A closed differential model for large-scale motion in HVBK fluids

¹ Laboratoire de Mécanique Appliquée, Université des sciences et de la Technologie USTMB - bp 1505 EL-Mnouar Oran, Algeria
² Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie Paris 6 - Case 162, 4 place Jussieu, 75252 Paris cedex 5, France

Received: 14 April 2006
Accepted: 17 July 2006

Abstract

The aim of this paper is to propose a closed differential model for large-scale motion in a superfluid, within the framework of the hydrodynamic model developed by Hall, Vinen, Bekarevich and Khalatnikov (HVBK). The scale separation is performed using a convolution filter, following the usual procedure of large-eddy simulation. In a second step, a general closure based on differential approximations of unknown non-linear terms is used to recover a fully self-consistent hydrodynamic model for large-eddy evolution. An important feature of the present closure is that it does not rely on any assumption dealing with the nature and the intensity of the interactions between small and resolved scales, and is therefore expected to have a large range of validity. The reliability of the proposed model is assessed by numerical results obtained in the case where the grid cutoff frequency is much higher than the Kolmogorov scale in the normal fluid and the dissipation scale associated with Kelvin waves in the superfluid. It is shown that an inertial range with a slope is recovered for the two components, in agreement with experimental data and numerical simulations based on other models.