arjun Jagannathan ,
Kraig B. Winters  and
Laurence Armi
Arjun Jagannathan*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Kraig B. Winters
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: agjagann@ucsd.edu
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Abstract

We investigate the dynamic stability of stratified flow configurations characteristic of hydraulically controlled downslope flow over topography. Extraction of the correct ‘base state’ for stability analysis from spatially and temporally evolving flows that exhibit instability is not easy since the observed flow in most cases has already been modified by nonlinear interactions between the instability modes and the mean flow. Analytical studies, however, can yield steady solutions under idealized conditions which can then be analysed for stability. Following the latter approach, we study flow profiles whose essential character is determined by recently obtained solutions of Winters & Armi (J. Fluid Mech., vol. 753, 2014, pp. 80–103) for topographically controlled stratified flows. Their condition of optimal control necessitates a streamline bifurcation which then naturally produces a stagnant isolating layer overlying an accelerating stratified jet in the lee of the topography. We show that the inclusion of the isolating layer is an essential component of the stability analysis and further clarify the nature and mechanism of the instability in light of the wave-interaction theory. The spatial stability problem is also briefly examined in order to estimate the downstream location where finite-amplitude features might be manifested in streamwise slowly varying flows over topography.

JFM classification

Instability: Instability Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 810 , 10 January 2017 , pp. 392 - 411
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Copyright
© 2016 Cambridge University Press 

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Jagannathan et al. supplementary movie

Isopycnals from a statistically steady state non-linear simulation of stratified flow over a smooth topography for the optimal upstream solution of Winters and Armi (2014). The spatial development of finite amplitude billow structures in the lee region can be observed in this movie.

Download Jagannathan et al. supplementary movie(Video)
Video 7.8 MB