Exact relations between Laplacian of near-wall scalar fields and surface quantities in incompressible viscous flow

Abstract

In this short paper, we derive the on-wall values and the wall-normal derivatives of the Laplacians of pressure and kinetic energy density at the wall for incompressible viscous flow past a stationary wall. The theoretical results reveal some interesting on-wall coupling pairs that are composed of the fundamental surface physical quantities (including skin friction, surface vorticity and surface pressure) and surface curvature. The exact results are valid for flow past any stationary curved wall, which are valuable for understanding the near-wall viscous flow very close to the wall.