Internal Waves Radiation by a Turbulent Jet Flow in a Stratified Fluid

Abstract

The radiation of internal gravity waves by stratified turbulent shear flows is encountered in many geophysical flows. Numerous applications include jet flows (Sutherland & Peltier 1994), grid-generated turbulence (Dohan & Sutherland 2003), boundary layers (Taylor & Sarkar 2007), collapse of mixed patches (Sutherland et al. 2007), wakes behind towed and self-propelled bodies (Lin & Pao 1979), and many others. The present paper deals with internal waves radiated by a jet flow that is created in the far wake of a sphere towed in a stratified fluid at large Froude and Reynolds numbers. Experimental studies of internal gravity waves (IW) radiated by a towed sphere and its wake were performed both in a linearly stratified fluid by Bonneton, Chomaz & Hopfinger (1993) (further referred to as BCH) and in the presence of a thermocline by Robey (1996). The results show that internal waves radiated by the sphere (i.e. the lee waves) are stationary with respect to the sphere, and their amplitude is inversely proportional to the sphere Froude number, defined as 2 / Fr V ND  (where N is the buoyancy frequency, and V and D are the towing speed and the sphere diameter). On the other hand, internal waves, radiated by the turbulent wake are not stationary with respect to the sphere, and their amplitude grows as Fr increases. Experimental results obtained by BCH and Robey (1996) show that if the Froude number is sufficiently large (Fr > 10), non-stationary IW supercede the lee waves. Experimental results obtained by BCH show that at early times (Nt = O(10)) internal waves are radiated due to the collapse of the vortex coherent structures developing in the near wake (Chomaz, Bonnet & Hopfinger (1993), further referred to as CBH). The wavelength of these waves (also called “random” waves) is of the order of the sphere diameter, and their dynamics is well described theoretically under an assumption that each collapsing coherent structure can be regarded as an impulsive source of IW. Visualization of the density distribution in a horizontal plane at a distance of three sphere radii below the towing axis at times Nt 40) random internal waves are superceded by waves whose initial spatial period is of the order of five sphere diameters. The isophase distribution of these waves, although being non-stationary with respect to the sphere, is reminiscent of the regular iso-phase pattern of the lee-waves. At sufficiently late times (Nt > 50), the random waves disappear, and there remain only coherent IW. BCH give no explanation of the observed dynamics of these coherent internal waves.