A new inviscid mode of instability in compressible boundary-layer flows

The stability of an almost inviscid compressible fluid flowing over a rigid heated surface is considered. We focus on the boundary layer that arises. The effect of surface heating is known to induce a streamwise acceleration in the boundary layer near the surface. This manifests in a streamwise velocity which exhibits a maximum larger than the free-stream velocity (i.e. the streamwise velocity exhibits an ‘overshoot’ region). We explore the impact of this overshoot on the stability of the boundary layer, demonstrating that the compressible form of the classical Rayleigh equation (which governs the development of short wavelength instabilities) possesses a new unstable mode that is a direct consequence of this overshoot. The structure of this new class of modes in the small wavenumber limit is detailed, providing a valuable confirmation of our numerical results obtained from the full inviscid eigenvalue problem.

Conserved integrals for inviscid compressible fluid flow in Riemannian manifolds

An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow in curved Riemannian manifolds in n >1 dimensions. All corresponding kinematic constants of motion are also determined, along with all Hamiltonian kinematic symmetries and kinematic Casimirs which arise from the Hamiltonian structure of the inviscid compressible fluid equations.

A Mathematical Model for a Vibrating Human Head

In this paper, a mathematical model has been formulated to study the vibration of the human head. In the mathematical analysis of the model, the skull is considered as an anisotropic spherical shell and brain matter is represented as an inviscid compressible fluid. Also, in the model, the translational acceleration is considered as a general function of time. The authors use the method of Laplace transformation to achieve the analytical solution of the problem, while the analytical expressions have been used to compute the stress distribution in the system by resorting to numerical techniques.

Damping of Flexural Vibration by Low-Density Foams and Granular Materials

The damping of flexural vibration by introduction of a layer of low-density foam or powder into a structure is investigated. First, we report on experiments in which a layer of foam attached to an aluminum beam gives rise to significant damping at frequencies high enough to induce standing waves in the foam layer. Next, we provide a simple model for such vibration in which the foam is treated as a two-dimensional elastic continuum in which waves can propagate and find that the model is in good agreement with the experiments. Then the results of experiments in which aluminum beams are filled with a low-density powder are presented. The powder-filled beams exhibit behavior qualitatively like that of the foam-filled beams, but we find that the powder can be adequately modeled as an inviscid compressible fluid.