Warm discharges in cold fresh water: 1. Line plumes in a uniform ambient.
Anthony Kay
2134/2713
https://repository.lboro.ac.uk/articles/preprint/Warm_discharges_in_cold_fresh_water_1_Line_plumes_in_a_uniform_ambient_/9381857
Turbulent buoyant plumes in cold fresh water are analysed, assuming a
quadratic dependence of density on temperature. The model is based on the
assumption that entrainment velocity is proportional to vertical velocity in
the plume. Numerical and asymptotic solutions are obtained for both rising
and descending plumes from virtual sources with all possible combinations of
buoyancy, volume and momentum fluxes. Physical sources can be identified as
points on trajectories of plumes from virtual sources.
The zero-buoyancy condition, at which the plume and the ambient have
equal densities but their temperatures are on opposite sides of the temperature
of maximum density, is of particular importance. If an upwardly buoyant plume
rising through a body of water reaches the surface before passing through its
zero-buoyancy level, it will form a surface gravity current; otherwise, the plume
water will return to the source as a fountain. The height at which zero buoyancy
is attained generally decreases as the source momentum flux increases: greater
plume velocity produces greater entrainment and hence more rapid temperature
change. Descending plumes, if ejected downwards against upward buoyancy,
may be classified as strongly or weakly forced according to whether they reach
the zero-buoyancy condition before being brought to rest. If they do, they
continue to descend with favourable buoyancy; otherwise, they may form an
inverted fountain. Once a descending plume has attained downward buoyancy,
it can continue to descend indefinitely, ultimately behaving like a plume in a
fluid with a linear equation of state. In contrast, a rising plume will eventually
come to rest however large its initial upward buoyancy and momentum fluxes
are.
2007-02-28 12:01:20
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Mathematical Sciences not elsewhere classified