Water entry of a body which moves in more than six degrees of freedom

The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical entry problem with a modified vertical displacement of the body and an elliptic region of contact between the liquid and the body surface. Low pressure occurrence is determined; this occurrence can precede the appearance of cavitation effects. Hydrodynamic forces are analysed for a rigid ellipsoid entering the water with 3 d.f. Experimental results with an oblique impact of elliptic paraboloid confirm the theoretical findings. The theoretical developments are detailed in this paper, while an application of the model is described in electronic supplementary materials

Non-linear fate of internal wave attractors

We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing

Energy cascade in internal wave attractors

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction

Impact of three-dimensional standing waves on a flat horizontal plate

International audienceA set-up is designed in order to study the wave impact on structures. These structures can be the stern part of cruiser, a fixed structure as a pier or the roof of LNG-tank. The traveling waves impact was already studied by Smith et al. (1998) but it seems difficult to elaborate a model except some empirical formulæ linking the drop height, the wavelength and the wave steepness. Barrholm (2001) as well studied the travelling wave impact underneath decks of platforms. His modelling is based on a two-dimensional Wagner model where the determination of the wetted surface is not a simple task. Here a simplified impact phenomenon is investigated since standing waves are generated

Ondes et instabilités de fronts en milieu tournant et stratifié

Fronts occur in the Earth oceans and atmosphere and separate masses of air of fluid of different temperature and different velocities. Their instabilities are relevant to the transport of heat and energy in the oceans and atmosphere, and are therefore very relevant for climate modeling. In this study, a front is generated in the laboratory in a density stratified and differentially rotating fluid, and the corresponding flow is investigated numerically using DNS. In former studies of fronts, mainly the frontal instability has been discusses and baroclinic instability and newly found Rossby Kelvin instability were reported (Flor et al 2011, Scolan 2011, and Scolan et al 2013). The exact state of the interface is very relevant for the type of instability and waves we may expect. We therefore focus on the interfacial dynamics, and consider the diffusion of vorticity and density at an interface as a function of Rossby and Schmidt number. We note the existence of interfacial Ekman layers, observe Kelvin Helmholtz instability and discuss Hölmböe instability as well as other wave types near the interface

Impact of inflated structures on a liquid free surface.

International audienceThere are many situations where inflated structures may hit violently a liquid free surface. One of them occurs during sea-landing of helicopters. As a matter of fact helicopters are equipped with inflated floaters. Those floaters are made of impermeable tissues which are almost inextensible and their flexural rigidity is small. These mechanical characteristics are difficult to reproduce at model scales, that is why we found more conventional inflated balloons like space hopper. Experiments have been carried out in the flume of Ecole Centrale Marseille. Only qualitative measurements have been performed. High speed camera provided the main features of the phenomenona. This abtract sums up this experimental campaign and the first attempts done in the numerical modellings thus yielding some comparisons. It is shown that simple linearized models- both structural and hydrodynamic models - can reproduce the early stage of penetration when impact occurs

Finite-size effects in parametric subharmonic instability

The parametric subharmonic instability in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared to numerical and experimental results. Because of the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory

Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity. The linear theory of the velocity potential is employed by assuming inviscid, incompressible fluid and irrotational flow. As the problem is set in 3-D space, the employment of the Wagner condition is essential. The set of equations we pose, is presented as a mixed boundary value problem for Laplace's equation in 3-D. Apart from the mixed-type of boundary conditions, the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface. We make some simple assumptions at the start but otherwise we proceed analytically. We find closed-form relations for the hydrodynamic variables, namely the time dependent potential, the pressure impulse, the shape of the wave front (from the contact point to beyond the cylinder) and the slamming force

Characterization of TiO2 nanoparticles in langmuir-blodgett films

In this work we have synthesized TiO2 nanoparticles, using either a sol–gel base catalysed process in the interior of CTAB reversed micelles (TiO2 CTAB sol), or the neutralization of a TiO2/H2SO4 solution in the interior of AOT reversed micelles. From the absorption and emission data of the TiO2 nanoparticles it is possible to conclude that in the sol–gel route there remains alkoxide groups in the structure, originating transitions lower than the energy gap of TiO2 semiconductor. These transitions disappear in the neutralization procedure, where the alkoxide groups are absent in the structure. We have assigned the observed indirect and direct optical transitions according to the anatase band structure. TiO2 Langmuir-Blodgett (LB) films were prepared either by direct deposition of titanium isopropoxide or by deposition of the TiO2 CTAB sol. These films showed photoluminescence, which was attributed to band-gap emission and to surface recombination of defect states