In this work, laminar transonic weakly three-dimensional flows at high Reynolds numbers in slender channels, as found in microsupersonic nozzles and turbomachines of micro-electro-mechanical systems, are considered. The channel height is taken so small that the viscous wall layers forming at the channel walls start to interact strongly rather than weakly with the inviscid core flow and, therefo...

We discuss two important topics of turbulence theory: inviscid limit and decay of the Fourier spectrum for the 2-D dissipative quasi-geostrophic (QGS) equations. In the first part we consider inviscid limits for both smooth and weak solutions of the 2-D dissipative QGS equations and prove that the classical solutions with smooth initial data tend to the solutions of the corresponding non-dissip...

In this paper we present analytical studies of three-dimensional viscous and inviscid simplified Bardina turbulence models with periodic boundary conditions. The global existence and uniqueness of weak solutions to the viscous model has already been established by Layton and Lewandowski. However, we prove here the global well-posedness of this model for weaker initial conditions. We also establ...

We study the large time asymptotic speeds (turbulent flame speeds sT ) of the simplified Hamilton-Jacobi (HJ) models arising in turbulent combustion. One HJ model is G-equation describing the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are HJ equations with convex (L...

The formation of lee wakes and vortices is explored in the context of stratified flow with uniform basic-state wind and stability past elongated free-slip ridges. The theory of inviscid flow past a ridge of small nondimensional height e is revisited using a weakly nonlinear semianalytic model to compute flow fields through O(e2). Consistent with previous work, the weakly nonlinear solutions sho...

The locomotion of a body through an inviscid incompressible fluid, such that the flow remains irrotational everywhere, is known to depend on inertial forces and on both the shape and the mass distribution of the body. In this paper we consider the influence of fluid viscosity on such inertial modes of locomotion. In particular we consider a free body of variable shape and study the centre-of-ma...

[1] The response of Hadley circulations to displacements of the latitude of maximum heating is investigated in idealized axisymmetric and eddy-permitting models. Consistent with an earlier study and with theory for the nearly inviscid limit (Lindzen and Hou, 1988), the strength of the Hadley circulation is sensitive to displacements of heating: the winter cell strengthens and summer cell weaken...

This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos–Leroux–Nedelec, we give a constructio...

The dynamics of one-dimensional, overdriven, hydrogen-air detonations predicted in the inviscid limit as well as with the inclusion of mass, momentum, and energy diffusion were investigated. The effect of resolution was studied for both shock-capturing and shockfitting in the inviscid limit, and it was found that shock-capturing required four times the amount of resolution of shock-fitting to p...

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In [22], Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler an...