ON THE SPECTRA OF TURBULENT VELOCITY-FIELD IN A STABLY STRATIFIED FLOW

This paper describes a method to solve the spectral equation for the balance of turbulent kinetic energy in a stably stratified turbulent shear flow. The cospectra of vertical momentum and heat flux are modelled with the aid of a basic eddy-viscosity (or turbulent exchange coefficient) function. For the term representing the inertial transfer of turbulent kinetic energy, Pao's [Phys. Fluids 8 (1965)] form is assumed. Analytical expressions for the three-dimensional kinetic energy spectrum as well as the cospectra of momentum and heat flux are obtained over the range of wave numbers k greater-than-or-equal-to k(b), which includes the inertial subrange k(b) << k << k(s) and the viscous subrange k > k(s)(k(b) and k(s) are the buoyancy and Kolmogorov wavenumbers, respectively). The two one-dimensional spectra, e.g., the kinetic energy spectra of the horizontal and vertical components of turbulence are derived from the three-dimensional kinetic energy spectrum. These one-dimensional spectra are compared with the measured data of Gargett et al. [J. Fluid Mech. 144 (1984)] for the case I (= k(s)/k(b)) = 630. Finally, we compute the basic eddy-viscosity function and discuss its behaviour.