Asymptotic Analysis of the Motion of a Low-Viscous Liquid Filling Half the Cylindrical Cavity
Yu. V. Pivovarov
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: incompressible fluid, Navier-Stokes equations, slip condition, weak boundary layer, vorticity, stream function
Abstract
A problem related to the plane-parallel steady motion of a low-viscosity incompressible fluid that fills half a rotating cylindrical cavity is under consideration. The Navier slip condition is imposed on the fluid - solid wall interface, and the condition for the absence of tangential stresses is imposed on the free boundary. The equation of the boundary layer considered on the entire boundary of the semicircle as a whole is reduced to a heat conduction equation by changing the variable. The solution to the problem is constructed in the form of a series, while the corner boundary layers are ignored. Calculations and comparisons with the solution built earlier using the finite difference method are performed.
|
