STORM SURGE

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STORM SURGE
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STORM SURGE
Composed of several attributes

• Barometric Coastal water response to low
  pressure at center of storm
• B) Wind stress frictional drag of wind blowing
  over water (generally greatest but dynamic
  effects of moving storm can be substantial
• C) Coriolis (bathystrophic) associated with
  current steering
• D) Wave setup, water elevation rise do to wave
  breaking momentum

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BAROMETRIC
Pressure at bottom of ocean must be constant if
the water and storm are stationary (a very simple
model assuming a flat bottom and no dynamic
effects)
Dean and Dalrymple
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BAROMETRIC
Far away (l), the pressure at the bottom, -h is
At the center of storm (0), the pressure at the
bottom is
Where Pa is atmopspheric pressure far away, ?b is
the increase in water surface level and ?P is the
difference in atmospheric pressure from that far
away and that at the storm center.
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BAROMETRIC
For hydrostatic conditions, the pressure must be
equal or else there would be a net force and a
corresponding acceleration of fluid.
or
simplify
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WIND STRESS
Where ? is the water density, Cf is a friction
coefficient and W is the wind speed
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WIND STRESS
Determine the force balance acting on a column of
fluid that is ?x wide and h?w high Where the ?w
increase in water level due to wind stress
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WIND STRESS
The force balance is
Where the first term is the pressure times the
area (per unit length) on the left face the
second term is the same but for the right
face the third term is the surface wind shear,
times distance over which it acts the fourth term
is the bottom shear times distance over which it
acts (note sign)
is small and taking the limit as the column width
goes to zero, we are left with
Assuming
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WIND STRESS
Note that as the water depth becomes shallower,
the surface slope is larger for the same wind
stress. Compare storm surges on the gulf and
east coast with wide continental shelves versus
the west coast with a narrow continental
shelf If we assume a constant stress and
constant depth we can solve the steady state 1d
equation
n ranges from 1.15 1.30
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WIND STRESS
Assuming n 1.2 and wind speed is 100 mph
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Coriolis
Happens due to wind driven currents moving along
the coast. Due to Coriolis force they have a
steering component to the right in the northern
hemisphere and left in the southern hemisphere.
This component must be balanced by a pressure
gradient for steady state conditions
f is the Coriolis parameter equal to
where omega is the angular rotation rate of the
earth (7.272x10-5 rad/s) and phi is the latitude
(i.e. more important near the poles) V is the
magnitude of the depth-averaged storm generated
current running along the coast.
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Wave Setup
When waves break, they release/transfer their
momentum into the water column. The momentum
transfer creates a net force in the direction of
wave motion. This net force must be balanced by
an opposing force. Here it is a pressure
gradient in the mean water level known as wave
setup. Wave setup begins at the breaker line and
can be thought of as a constant sloping increase
in water level until the shore is
reached. Assuming the spilling breaker
assumption applies where the wave height is a
constant fraction of the water depth, often
assumed to be 0.78, but can range from 0.4 to
above 0.78, the relationship for the set up at
the still water level boils down to
Set up at still water level is about 20 of
breaker height.