Chapter III
Numerical Modeling
31
Table III-1 Symbols and Significations in Continuity and Momentum Equations.
The horizontal stress terms are described using a gradient-stress relationship, which is simplified
as follows:
Equation III-4
Equation III-5
The surface and bottom boundary conditions for u, v, and w are as follows:
Equation III-6
Equation III-7
Equations of wave action conservation
The fundamental equation that describes wave action is the equilibrium equation, expressed in
either Cartesian or spherical coordinates.
Symbol
Signification
Symbol
Signification
t
Time.
A
Horizontal viscosity.
Pa
Atmospheric pressure.
g
Gravity acceleration.
x. y , z
Cartesian coordinates.
í µí½ í µí²
Water density.
η
Surface elevation.
í µí±º í µí²í µí² ,í µí±º í µí²í µí²
í µí±º í µí²í µí² ,í µí±º í µí²í µí²
Component of the radial tensor.
d
Water depth.
í µí½ í µí²
Turbulent vertical viscosity.
h = η+d
Total water depth.
í µí½ í µí¿
The reference density of water.
u, v , w
Velocity components in the
x, y, and z directions.
S
Amplitude of discharge caused by
point sources.
(í µí² í µí² ,í µí² í µí² )
Velocity at which water is
discharged into the ambient
water.
f = 2Ω sinΦ Coriolis parameter {Ω is the
angular velocity and Φ is the
geographical latitude}.
(í µí½ í µí²í µí² , í µí½ í µí²í µí² ) x and y components of
surface wind stress.
(í µí½ í µí²í µí² ,í µí½ í µí²í µí² )
x and y components of bottom
wind stress.
Numerical Modeling
31
Table III-1 Symbols and Significations in Continuity and Momentum Equations.
The horizontal stress terms are described using a gradient-stress relationship, which is simplified
as follows:
Equation III-4
Equation III-5
The surface and bottom boundary conditions for u, v, and w are as follows:
Equation III-6
Equation III-7
Equations of wave action conservation
The fundamental equation that describes wave action is the equilibrium equation, expressed in
either Cartesian or spherical coordinates.
Symbol
Signification
Symbol
Signification
t
Time.
A
Horizontal viscosity.
Pa
Atmospheric pressure.
g
Gravity acceleration.
x. y , z
Cartesian coordinates.
í µí½ í µí²
Water density.
η
Surface elevation.
í µí±º í µí²í µí² ,í µí±º í µí²í µí²
í µí±º í µí²í µí² ,í µí±º í µí²í µí²
Component of the radial tensor.
d
Water depth.
í µí½ í µí²
Turbulent vertical viscosity.
h = η+d
Total water depth.
í µí½ í µí¿
The reference density of water.
u, v , w
Velocity components in the
x, y, and z directions.
S
Amplitude of discharge caused by
point sources.
(í µí² í µí² ,í µí² í µí² )
Velocity at which water is
discharged into the ambient
water.
f = 2Ω sinΦ Coriolis parameter {Ω is the
angular velocity and Φ is the
geographical latitude}.
(í µí½ í µí²í µí² , í µí½ í µí²í µí² ) x and y components of
surface wind stress.
(í µí½ í µí²í µí² ,í µí½ í µí²í µí² )
x and y components of bottom
wind stress.