Stabilities of Parallel Flow and Horizontal Convection

TL;DR

This paper analyzes the stability of 2D parallel flows with a new criterion and reports numerical simulations of partial-penetrating flow in horizontal convection at high Rayleigh numbers, revealing a shallow circulation cell.

Contribution

It introduces a more restrictive stability criterion for inviscid parallel flow and provides the first numerical simulation of partial-penetrating flow in horizontal convection.

Findings

New stability criterion for inviscid parallel flow

Numerical evidence of partial-penetrating flow at high Rayleigh numbers

Shallow circulation cell consistent with experimental observations

Abstract

In the first part, the stability of two-dimensional parallel flow is discussed. A more restrictively general stability criterion for inviscid parallel flow is obtained analytically. In the second part, we report the numerical simulations of the partial-penetrating flow in horizontal convection within a squire cavity tank at high Rayleigh numbers $10^7<Ra<10^{10}$. The fast estab but slowly steadied flow is simulated, where a shallow and closed circulation cell is obtained numerically as partial-penetrating flow for the first time, which is consistent with the experiment.