Secularly growing oscillations in a stratified rotating fluid

Abstract

A simple exact solution of the Boussinesq equations of motion, thermal energy, and mass conservation is obtained for an oscillatory flow regime in a stably stratified rotating fluid. The flow is unbounded and characterized by velocity gradients that vary with time but are spatially uniform-the basic state of Craik-Criminale flows. The solution describes an oscillatory convergent-divergent flow in which the linear (normal) strain rates are periodic. However, two of the shear strain rates are forced by the linear strain rates, and their amplitudes grow linearly with time.

Geometric structure of pseudo-plane quadratic flows

“…Hydrodynamic stability therefore becomes an essential problem in fluid mechanics. It examines the temporal evolution of a small perturbation on a steady laminar flow, and the basic flow is said to be unstable if the perturbation grows in amplitude with time (Lagnado et al 1984, Craik and Criminale 1986, Dritschel 1990, Salhi et al 1996, Shapiro and Fedorovich 2012.…”

“…The velocity gradient and strain rate are spatially uniform. Due to this unique property, quadratic flow has been commonly used as mean flow in turbulence model and hydrodynamic stability analysis (Lagnado et al 1984, Craik and Criminale 1986, Salhi et al 1996, Shapiro and Fedorovich 2012.…”