Cyclone and Storm Surge - Iczmpwb.org

4.19
because the water level is of primary importance. Integrating (1) to (3) in the vertical from z = − h to z = ζ
and using conditions (5) to (7) one gets:
∂ζ
∂
∂
+ [( ζ + h)
u] + [( ζ + h)
v] = 0
∂t
∂x
∂y
(8)
∂u
∂u
∂u
1 ⎡ ∂
2
2
∂
⎤
+ u + v − f v+
⎢ ( ζ + h)(
u -u
) + ( ζ + h)(
uv−uv)
⎥
∂t
∂x
∂y
( ζ + h)
⎣∂x
∂y
⎦
∂ζ
1 ∂pa
1
= −g
− + [ Fs−FB]
∂x
ρ ∂x
( ζ + h)
ρ
(9)
∂v
∂v
∂v
1 ⎡ ∂
∂
+ u + v + f u + ⎢ ( ζ + h)(
uv−u v)
+
∂t
∂x
∂y
( ζ + h)
⎣ ∂x
∂y
∂ζ
1 ∂pa
1
=- g − + [ Gs
−GB]
∂y
ρ ∂y
( ζ + h)
ρ
2 2
⎤
( ζ + h) ( v −v
) ⎥
⎦
(10)
where: over bars denote the depth averaged values, e. g.,
1
( u,
v)
=
( ζ + h)
ζ
∫
- h
( u,
v)d
z,
(11)
ζ
2
(
2 2
1
2
u , v ) = ( u , v )d z,
( ζ + h)
∫
- h
(12)
1
( uv)
=
( ζ + h)
ζ
∫
- h
uv
d z,
(13)
In most of the storm surge simulation models, the non-linear advective terms have been neglected
mainly on the basis of scale analysis. This is justifiable when the characteristic amplitude of the surge is
smaller than the characteristic depth of the basin. But in shallow water regions, particularly at the head of
the Bay of Bengal, the non-linear terms are of special importance and must be retained in the