Horizontal exchange flows driven by spatial variation of buoyancy
fluxes through the
water surface are found in a variety of geophysical situations. In all
examples of such
flows the timescale characterizing the variability of the buoyancy fluxes
is important
and it can vary greatly in magnitude. In this laboratory study we focus
on the effects
of this unsteadiness of the buoyancy forcing and its influence on the resulting
flushing
and circulation processes in a cavity. The experiments described all start
with
destabilizing forcing of the flows, but the buoyancy fluxes are switched
to stabilizing
forcing at three different times spanning the major timescales characterizing
the
resulting cavity-scale flows. For destabilizing forcing, these timescales
are the flushing
time of the region of forcing, and the filling-box timescale, the time
for the cavity-scale
flow to reach steady state. When the forcing is stabilizing, the major
timescale is the
time for the fluid in the exchange flow to pass once through the forcing
boundary layer.
This too is a measure of the time to reach steady state, but it is generally
distinct from
the filling-box time. When a switch is made from destabilizing to stabilizing
buoyancy
flux, inertia is important and affects the approach to steady state of
the subsequent
flow. Velocities of the discharges from the end regions, whether forced
in destabilizing
or stabilizing ways, scaled as
u∼(Bl)1/3 (where B is
the forcing buoyancy flux and l is
the length of the forcing region) in accordance with Phillips' (1966)
results. Discharges
with destabilizing and stabilizing forcing were, respectively,
Q−∼(Bl)1/3H
and
Q+∼(Bl)1/3δ
(where H is the depth below or above the forcing plate and δ
is the boundary
layer thickness). Thus
Q−/Q+>O(1)
provided H>O(δ), as was certainly the case in
the experiments reported, demonstrating the overall importance of the flushing
processes occurring during periods of cooling or destabilizing forcing.
A convex approach to steady state moment analysis for stochastic chemical reactions
