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On the penetration of a turbulent layer into stratified fluid

Published online by Cambridge University Press:  29 March 2006

H. Kato  and
O. M. Phillips
H. Kato
Affiliation:
Mechanics Department, The Johns Hopkins University, Baltimore, Maryland Present address: Port and Harbour Research Institute, 3-1-1 Nagase, Yokouska, Japan.
O. M. Phillips
Affiliation:
Mechanics Department, The Johns Hopkins University, Baltimore, Maryland
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Abstract

An experiment is described in which a constant stress is applied to the surface of an initially quiescent tank of fluid with a uniform density gradient. The development of the turbulent layer by entrainment of the underlying fluid is described and it is found that the entrainment coefficient E, the ratio of the entrainment velocity ue to the friction velocity u* is given in terms of the depth D of the mixed layer and the density jump δρ across the entrainment interface by the relation \[ E = \frac{u_e}{U_{*}} = 2.5\frac{\rho_0u^2_{*}}{g\delta\rho D}. \] The rate of increase of potential energy of the stratified fluid was found to be proportional to the rate of dissipation of kinetic energy per unit area in the turbulent layer. The form of these results is consistent with those found by Turner with an agitation tank, but the parameters used here allow direct application to entrainment in the ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 4 , 28 July 1969 , pp. 643 - 655
Copyright
© 1969 Cambridge University Press

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