Vertical Penetration of Double-Diffusive Water Plumes Discharged Vertically Downward

Abstract

Previously, it was shown that, in Turner’s formula which predicts the penetration depth of negatively buoyant jets, the classical initial densimetric Froude number should be replaced by an initial effective Froude number if the formula is applied to a heated water jet discharged downward. In the present paper, this conclusion is extended to double-diffusive plumes with two buoyancy components (heat and salt) which both oppose the downward flow. A new effective Froude number is introduced for double-diffusive plumes. For the calculation of the penetration depth a modified version of the integral Fan–Brooks model has been used. The same model is used to calculate the vertical penetration in the strongly nonlinear regions around the density maxima that appear in water at some special values of temperature and salinity. It is found that the penetration depth becomes very large if the existing ambient temperature and salinity are close to density extremum values and becomes infinite if the existing ambient temperature and salinity coincide with the maximum density values.