We study the low Mach low Freude numbers limit in the compressible Navier-Stokes equations and the transport equation for evolution of an entropy variable – the potential temperature Θ. We consider the case of well-prepared initial data on ”flat” tours and Reynolds number tending to infinity, and the case of ill-prepared data on an infinite slab. In both cases, we show that the weak solutions t...

We report research experience in applying an Unsteady Reynolds-Averaged Navier-Stokes (URANS) solver for the prediction of time-dependent flows in the presence of an active flow control device. The configuration under consideration is a synthetic jet created by a single diaphragm piezoelectric actuator in quiescent air. Time-averaged and instantaneous data for this case were obtained at Langley...

We investigate the nonlinear dynamics of turbulent shear flows, with and without rotation, in the context of a simple but physically motivated closure of the equation governing the evolution of the Reynolds stress tensor. We show that the model naturally accounts for some familiar phenomena in parallel shear flows, such as the subcritical transition to turbulence at a finite Reynolds number and...

We are interested in a model for diphasic fluids in thin flows taking into account both the hydrodynamical and the chemical effects at the interface between the two fluids. A limit problem in “thin films” is introduced heuristically. It is a system coupling the Reynolds equation and the hydrodynamical Cahn-Hilliard equation. We study the mathematical properties of this system, and prove an exis...

(i) For laminar flow (1) has been derived in [7] for f = −H ′′. A first analysis of that case is in [6]. Moreover this equation is also considered in the context of shock profiles in plasmas [2]. (ii) For turbulent flow in a certain distinguished limit concerning the Reynolds number and the Froude number eq. (1) has been derived in [3,4] with f = H . A multiple scales analysis of the full flow ...

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear...

Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerk...