Downslope Windstorms - RAL - UCAR

Long’s Hydraulic Jump (1953a)
Long’s Hydraulic Jump (1953a)
• Homogeneous fluid flowing over
ridge-like obstacle. Assume flow is
in hydrostatic balance and
bounded by free surface.
• Consider y-independent motions
• Assume steady-state flow.
u
∂
∂
u
x
+
g
∂
∂
D
x
+
g
∂
∂
h
x
= 0
Where D is the thickness of the fluid
and h is the obstacle height.
Using the continuity equation
1 ∂ ( D + h ) ∂ h
∂ ( uD )
(1 − ) =
Most people Interpret Fr
2
= 0
Fr ∂ x ∂ x
2
as the Froude #. Here it is
we get:
a ratio of the fluid speed to
∂ x
where
the propagation speed of
shallow linear gravity waves
2
2 u
Fr
=
gD
So the free surface can either rise or
fall depending on the magnitude of Fr 2