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 −5/3 slope is recovered for the two components, in agreement with experimental data and numerical simulations based on other models.

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The merchant ships are continuously recruited by the world meteorological organization (WMO) as Voluntary Observing Ship (VOS) for the collect of meteorological parameters at the ocean surface. VOS meteorological observation includes many parameters such as the wind speed measured by anemometers. This measurement is biased by the presence of ship and superstructure. Little work was carried out in this field. Between them we find the experimental work at a low speed wind tunnel of Southampton University which studies the airflow distortion over simple models (generic models) of VOS merchant ship. This study presents numerical results of a 3D simulation analyzing airflow effect above the bridge of a generic merchant ship models involved in VOS. For this purpose three-dimensional, stationary and turbulent, numerical simulation has been achieved the flow over the bridge of a tanker and a container ship at 1/ 46 scale using a numerical code and CFX code with turbulence k-ε models. This numerical study allows us to know the position of the line of equality as well as the zone of acceleration and deceleration of the flow. The results obtained numerically by numerical code and CFX code are compared with those obtained experimentally in the wind tunnel of Southampton University. Numerical results are in a good agreement with experimental results and can be used as a reference to find the position of the equality line and to know the error range in of the anemometer velocity reading.

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