If a sill-enclosed basin, connected to a large reservoir, is suddenly
subjected to a
de-stabilizing surface buoyancy flux, it will first mix vertically by turbulent
convection
before the resulting lateral buoyancy gradient generates a horizontal exchange
flow
across the sill. We present a study which examines the unsteady adjustment
of such
a basin under continued steady forcing. It is shown, through theoretical
development
and laboratory experimentation, that two consecutive unsteady regimes characterized
by different dynamic balances are traversed as the flow approaches a steady
state.Once established the exchange flow is controlled at the sill crest where
it is
hydraulically critical. In the absence of a lateral contraction, the single
control at the
sill crest allows a range of submaximal exchange states with the flow at
the sill being
dependent not only on the forcing and geometrical parameters but also on
mixing
conditions within the basin which are, in turn, dependent on the sill exchange.
The
sill–basin system is therefore strongly coupled although it remains
isolated from the
external reservoir conditions by a region of internally supercritical flow.
Results from
the laboratory experiments are used to demonstrate the link between the
forcing and
the exchange flow at the sill. Steady-state measurements of the interior
mean velocity
and buoyancy fields are also compared with previous analytical models.
Boundary-Layer Formulation of Dendritic Growth: Existence of a Family of Steady-State Needle Solutions
