The Energetics of Entrainment Across a Density Interface

Roland B. Stull Department of Atmospheric Sciences, University of Washington, Seattle 98195

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Abstract

A theory of the fluid entrainment rate into a turbulent, mixed layer across a horizontal density interfaceis presented. By integrating the turbulent kinetic energy equation over the depth of the mixed layer and assuming that turbulence dissipation rates are proportional to production rates, an equation is derived relatingthe potential energy change and entrainment rate to four major terms: 1) buoyant production of energy dueto heating at the earths surface; 2) mechanical production due to wind shear at the earths surface; 3) mechanical production due to wind shear and dynamic instabilities such as Kelvin-Helmholtz waves at theversion interface; and 4) energy losses due to internal gravity waves. It is shown that most previously published theories are just special cases of this more general energetics theory.

Abstract

A theory of the fluid entrainment rate into a turbulent, mixed layer across a horizontal density interfaceis presented. By integrating the turbulent kinetic energy equation over the depth of the mixed layer and assuming that turbulence dissipation rates are proportional to production rates, an equation is derived relatingthe potential energy change and entrainment rate to four major terms: 1) buoyant production of energy dueto heating at the earths surface; 2) mechanical production due to wind shear at the earths surface; 3) mechanical production due to wind shear and dynamic instabilities such as Kelvin-Helmholtz waves at theversion interface; and 4) energy losses due to internal gravity waves. It is shown that most previously published theories are just special cases of this more general energetics theory.

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