Validity of steady Prandtl layer expansions
Yan Guo, Sameer Iyer
Abstract
Abstract Let the viscosity for the 2D steady Navier‐Stokes equations in the region and with no slip boundary conditions at . For , we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer. Our uniform estimates in ε are achieved through a fixed‐point scheme: for solving the Navier‐Stokes equations, where are the tangential and normal velocities at , DNS stands for of the vorticity equation for the normal velocity v , and the compatibility ODE for at .
Topics & Concepts
Prandtl numberBoundary layerBlasius boundary layerMathematicsVorticityMathematical analysisOdeNavier–Stokes equationsTurbulent Prandtl numberBoundary value problemBoundary layer thicknessSlip (aerodynamics)MechanicsBoundary (topology)PhysicsVortexThermodynamicsNusselt numberCompressibilityReynolds numberTurbulenceHeat transferNavier-Stokes equation solutionsFluid Dynamics and Turbulent FlowsAdvanced Mathematical Modeling in Engineering