Force on a body in a continuously stratified fluid. Part 2. Sphere

Abstract

In this paper the experimental study presented in Part 1 is extended to the three-dimensional case. The in-line force coefficients (added mass and damping) of a sphere oscillating horizontally in a uniformly stratified fluid of limited depth and in a smooth pycnocline are evaluated from Fourier-transforms of the experimental records of impulse response functions. The hydrodynamic loads in the three- and two-dimensional cases are shown to be essentially different, notably in the low-frequency limit, where the damping in the three-dimensional case is zero, while in the two-dimensional case it is maximized due to phenomena akin to blocking. The generalization of the experimental results for affinely similar geometries is discussed. It is found that, as the characteristic vertical extent of stratification decreases, the mean power of internal waves radiated by the oscillating sphere reduces and the maximum of the frequency spectrum of wave power shifts toward lower frequency, which is qualitatively similar to the effects observed in the two-dimensional case. Physically, horizontal stratified waveguides act as low-pass filters since internal waves with nearly vertical group-velocity vector cannot be effectively radiated from oscillating bodies.