Search results for "Turbulent Prandtl number"

showing 3 items of 3 documents

Existence and Singularities for the Prandtl Boundary Layer Equations

2000

Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.

Applied MathematicsMathematical analysisPrandtl numberComputational MechanicsReynolds numberBoundary layer thicknessPhysics::Fluid Dynamicssymbols.namesakeBoundary layerInviscid flowBlasius boundary layersymbolsTurbulent Prandtl numberReynolds-averaged Navier–Stokes equationsMathematicsZAMM
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High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

2013

Abstract 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 time, a separation singularity. We investigate the different stages of unsteady separation for Navier–Stokes solution at different Reynolds numbers Re = 103–105, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers Re = 104–105. We also investi…

D'Alembert's paradoxGeneral Computer SciencePrandtl numberMathematics::Analysis of PDEsFOS: Physical sciencesPhysics::Fluid Dynamicssymbols.namesakeMathematics - Analysis of PDEsHagen–Poiseuille flow from the Navier–Stokes equationsFOS: MathematicsSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematicsMathematical analysisGeneral EngineeringFluid Dynamics (physics.flu-dyn)Reynolds numberPhysics - Fluid DynamicsMathematical Physics (math-ph)Non-dimensionalization and scaling of the Navier–Stokes equationsBoundary layersymbolsTurbulent Prandtl numberReynolds-averaged Navier–Stokes equationsBoundary layer Unsteady separation Navier Stokes solutions Prandtl’s equation High Reynolds number flows.Analysis of PDEs (math.AP)
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Well-posedness of Prandtl equations with non-compatible data

2013

In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.

Well-posed problemApplied MathematicsPrandtl numberGeneral Physics and AstronomyStatistical and Nonlinear PhysicsNavier-Stokes equations Boundary Layer Theory.Physics::Fluid Dynamicssymbols.namesakesymbolsCalculusApplied mathematicsBoundary value problemTurbulent Prandtl numberSettore MAT/07 - Fisica MatematicaMathematical PhysicsWell posednessVariable (mathematics)Mathematics
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