Search results for "Zero viscosity limit"

showing 5 items of 5 documents

Existence and uniqueness for Prandtl equations and zero viscosity limit of the Navier-Stokes equations

2002

The existence and uniqueness of the mild solution of the boundary layer (BL) equation is proved assuming analyticity of the data with respect to the tangential variable. Moreover we use the well-posedness of the BL equation to perform an asymptotic expansion of the Navier-Stokes equations on a bounded domain.

Bounday layer analysis zero viscosity limit Navier-Stokes equations
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High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex array

2008

Numerical solutions of Prandtl’s equation and Navier Stokes equations are considered for the two dimensional flow induced by an array of periodic rec- tilinear vortices interacting with an infinite plane. We show how this initial datum develops a separation singularity for Prandtl equation. We investigate the asymptotic validity of boundary layer theory considering numerical solu- tions for the full Navier Stokes equations at high Reynolds numbers.

PhysicsPrandtl numberMathematical analysisMathematics::Analysis of PDEsReynolds numberNon-dimensionalization and scaling of the Navier–Stokes equationsunsteady separationReynolds equationPhysics::Fluid DynamicsFlow separationsymbols.namesakeBoundary layerPrandtl equation interactive viscous–inviscid equation.Navier Stokes solutionsymbolszero viscosity limitNavier–Stokes equationsReynolds-averaged Navier–Stokes equationsSettore MAT/07 - Fisica Matematica
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Numerical study of the primitive equations in the small viscosity regime

2018

In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.

PhysicsSingularity tracking methodApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsPrimitive equationMechanicsSlip (materials science)Vorticity01 natural sciences010305 fluids & plasmasPhysics::Fluid DynamicsBoundary layerDipole0103 physical sciencesPrimitive equationsGravitational singularity0101 mathematicsZero viscosity limitPressure gradient
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Zero viscosity limit of the Oseen equations in a channel

2001

Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics.

Solution formulaApplied MathematicsPrandtl numberMathematical analysisMathematics::Analysis of PDEsAnalysiAsymptotic expansionEuler equationsComputational Mathematicssymbols.namesakeBoundary layerElliptic operatorBoundary layerAsymptotic expansion; Boundary layer; Oseen equations; Solution formula; Zero viscosity limit; Mathematics (all); Analysis; Applied MathematicssymbolsInitial value problemMathematics (all)Boundary value problemViscosity solutionOseen equationZero viscosity limitAnalysisOseen equationsMathematics
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Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions

2010

In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…

Unsteady Separation Phenomena High Reynolds Flows Navier-Stokes equations Prandtl equations zero viscosity limit Boundary Layer theorySettore MAT/07 - Fisica Matematica
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