Related papers: A novel approach for deriving the stable boundary …
We investigate the boundary-value problem of atmospheric Ekman flows with piecewise-uniform eddy viscosity. In addition we present a method for finding more general solutions by considering eddy viscosity as an arbitrary step-function. We…
Theoretical analyses of the hurricane boundary layer have traditionally relied on slab models, which provide a limited description of wind profiles. Literature on height-resolving methods is typically based on linear analyses, which may…
In this work, eddy diffusivity is derived from the energy spectra for the stable and convective regimes in the planetary boundary layer. The energy spectra are obtained from a spectral model for the inertial subrange that considers the…
The boundedness of stable solutions to semilinear (or reaction-diffusion) elliptic PDEs has been studied since the 1970's. In dimensions 10 and higher, there exist stable energy solutions which are unbounded (or singular). This note…
Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses…
This is our response to a comment by Walter Eifler on our paper `A simple model for the short-time evolution of near-surface current and temperature profiles' (arXiv:physics/0503186, accepted for publication in Deep-Sea Research II).…
We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer representation, which is valid for conventionally neutral (CNBL) and…
We perform a linear and entropy stability analysis for wall boundary condition procedures for discontinuous Galerkin spectral element approximations of the compressible Euler equations. Two types of boundary procedures are examined. The…
To date no satisfying model exists to explain the mean velocity profile within the whole turbulent layer of canonical wall bounded flows. We propose a modification of the velocity profile expression that ensues from a recently proposed…
For a general class of hyperbolic-parabolic systems including the compressible Navier-Stokes and compressible MHD equations, we prove existence and stability of noncharacteristic viscous boundary layers for a variety of boundary conditions…
The construction of Ekman boundary layer solutions near the non-flat boundaries presents a complex challenge, with limited research on this issue. In Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483], the Ekman…
The aim of this study is to improve the prediction of near-wall mean streamwise velocity profile $U^+$ by using a simple method. The $U^+$ profile is obtained by solving the momentum equation which is written as an ordinary differential…
We are concerned with stable solutions to reaction-diffusion elliptic PDEs. We begin with regularity questions, first addressing the classical Laplacian. In joint work with Figalli, Ros-Oton, and Serra, we proved that stable solutions are…
We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier-Stokes equations we derive a second order weighted residual integral boundary layer equation,…
Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system…
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather…
We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equations with inflow [outflow] boundary conditions, under the…
An eigenvalue equation, for linear instability modes involving large scales in a convective hydromagnetic system, is derived in the framework of multiscale analysis. We consider a horizontal layer with electrically conducting boundaries,…
Oleinik's \emph{no back-flow} condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain $R\subset \mathbb{R}^2$. It also allowed us to find a limit formula for Dorodnitzyn's stationary…
Sediment transport over wave-induced ripples is a very complex phenomenon where available models fail to provide accurate predictions. For coastal engineering applications, the 1-DV advection-diffusion equation could be used with an…