2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230919In 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.physics/0512208, physics/0601043, physics/0601112, physics/0603177, physics/0605167, physics/0702037Fluid DynamicsAtmospheric and Oceanic Physicstext