ü) = angular velocity of earth
(7.29 x 10"5 radians/second);
= geographical latitude;
rsx» Tsy = x and y components of surface wind stress;
= x and y components of bottom stress;
p = mass density of water;
Wæ, Ww = x and y components of wind speed;
Ç = atmospheric pressure déficit in head of water;
ç = astronomical tide potential in head of water;
u, v = x and y components, respectively, of current
velocity;
P = précipitation rate (depth/time);
g = gravitational accélération; and
6 = angle of wind measured counterclockwise from
the x axis.
Equations 3-50 and 3-51 are approximate expressions for the équations
of motion and Equation 3-52 is the continuity relation for a fluid of
constant density. These basic équations provide, for ail practical purposes, a complété description of the water motions associated with nearly
horizontal flows such as the storm surge problem. Since these équations
satisfactorily describe the phenomenon involved, a nearly exact solution
can only be obtained by usîng these relations in complété form.
It is possible to obtain useful approximations by ignoring some tenus
in the basic équations when they are either équivalent to zéro or are
negligible, but accurate solutions can be achieved only by retaining the
full two-dimensional characteristics of the surge problem. Various simplifications (discussed later) can be made by ignoring some of the physical processes. These simplifications may provide a satisfactory estimate,
but they must always be considered as only an approximation.
In the past, simplified methods were used extensively to evaluate
storm surge because it was necessary to make ail computations manually.
Manual solutions of the complété basic équations in two dimensions were
prohibitively expensive because of the enormous computational e fort.
With high speed computers, it is possible to résolve the basic hypodynamie relations efficiently and economically. As a resuit of comp
several workers hâve recently developed useful mathematical mo e
computing storm surge. These models hâve substantially improved accuracy,
and provide a meansfor évaluâting the surge in the two horizontal dimensions. These more accurate methods. are not covered here, but are highly
recommended for resolving storm-surge problems where more exaetness
3-95
(7.29 x 10"5 radians/second);
rsx» Tsy = x and y components of surface wind stress;
= x and y components of bottom stress;
p = mass density of water;
Wæ, Ww = x and y components of wind speed;
Ç = atmospheric pressure déficit in head of water;
ç = astronomical tide potential in head of water;
u, v = x and y components, respectively, of current
velocity;
P = précipitation rate (depth/time);
g = gravitational accélération; and
6 = angle of wind measured counterclockwise from
the x axis.
Equations 3-50 and 3-51 are approximate expressions for the équations
of motion and Equation 3-52 is the continuity relation for a fluid of
constant density. These basic équations provide, for ail practical purposes, a complété description of the water motions associated with nearly
horizontal flows such as the storm surge problem. Since these équations
satisfactorily describe the phenomenon involved, a nearly exact solution
can only be obtained by usîng these relations in complété form.
It is possible to obtain useful approximations by ignoring some tenus
in the basic équations when they are either équivalent to zéro or are
negligible, but accurate solutions can be achieved only by retaining the
full two-dimensional characteristics of the surge problem. Various simplifications (discussed later) can be made by ignoring some of the physical processes. These simplifications may provide a satisfactory estimate,
but they must always be considered as only an approximation.
In the past, simplified methods were used extensively to evaluate
storm surge because it was necessary to make ail computations manually.
Manual solutions of the complété basic équations in two dimensions were
prohibitively expensive because of the enormous computational e fort.
With high speed computers, it is possible to résolve the basic hypodynamie relations efficiently and economically. As a resuit of comp
several workers hâve recently developed useful mathematical mo e
computing storm surge. These models hâve substantially improved accuracy,
and provide a meansfor évaluâting the surge in the two horizontal dimensions. These more accurate methods. are not covered here, but are highly
recommended for resolving storm-surge problems where more exaetness
3-95