Internal wave drift of a neutrally buoyant sphere

Abstract

We studied the motion of neutrally buoyant spheres induced by internal waves in a linearly stratified fluid with moderate Reynolds numbers (200-300). The characteristic scale of the sphere is much smaller than the wavelength (D/λ < 0.05), so we apply Morison’s equation, which is a semi-empirical formula to estimate the force on underwater structures, to model the drag force and motion of the sphere. In our 5-metre long wave tank, a mode-1 internal wave was generated by a wave generator to study the motion of the spheres. Experimental results show that, similar to surface waves, there exists a wave induced drift of the sphere resulting from the phase lag between the motion of the sphere and the fluid. The magnitude and direction of the drift velocity ud can be affected by many parameters, including the initial phase of the wave generator, depth of the sphere, and frequency of the internal waves. An empirical formula for ud will be introduced and will be compared to the theoretical results from a numerical simulation. For the vertical motion of the sphere, both the experiment and numerical simulation show that at low frequency of the internal waves (ω/N < 0.2), a series of harmonics of ω appear in the vertical motion.