Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space

TL;DR

This paper establishes conditions under which enstrophy decays in 2D shear flows and identifies parameter regions with distinct wave propagation characteristics.

Contribution

It extends Synge's method to determine regions of non-growth for enstrophy in shear flows, revealing a broader decay region than kinetic energy and distinct propagation regimes.

Findings

Enstrophy decays monotonically in certain parameter regions.

The parameter space is divided into two regions with different wave behaviors.

The decay region for enstrophy exceeds that for kinetic energy.

Abstract

This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's procedure (1938) to the initial-value problem allowed us to find the region of the wavenumber-Reynolds number map where the enstrophy of any initial disturbance cannot grow. This region is wider than the kinetic energy's one. We also show that the parameters space is split in two regions with clearly distinct propagation and dispersion properties.