STORM SURGE

Composed of several attributes: A)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

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

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, ηb is the increase in water surface level and ΔP is the difference in atmospheric pressure from that far away and that at the storm center.

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

WIND STRESS Where ρ is the water density, Cf is a friction coefficient and W is the wind speed

WIND STRESS Determine the force balance acting on a column of fluid that is Δx wide and h+η w high Where the η w increase in water level due to wind stress

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) Assuming is small and taking the limit as the column width goes to zero, we are left with

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

WIND STRESS Assuming n = 1.2 and wind speed is 100 mph

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.

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.