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Communication Dans Un Congrès Année : 2022

Added mass in the presence of density stratification

Résumé

Added mass represents the additional inertia experienced by a body as it moves through a fluid, owing to the flow that this motion generates within the fluid. Being involved in the energy and impulse of the fluid, together with the dipole strength of the body and the hydrodynamic force exerted on it, added mass characterizes the flow both globally and locally. When the fluid can support the propagation of waves, inertial added mass, a real number at any given frequency, is complemented by an imaginary part associated with wave drag. The concept of added mass is extended to stratified fluids and internal gravity waves. The stratification is assumed uniform, the fluid inviscid, the waves linear and the Boussinesq approximation valid. The added mass coefficients of two oscillating bodies, an elliptic cylinder in two dimensions and a spheroid of vertical axis in three dimensions, are determined based on results obtained with the boundary integral method (Voisin 2021). Fourier inversion allows the frequency variations of the coefficients to be interpreted as a new memory integral for the force exerted on the body. Two applications are discussed: the wave energy, of particular importance for the internal tide, in whose context it is known as conversion rate (Garrett & Kunze 2007); and buoyancy oscillations, namely the free oscillations by which a displaced body returns back to equilibrium, of particular importance for midwater floats (Voorhis 1971; Cairns, Munk & Winant 1979; Goodman & Levine 1990; D'Asaro 2018). These theoretical results are compared to experiment for two types of buoyancy oscillations: those undergone by a sphere displaced from its neutral buoyancy level then released (Larsen 1969; Levitskii & Chashechkin 1999; Biró et al. 2008; Vasil'ev & Chashechkin 2009); and the oscillations of a ludion or Cartesian diver (Le Gal et al. 2022). The influence of viscosity at high Stokes number is discussed, together with the relation to measurements of added mass by the impulse response method (see Ermanyuk 2000 and Brouzet et al. 2017 and the references therein).
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Dates et versions

hal-03758723 , version 1 (23-08-2022)

Identifiants

  • HAL Id : hal-03758723 , version 1

Citer

Bruno Voisin. Added mass in the presence of density stratification. IUTAM Symposium "Particles, Drops and Bubbles in Stratified Environments", Jul 2022, Toulouse, France. ⟨hal-03758723⟩

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