ocean waters often show layered structures especially where exchange flow between two basins occurs. these structures are often attributed to processes such as double.diffusive convection, internal waves, turbulent modulated mixing. in this paper by examining the vertical structures of temperature, salinity and density, of the middle parts of caspian sea it is shown that such layered structure ...

The propagation of waves is said to be diffusionless, and the corresponding governing PDE (or system) is said to satisfy Huygens’ principle if the waves due to compactly supported sources have sharp aft fronts. The areas of no disturbance behind the aft fronts are called lacunae. Diffusionless propagation of waves is rare, whereas its opposite—diffusive propagation accompanied by aftereffects—i...

geophysical fluids such as atmosphere and ocean often have stable density stratification; hence internal gravity waves are generated and propagated through them which are important in momentum and energy transfer in these media. these waves are also believed to generate layered structures in such media. recently there have been numerous theoretical, experimental and numerical studies on the way...

We consider scalar hyperbolic conservation laws with a nonconvex flux, in one space dimension. Then, weak solutions of the associated initial-value problems can contain undercompressive shock waves. We regularize the hyperbolic equation by a parabolic-elliptic system that produces undercompressive waves in the hyperbolic limit regime. Moreover we show that in another limit regime, called capill...

This paper is devoted to study a problem of plane waves reflection at a traction-free surface of a pre-stressed functionally graded piezoelectric material (FGPM). The effects of initial stress and material gradient on the reflection of plane waves are studied in this paper. Secular equation has been derived analytically for the pre-stressed FGPM half-space and used to show the existence of two ...

It has long been a standard practice to neglect diffusive effects in stability analyses of detonation waves. Here, with the principal aim of quantifying the impact of these oft-neglected effects on the stability characteristics of such waves, we use numerical Evans-function techniques to study the (spectral) stability of viscous strong detonation waves—particular traveling-wave solutions of the...

The role of thermodiffusive generation of concentration fluctuations via the Soret effect, their contribution to the buoyancy forces that drive convection, the advective mixing effect of the latter, and the diffusive homogenisation are compared and elucidated for oscillatory convection. Numerically obtained solutions of the field equations in the form of spatially extended relaxed traveling wav...

The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusi...

In this paper we present an intuitive explanation for the non-uniqueness of the traveling wave speed in the Fisher equation, showing a similar non-uniqueness property in the case of inviscid traveling waves. More precisely, we prove that traveling waves of the Fisher equation with wave speed c > 0 converges to the inviscid traveling wave with speed c > 0 as the diffusion vanishes. A complete di...

The time harmonic Green function for a point load in an unbounded fluid-saturated porous solid is derived in the context of Biot's theory. The solution contains the two compressional waves and one transverse wave that are predicted by the theory and have been observed in experiments. At low frequency, the slow compressional wave is diffusive and only the fast compressional nd transverse waves r...