Convection plays a major role in a variety of natural hydrodynamic systems. Those
in which convection drives exchange flows through a lateral contraction and/or over
a sill form a special class with typical examples being the Red and Mediterranean
Seas, the Persian Gulf, and the fjords that indent many coastlines. The present work
focuses on the spatial distribution and scaling of the density difference between the
inflowing and outflowing fluid layers. Using a long water-filled channel, fitted with
buoyancy sources at its upper surface, experiments were conducted to investigate the
influence of the geometry of the strait and the channel as well as the magnitude of
the buoyancy flux. Two different scaling laws, one by Phillips (1966), and one by
Maxworthy (1994, 1997) were compared with the experimental results. It has been
shown that a scaling law for which
g′ = kB02/3x/h4/3
best describes the distribution
of the observed density difference along the channel, where B0
is the buoyancy flux, x
the distance from the closed end of the channel, h its height at the open end (sill) and
k a constant that depends on the details of the channel geometry and flow conditions.
This result holds for the experimental results and appears to be valid for a number
of natural systems as well.