2D Stokes Flow in a Lid-Driven Cavity

cavity aspect ratio (W/H) =

0.2

0.25

0.5

0.75

1

2

3

4

This Demonstration illustrates the steady eddy structure in a 2D driven cavity problem (see [2] and [3]). The stream lines, which at steady state are everywhere tangent to the velocity field, are computed from the stream function (

ψ

) and vorticity (

ω

) formulation for Stokes flow

2

∇

ψ=-ω,

2

∇

ω=0

,

subject to the no-slip boundary conditions along the cavity walls. The lid of the cavity moves at unit speed (in appropriate dimensionless variables) from left to right in the figure. You can change the aspect ratio

γ

of the cavity to explore the eddy structure. As the aspect ratio

γ

(which is width/height) is decreased beyond some critical value, a series of counter-rotating eddies appear in the cavity. Above the critical value (

γ

somewhere between 0.7 and 0.5), there is a single primary eddy; below the critical value there are two or more primary eddies at almost equal spacing. (Moffat eddies, an infinite sequence of eddies of ever-decreasing intensity, always exists at the lower corners of the cavity.)