Monochromatic internal waves from oscillating objects

International audienceRealization that mixing in the ocean owes much to the generation of internal tides by the ebb and flow of the surface tide over continental slopes, on one hand, and advent of the synthetic schlieren method for the measurement of internal waves in the laboratory, on the other hand, have led to a regain of interest in the generation of monochromatic internal gravity waves. This problem is tackled here in two parts. First, the structure of the waves from an arbitrary monochromatic source term is investigated. Waves are radiated along beams, of inclination to the vertical determined by the frequency, while the structure of the waves inside the beams is determined by additional phenomena such as the size of the forcing and the viscosity of the fluid. Transitions take place, between regions where each phenomenon dominates in turn. Near-field effects are prominent in three dimensions, and are proposed as an explanation for the discrepancy between experiment and existing, far-field, theories. Secondly, the determination of the source terms equivalent to oscillating circular cylinders and spheres is considered. The variations of their added mass with frequency is predicted, and is shown to coincide with experiment. Taking these into account, the radiated energy is shown to exhibit a maximum at a practically constant fraction of the buoyancy frequency, independent from the direction of oscillation. Implications for stratified turbulence are discussed