  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.
