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In a turbulent boundary layer over a smooth flat plate with zero pressure gradient, the intermediate structure between the viscous sublayer and the free stream consists of two layers: one adjacent to the viscous sublayer and one adjacent to…
The Navier boundary condition for velocity slip on flat surfaces, when expressed in tensor form, is readily extended to surfaces of any shape. We test this assertion using molecular dynamics simulations of flow in channels with flat and…
This paper investigates the steady axisymmetric structure of the cold boundary-layer flow surrounding fire whirls developing over localized fuel sources lying on a horizontal surface. The inviscid swirling motion found outside the boundary…
In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary…
In an incompressible velocity field, the surface area of a volume varies with time, but volume remains unchanged. If incidentally the surface becomes spherical along time, the area reaches a local minimum, since sphere has the least area…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
In this paper axisymmetric solutions of the Navier-Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in…
This paper is concerned with the validity of the Prandtl boundary layer theory in the inviscid limit of the steady incompressible Navier-Stokes equations, which is an extension of the pioneer paper (Y. Guo et al., 2017, Ann. PDE) from a…
Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field $\bm{u}$ when the system is segregated into two phases (at low temperatures) with a sharp interface between them. $\bm{u}$…
In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall is proposed. Unlike existing approaches, the proposed transformation successfully…
The classical Prandtl-Batchelor theorem (Prandtl 1904; Batchelor 1956) states that in the regions of steady 2D flow where viscous forces are small and streamlines are closed, the vorticity is constant. In this paper, we extend this theorem…
In this paper, the solutions of Navier-Stokes equations with Dirichlet boundary conditions governing 2-D incompressible fluid flows are considered. A condition for boundary layer separation, which is determined by initial values and…
We consider a mathematical model for the interactions of an elastic body fully immersed in a viscous, incompressible fluid. The corresponding composite PDE system comprises a linearized Navier-Stokes system and a dynamic system of…
In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…
We develop a neutral vortex fluid theory on closed surfaces with zero genus. The theory describes collective dynamics of many well-separated quantum vortices in a superfluid confined on a closed surface. Comparing to the case on a plane,…
Dependence of boundary layer thickness on layer height in laminar and transient regimes is studied for convection from localised heat source with an open surface. The measurements of Nusselt number and characteristic frequency of thermal…
We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition,…
We analyze the steady motion of a viscous incompressible fluid in a three-dimensional channel containing an obstacle through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by a fairly general datum and the…
In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…