Break-away separation for high turbulence intensity and large Reynolds number

Massive flow separation from the surface of a plane bluff obstacle in an incompressible uniform stream is addressed theoretically for large values of the global Reynolds number Re. The analysis is motivated by a conclusion drawn from recent theoretical results which is corroborated by experimental findings but apparently contrasts with common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation never attains a fully developed turbulent state, even for arbitrarily large Re. Consequently, the boundary layer exhibits a certain level of turbulence intensity that is linked with the separation process, governed by local viscous-inviscid interaction. Eventually, the latter mechanism is expected to be associated with rapid change of the separating shear layer towards a fully developed turbulent one. A self-consistent flow description in the vicinity of separation is derived, where the present study includes the predominantly turbulent region. We establish a criterion that acts to select the position of separation. The basic analysis here, which appears physically feasible and rational, is carried out without needing to resort to a specific turbulence closure

Dissipative Waves in Fluids Having Both Positive and Negative Nonlinearity

The present study examines weakly dissipative, weakly nonlinear waves in which the fundamental derivative changes sign. The undisturbed state is taken to be at rest, uniform and in the vicinity of the 0 locus. The cubic Burgers equation governing these waves is solved numerically; the resultant solutions are compared and contrasted to those of the invisced theory. Further results include the presentation of a natural scaling law and inviscid solutions not reported elsewhere

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

CISM Course on Nonlinear Waves in Real Fluids

The study of materials which exhibit new and unconventional properties is of central importance for the devel- opment of advanced and refined technologies in many fields of engineering science. In this connection there has been a rapidly growing interest in real fluid effects on wave phenomena in the past few years. A prominent example is provided by Bethe-Zel'dovich-Thompson (BZT) fluids which have the distinguishing feature that they exhibit negative nonlinearity over a finite range of temperature and pressures in the pure vapour phase. However, two phase flows with and without phase change are an even richer source of new unexpected and previously thought impossible phenomena. Topics covered by this volume include waves in gases near the critical point, waves in retrograde fluids, temperature waves in superfluid helium and density waves in suspensions of particles in liquids. Clearly, the aim of the various contributions is twofold. First, they are intended to provide scientists and engineers working in these and related areas with an overview of various new physical phenomena as for example expansion shocks, sonic shocks, shock splitting, evaporation and liquafaction shocks and the experimental techniques needed to study these phenomena. Second, an attempt is made to discuss aspects of their mathematical modeling with special emphasis on properties which these phenomena have in common

On the non-linear distortion of waves generated by flat plates under harmonic excitations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23086/1/0000003.pd