Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Abstract

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.

References in corpus (3)

• Singularity formation for Prandtl's equations
• High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex
• Singularities of Euler flow? Not out of the blue!

Cited by in corpus (5)

• Energy dissipation caused by boundary layer instability at vanishing viscosity
• Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array
• Numerical study of the long wavelength limit of the Toda lattice
• Turbulence compressibility reduction with helicity
• Separation of the two-dimensional unsteady Prandtl boundary layers under an adverse pressure gradient