Resonances of Internal Gravity Waves in Stratified Shear Flows

Patrice Le_Gal
IRPHE - Aix Marseille Université - CNRS - Centrale Marseille

P. Le Gal, G. Facchini, J. Chen, S. Le Dizès, M. Le Bars, B. Favier, IRPHE, Aix Marseille Univ., CNRS, Centrale Marseille, France

U. Harlander, I.D. Borcia, Dept. of Aerodynamics and Fluid Mechanics Brandenburg Univ. of Technology, Cottbus, Germany

W. Meng, Dept. of Mechanical Engineering, Univ. of California, Berkeley, CA 94709, USA

We will present here a new instability mechanism that affects the Plane Couette flow and the Plane Poiseuille flow when these flows are stably stratified in density along the vertical direction, i.e. orthogonal to the horizontal shear. Stratified shear flows are ubiquitous in nature and in a geophysical context, we may think to water flows in submarine canyons, to winds in deep valleys, to currents along sea shores or to laminar flows in canals where density stratification can be due to temperature or salinity gradients. Our study is based on two sets of laboratory experiments with salt stratified water flows, on linear stability analyses and on direct numerical simulations. It follows recent investigations of instabilities in stratified rotating or non rotating shear flows: the stratorotational instability [2],[3], the stratified boundary layer instability [4] where it was shown that these instabilities belong to a class of instabilities caused by the resonant interaction of Doppler shifted internal gravity waves. Our laboratory experiments for Plane Couette and Plane Poiseuille flows, based on visualizations and PIV measurements, show in both cases the appearance of braided wave patterns when the experimental parameters, depending on the Reynolds and Froude numbers, are above a threshold. The non linear saturation of the instability leads to a meandering in the horizontal plane arranged in layers stacked along the vertical direction [5]. Comparison with theoretical predictions for the instability threshold and the critical wavenumbers calculated by linear analysis is excellent. Moreover, direct numerical simulations permit to complete the description of this instability that can be interpreted as a resonant interaction of boundary trapped waves [6].

[1] S. Orszag, JFM 50(4), 689-703, 1971.

[2] M. Le Bars & P. Le Gal, Phys. Rev. Lett. 99, 064502, 2007.

[3] G. Rüdiger, T. Seelig, M. Schultz, M. Gellert, Ch. Egbers & U. Harlander, GAFD,111, 429-447, 2017.

[4] J. Chen, Y. Bai, & S. Le Dizès, JFM 795, 262-277, 2016.

[5] D. Lucas, C.P. Caulfield, R. R. Kerswell, arXiv:1808.01178, 2019.

[6] G. Facchini, B. Favier, P. Le Gal, M. Wang, M. Le Bars, JFM 853, 205-234, 2018.