Influence of buoyancy and rotation on equations for the turbulent length scale

The paper discusses the problem of suitably accounting for the effects of body forces in equations for determining the turbulent length scale. For the example of the dissipation-rate equation, a body-force correction is suggested in which one of the empirical constants in the equation is made a function of the flux Richardson number based on the extra production of the lateral fluctuations due to body forces. This flux Richardson number is shown to be a more generally applicable parameter for both buoyant and rotating flows than is the more conventional gradient Richardson number. Calculations obtained with the modified dissipation equation are presented for buoyant and swirling jets. Good agreement with experiments is obtained in both cases with the same empirical constant in the body-force correction. For the first time, the modified dissipation equation allows exactly the same model to be used for vertical and horizontal buoyant jets.