相关论文: Turbulent boundary layer equations
The transitional boundary layer flow over a flat plate is investigated. The boundary layer flow is known to develop unstable Tollmien-Schlichting waves above a critical value of the Reynolds number. However, it is also known that this…
The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient…
This paper concerns the validity of the Prandtl boundary layer theory for steady, incompressible Navier-Stokes flows over a rotating disk. We prove that the Navier Stokes flows can be decomposed into Euler and Prandtl flows in the inviscid…
This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\times \mathbb{R}_{+}$, assuming…
The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…
In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier Stokes equations. We then recall classical physical instability results, and give a short educational…
The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to…
We compute the solutions of Prandtl's and Navier-Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl's equation develops, in a finite…
In a series of papers (see \cite{CDT02} and the pertinent references therein) the 3D Navier-Stokes-$\alpha$ model were shown to be a useful complement to the 3D Navier-Stokes equations; and in particular, to be a good Reynolds version of…
We present an extended version of an invited talk given on the International Conference "Turbulent Mixing and Beyond". The dynamical and statistical description of stably stratified turbulent boundary layers with the important example of…
An irrotational solution is derived for the steady-state Navier-Stokes equations that approximately satisfies the boundary conditions for flow over a finite flat plate. The nature of the flow differs substantially from boundary layer flow,…
Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of…
The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
Approximate analytical solution of two dimensional problem for stationary Navier-Stokes, continuity and Fourier-Kirchhoff equations describing free convective heat transfer from isothermal surface of half infinite vertical plate is…
This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the…
We discuss a simple analytical model of the turbulent boundary layer (TBL) over flat plane. The model offers an analytical description of the profiles of mean velocity and turbulent activity in the entire boundary region, from the viscous…
In this paper, we investigate the asymptotic behavior of solutions to the Navier-Stokes equations in the half-plane under high Reynolds number conditions, where the initial vorticity belongs to the Yudovich class and is supported away from…
We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions.