Added mass for motion in density-stratified fluids

Bruno Voisin (1)

1 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

In a density-stratified fluid, owing to the generation of internal gravity waves, the added mass of a moving body becomes anisotropic and frequency-dependent. Two definitions of added mass, equivalent in a homogeneous fluid, become different: one based on the impulse of the fluid, and the other on the pressure on the body. We start by deriving a Kirchhoff-Helmholtz integral for internal waves, extending earlier attempts, and deduce from it the relation between the two definitions. We then calculate the motion of the fluid for oscillating spheres and cylinders, extending earlier results, and deduce from it the coefficients of added mass, consistent with experiment. At frequencies large compared with the buoyancy frequency the coefficients take their values in a homogeneous fluid (1/2 for the sphere and 1 for the cylinder); at frequencies smaller than the buoyancy frequency they become complex, of real part associated with added mass in the usual sense and imaginary part associated with wave drag. These variations are related by Fourier transformation to the free oscillations, consistent with experiment, of the bodies displaced from their neutrally buoyant levels then released.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Bruno Voisin. Added mass for motion in density-stratified fluids. 7th Euromech Fluid Mechanics Conference, Sep 2008, Manchester, United Kingdom. ⟨hal-00582889⟩