Predominance of pressure transport in spatial energy budget for a mixing layer approaching absolute instability

TL;DR

This study reveals that near the absolute instability threshold in a mixing layer, pressure transport overwhelmingly dominates the energy budget, highlighting its key role in disturbance growth and instability development.

Contribution

It demonstrates that pressure transport becomes the primary energy transfer mechanism at the onset of absolute instability in an inviscid mixing layer.

Findings

Pressure transport dominates energy budget at critical condition

Growth of disturbances is mainly due to pressure transport

Pressure work redistributes disturbance energy in streamwise direction

Abstract

In this letter, we report the outcome of a spatial energy budget performed for the linear convective instability of the plane incompressible mixing layer within the inviscid framework. We find that, as the critical condition for the onset of absolute instability is approached, the integrated pressure-transport term becomes increasingly more prominent as compared to the integrated production term and it dominates the energy budget completely at the critical condition. This implies that, near the threshold of absolute instability, the growth of disturbances is almost entirely due to the pressure transport mechanism (rather than the production mechanism), which is a striking result. The part of the pressure-transport term that represents the work done by the fluctuating pressure forces is seen to be primarily responsible for the observed shift in the energy balance. These results can help us better understand the physical processes causing absolute instability in a mixing layer. In particular, the redistribution of disturbance energy in streamwise direction by fluctuating pressure, which is "non-local" in character for incompressible flows, seems to play a key role in this respect.