Adiabatic waves along interfacial layers near the critical pointOndes adiabatiques le long des interfaces près du point critique

Near the critical point, isothermal interfacial zones are investigated starting from a non-local density of energy. From the equations of motion of thermocapillary fluids, we point out a new kind of adiabatic waves propagating along the interfacial layers. The waves are associated with the second derivatives of densities and propagate with a celerity depending on the proximity of the critical point. To cite this article: H. Gouin, C. R. Mecanique 332 (2004).     

Numerical tests and properties of waves in radiating fluids

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare the solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.     

Acousto-optical spectrum analysis of ultra-high-frequency radio-wave analogue signals with an improved resolution exploiting the collinear acoustic wave heterodyning

This article is devoted to the problem of improving the frequency resolution inherent in a parallel acousto-optical spectrum analysis via involving an additional nonlinear phenomenon into the data processing. In so doing, we examine possible application of the wave heterodyning to the real-time scale acousto-optical analysis of the frequency spectrum belonging to ultra-high-frequency radio-wave signals peculiar, for example, for radio-astronomy. The nonlinear process of wave heterodyning is realized through providing a co-directional collinear interaction of the longitudinal acoustic waves of finite amplitudes. This process, which is beforehand studied theoretically and investigated experimentally via the acousto-optical technique as well, allows us either to improve the frequency resolution of spectrum analysis at a given frequency range or to increase by a few times the current frequencies of radio-wave signals under processing. The first step along this way is connected with the experimental modeling of the acoustic wave heterodyning in solids via exploitation of the specific acousto-optical cell based on a liquid, which allows the simplest realization of a cell with the needed properties. Then, these theoretical and practical findings are used in our experimental studies aimed at creating a new type of acousto-optical cells, which are able to improve the resolution inherent in acousto-optical spectrum analyzer operating over ultra-high-frequency radio-wave signals. In particular, the possibility of upgrading the frequency resolution through the acoustic wave heterodyning is experimentally demonstrated using the cell made of lead molybdate crystal. The obtained results demonstrate practical efficiency of the novel approach presented.     

Experimental and numerical study of an aquaculture net cage with floater in waves and current

The mooring loads on an aquaculture net cage in current and waves are investigated by dedicated model tests and numerical simulations. The main purpose is to investigate which physical effects are dominant for mooring loads, and in this respect, to investigate the validity of different rational hydrodynamic load models. Also structural and numerical aspects are investigated. The model tests are performed to provide benchmark data, while the numerical model is used to study the effect and sensitivity of different load models and parameters.Compared to a realistic aquaculture plant, the total system is simplified to reduce the complexity. The system does, however, include all the four main components of an aquaculture plant: net cage, floater, sinker weights and moorings. The net cage is bottomless, flexible and circular. It is attached to a circular, elastic floater at the top and has 16 sinker weights at the bottom. The system is nearly linearly moored with four crow feet mooring lines.The loads are measured in the four mooring lines. A systematic variation of current only, wave only as well as combined current and wave conditions is carried out. The numerical simulation results are first benchmarked towards the experimental data. The mean loads in general dominate over the dynamic part of the loads in combined current and waves, and they significantly increase in long and steep waves, relative to current only. Next, a sensitivity study is carried out. A rigid floater significantly alters the loads in the mooring lines compared to a realistic, elastic floater. The theoretical model for the wave matters. The mooring loads are rather insensitive to a majority of the parameters and models, in particular: frequency dependent added mass of the floater and nonlinear restoring loads. It seems not to be necessary to represent the net cage with a very fine numerical mesh.     

Scattered waves and motions of marine vessels advancing in a seaway

The steady forward motion of a marine vessel modifies the incident and scattered waves as well as its dynamic characteristics in a seaway. Small amplitude assumptions of the surface waves and vessel dynamic responses lead to linearization of the potential flow problem and its solution in the frequency domain. The mathematical formulation adopts a translating coordinate system at the vessel forward speed. The free surface boundary condition accounts for the modification of the uniform current around the vessel and a new radiation condition takes into account the Doppler shift of the scattered waves. A boundary element model, based on the Rankine source distribution, describes the steady and oscillatory flows around the vessel. Stokes’ theorem allows evaluation of the surface integrals involving the so-called m-terms due to oscillation of the vessel in a current. Through a numerical experiment with a Wigley hull form, we establish the convergence of the numerical model, verify the radiation condition, and examine the scattered wave patterns for a full range of forward speeds. Previous laboratory data provides validation of the computed hydrodynamic coefficients and dynamic response as well as the potential flow model for general seakeeping applications.     

The calculation of Green's functions in three dimensional hydrodynamic gravity wave problems

We have studied the problem of calculating Green's functions in three dimensional hydrodynamic gravity wave problems. A number of new expressions for these functions are presented for both finite and infinite depths. Various techniques for accelerating the convergence of some infinite series in these expressions are investigated and compared with the normal methods of evaluation. A significant improvement in the efficiency of the calculation is found using the results described in this paper.     

Analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates

The analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates is presented by means of the matrix methods in conjunction with Fourier transformation technigues. It provides a closed-form representation of the electromagnetic field over the whole multilayer regions. The treatment does not limit the direction of the biased magnetic field and the numbers of the coated dielectric plates. Numerical results are presented and compared with that calculated with the method in ref.[1], and full-waveguide-band bandwidth for 47.5°±1.5° rotation angle is obtained for transmission type rotator in W band. Calculation for reflection type rotator is also presented and compared with the experiments.