7 - Hydrodynamic Damping

Summary

Key concepts

Damping is a fundamental as well as practical problem in fluid dynamics. It deals with small amplitude oscillations of a body (e.g., a cable in the ocean environment). The classical solutions of Stokes (1851) and Wang (1968), valid only for K ≪ 1 and β ≫ 1, have shown that the oscillatory boundary layer gives rise to skin friction and normal pressure and, hence, to damping force, in anti-phase with velocity. Its prediction for large as well as small components of offshore structures is rather difficult. It gives rise to fascinating flow phenomena, and opens new questions on flow instabilities: Honji instability and the symmetry breaking in an ever decreasing K and increasing β environment render the analytical as well as the experimental understanding of damping a challenge worth pursuing.

Introduction

Often, a distinction is made between bodies subjected to vortex-shedding excitation and those (e.g., a TLP) that undergo simple sinusoidal motion at very small amplitudes and high frequencies in water, presumably due to excitation that comes from outside, i.e., not caused by the flow itself. The latter is called “hydrodynamic damping” or “viscous damping,” meaning the decrease of the amplitude of an oscillation by forces in anti-phase with velocity. There are two reasons for such a distinction: The classical solution of Stokes (see also Wang), valid for K ≪ 1 and β ≫ 1, has shown that the oscillatory boundary layer gives rise to skin friction and normal pressure, and hence, to a damping force, in anti-phase with the velocity.