Effect of a harmonic surface pressure on wave propagation over a beach.

The objective is to study the harmonic forced wave motion over a beach by a finite Fourier transform technique. The constructed approximate solution has a logarithmic singularity at the shoreline. It accounts for reflexion and local perturbations. Trapping of waves may take place for particular choices of the applied surface pressure excess. The case of a wave incident against a cliff with horizontal bottom is solved exactly. The method deals invariably with a variety of bottom shapes, including the case where there is an additional corrugation of the bottom on a finite interval. Other bottom boundary conditions than impermeability can be treated as well. The results may be of interest in several practical applications, in particular the evaluation of the reflected wave. Numerical applications for a plane sloping beach, a parabolic-type beach and a shelf-type beach are presented and the systems of streamlines have been drawn over and in the proximity of the beach.

Multiple wave scattering by submerged obstacles in an infinite channel of finite depth with surface pressure excess.

The objective is to study the combined effect of an incident wave, a surface pressure excess and a finite number of submerged obstacles, in the phenomenon of power transfer to an infinite fluid layer of finite depth. The incident wave and the surface pressure excess have the same harmonic time dependence, a fact that allows to eliminate time altogether and consider only steady-state solutions. The surface pressure excess simulates the effect of winds blowing above the water surface in oceans. The technique used in a first part of the paper relying upon the use of finite Fourier transform and separation of variables is extended here to this end. The method allows to separate local perturbations from progressive or standing wave. Our formulae yield the exact solution in closed form in the absence of obstacles, and provide a clearer insight into the flow properties, as compared to previous investigations. Applications are given for discontinuous surface pressure functions. We put in evidence solutions with no outgoing waves, for which the energy transmitted by the surface pressure is exhausted in generating a standing wave, together with local perturbations. Two numerical applications without/with obstacles, for a parabolic surface pressure profile, allow to assess the energy transfer from the pressure-obstacles system to the fluid. The results may be of interest in the field of oscillating water columns and, generally, water power converting technology.

Nonlinear Rayleigh wave propagation in a layered half-space in dual-phase-lag.

We investigate nonlinear Rayleigh wave propagation in a layered thermoelastic medium composed of a slab rigidly bonded to the surface of a half-space under prescribed external thermal boundary conditions within the dual-phase-lag theory. The heat conduction coefficient for both the slab and the matrix have a linear dependence on temperature. Our aim is to assess the effect of temperature dependence of the heat conductivity, as well as the thermal relaxation times, on the process of wave propagation in the layered medium. Poincaré expansion of the solution in a small parameter and the generation of higher harmonics allow to evaluate the coefficient of this nonlinear coupling in the slab through heat wave propagation measurement. For the used numerical values, the results show that some characteristics of the problem, e.g. the temperature, heat flux and one stress component suffer jumps at the interface, while the other stress components are continuous there. The jump in the heat flux is noticeable only in the first order of nonlinearity. The existence of jumps at the interface may be of interest for measurements. Comparison with the case of the half-space showed that the presence of the slab contributes to faster damping of the solution with depth in the half-space.

Nonlinear Rayleigh wave propagation in thermoelastic media in dual-phase-lag.

A model of generalized thermoelasticity within dual-phase-lag is used to investigate nonlinear Rayleigh wave propagation in a half-space of a transversely isotropic elastic material. It is assumed that the coefficient of heat conduction is temperature-dependent, a fact that plays an important role in the coupling behaviour analysis of thermoelastic and piezo-thermoelastic solids. Taking such a dependence into account becomes a necessity at higher temperatures and in nano-structures, when the material properties can no longer be considered as constants. Normal mode analysis is applied to find a particular solution to the problem under consideration. A concrete case is solved under prescribed boundary conditions and tentative values of the different material coefficients. The results are discussed to reveal the effect of temperature dependence of the heat conduction coefficient, as well as the thermal relaxation times, on nonlinear Rayleigh wave propagation. All quantities of practical interest are illustrated in two-and three-dimensional plots. The presented results may be useful in the detection of the second harmonic amplitudes through measurements related to the propagating heat wave.

On a two-dimensional model of generalized thermoelasticity with application.

A 2D first order linear system of partial differential equations of plane strain thermoelasticity within the frame of extended thermodynamics is presented and analyzed. The system is composed of the equations of classical thermoelasticity in which displacements are replaced with velocities, complemented with Cattaneo evolution equation for heat flux. For a particular choice of the characteristic quantities and for positive thermal conductivity, it is shown that this system may be cast in a form that is symmetric t-hyperbolic without further recurrence to entropy principle. While hyperbolicity means a finite speed of propagation of heat waves, it is known that symmetric hyperbolic systems have the desirable property of well-posedness of Cauchy problems. A study of the characteristics of this system is carried out, and an energy integral is derived, that can be used to prove uniqueness of solution under some boundary conditions. A numerical application for a finite slab is considered and the numerical results are plotted and discussed. In particular, the wave propagation nature of the solution is put in evidence.

A study of prey-predator relations for mammals.

In this paper, we present a prey-predator nonlinear model for mammals, consisting of large- and small-size prey species with group defence, in a partially protected habitat. If the prey size is small, then it is more prone to the predator at higher densities. Conversely, large prey size at higher densities tend to develop group defence. Therefore, the predator will be attracted towards that area where prey are less in number. A new physical constant has been introduced into the radiation-type condition on that part of the boundary where interaction between prey and predator takes place. This constant allows us to efficiently model group defence capabilities of the herds and its numerical values have to be determined for different pairs of prey-predator species from field observations. A way of measuring the constants involved in the model is suggested. Numerical results are provided and thoroughly discussed for a habitat of circular shape. The obtained results show that in the region away from the protected area, the density of large-size prey species is higher than that of small-size prey species, a fact that is in accordance with observations.