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Added mass in the presence of stratification

Séminaire Bruno Voisin (LEGI)

Mercredi 27 septembre 2023

Amphithéâtre Nougaro

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Added mass represents the additional inertia experienced by a body as it moves through a fluid, owing to the flow that this motion generates in the fluid. At its core, added mass pertains to the irrotational dynamics of inviscid fluids. When, in addition, the fluid supports the propagation of waves, added mass becomes complex and varies with the frequency; its real part represents inertia and its imaginary part wave damping. When the size of the body becomes small, viscosity comes into play, so that added mass combines its effect with Stokes resistance and the Bassett-Boussinesq memory force.

In the presence of density stratification, added mass is affected by the propagation of internal gravity waves. Its relation to the dipole strength of an oscillating rigid body is clarified, allowing its calculation from a boundary integral representation of the body. An ellipse in two dimensions and a spheroid in three dimensions are considered, for translational motion only.

In the time domain a new memory force is associated with the stratification. Its kernel combines algebraic or exponential decay (for vertical and horizontal motions, respectively) with oscillations at the buoyancy frequency. In the frequency domain, for oscillations of fixed excursion, the power output of an oscillating body is seen to be a maximum at about 0.8 times the buoyancy frequency.

Added mass is then applied to three types of buoyancy oscillations by which a body, whose neutral equilibrium has been disturbed, goes back to this equilibrium: a buoyant body displaced from its neutral level then released, with applications to the dynamics of Lagrangian floats; the impulse response method for the measurement of added mass; and the free oscillations of a Cartesian diver subjected to an external modulation of the hydrostatic presssure then released. Successful comparison with experiment requires inclusion of Bassett-type boundary-layer dissipation.