Cyclone and Storm Surge - Iczmpwb.org

4.17
constant, but depends on the strength and duration of the winds. The effects of strong wind blowing for a
few consecutive days are reflected in the rate of flow. Currents to the north-east generally persist longer
and flow at greater speed because of the stronger south-west monsoons. The vertical circulation in the
Bay of Bengal is the upwelling/downwelling process which is almost seasonal in nature.
4.7. Mathematical Formulation of Storm Surge
In the formulation of the model, the sphericity of the earth's surface is ignored. A system of rectangular
Cartesian coordinates is used in which the origin, O, is in the equilibrium level of the sea surface. Ox
points towards the east, Oy points towards the north and Oz is directed vertically upwards. The
displaced position of the free surface is given by z =ζ (x,y,t) and the position of the sea floor by z = −
h(x,y). Under these conditions, the basic hydrodynamic equations of continuity and momentum for the
dynamical process in the sea may be given by
∂u
∂x
∂v
+
∂y
∂w
+ = 0
∂z
(1)
∂u
∂u
∂u
∂ u
+ u + v + w −
∂t
∂x
∂y
∂z
fv =
1 ∂p
1 ∂τ
x
+
ρ ∂x
ρ ∂z
(2)
∂v
∂t
+
u
∂ v
∂x
+
v
∂v
∂y
+
w
∂v
∂z
+
fu
=
−
1 ∂p
ρ ∂y
+
1 ∂τ
ρ ∂z
y
(3)
∂w
+ u
∂t
∂w
∂w
∂w
+ v + w
∂x
∂y
∂z
1 ∂p
= −
ρ ∂z
− g
(4)
where,
u,v,w : Renolds averaged component of velocity in the direction of
x,y, and z respectively,
t : time,
p : pressure,
ρ : density of seawater assumed homogenous and incompressible,
f : Coriolis parameter, f = 2ωsinφ
g : acceleration due to gravity,