L-c
Figure 4-1. Two-dimensional wavy channel between a flat plate at the top and a sinusoidal plate
at the bottom. Also indicated are the coordinate system and the channel geometries,
including wavelength L, wave amplitude A, and average channel width H.
(a)
p(x 7, y)
#(x- 7.y)
(b)
C
Y
(x + r, y)
A(x+r, y)
A
D
4'- P(x)
Figure 4-2. Boundary conditions and contour path used in the analytical solution. (a) One
period of a wavy channel with boundary condition at both ends. (b) Contour path for
the Cauchy integral over one period of a wavy channel.
1