The Influence of Surface Waves on the Stability of a ... - aerade

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APPJ3NDMI
Calculation <strong>of</strong> Velocltg Pr<strong>of</strong>Iles on a
Wavy <strong>Surface</strong> with As.ymptotlc SudiOn
Consuler the boundary layer flow over a wavy surface, with free
stream velocity U at infknty and U, at the edge <strong>of</strong> the boundary
2F.x
layer. <strong>The</strong> height <strong>of</strong> the surface 1s gIvenby y = h cos - , where
h. ( L )
E 1s small and its square negllglble.
where H+
<strong>The</strong> equations <strong>of</strong> motion and <strong>of</strong> momentum are respectively
$+ (H+2) U, a -&= au +
If non-dz.menslons.1 variables defined by
Ul
0
au
dy,-iiy'
u1 = u s 27cc VY ve
u ) v'=vs, x'=y , Y - "
l--H, ,t=s Y
are mtmduced, the equations maybe wrl'cten
2
au,’
u’ au’.
ax’ u =Qi-ui dx’+
0 2 UL auf _
0’ a;,
s+ (H+2) -
u1 tm-
VS
“s UL ii&
(7 U zEdy'2
(2)
(3)
(4)
-(g ~[-+(&y&q] (5)
Dropping the primes, end introducing the non-dimensional parameter
-9-
(6)