(a) Quasi-Static Method for Prédiction of Hurricane Surge.
This method for determining open-coast storm surge is based on theoretical
approximations of the governing hydrodynamic équations originally proposed
by Freeman, Baer, and Jung (1957). The term quasi-static method is used
here to emphasize that this method should be restricted to slow-moviug,
large-scale storm Systems. This method is called the Bathystrophic Storm
Tide Theory and, unlike earlier one-dimensional théories, some of the
effects of longshore flow and the apparent Coriolis force are considered.
Such an approximation of the theory can be described as a quasi-static
method in which a numerical solution is obtained by successively integrating wind stresses over the Continental Shelf from its seaward edge to the
shore for a predetermined interval of time.
This simplified method assumes that storm surge responds instantaneously to the onshore wind stresses, advection of momentum can be ignored,
longshore sea surface is uniform, and no flow is assumed normal to the
shore which is treated as a seawall. Barometric effects and précipitation also can be neglected. Setup due to atmospheric pressure différence
can be estimated from another source, and added to the final design water
level. Based on the preceding assumptions, Equations 3-50 and 3-51 reduce
to
as
gD — =
ôx
~
SX
fV + —
P
dV _ rsy Tby
dt
P
(3-53)
(3-54)
Conservation of mass is not considered because, (1) there is no flow
perpendicular to shore, (2) the longshore flow is assumed independent of
y and, (3) the water level is assumed slowly changing. The forces (expressed in mass times accélération per unit area) involved and the corresponding response of the sea for the bathystrophic approximation are shown
in Figure 3-45. As indicated in the figure, the surface shear force acting in the x-direction tqa. and the apparent Coriolis force is balanced
by the hydrostatic pressure force pgA(9S/3x). Moreover, the surface shear
force acting in the y-direction
is balanced by the bottom shear
force
and the inertial force p(3V/3t).
Bretschneider and Collins (1963) developed a computational model
based on this Bathystrophic Theory and applied it to open-coast surge
Problems for the région around Corpus Christi, Texas. Marinos and
Woodward (1968) modified the Bretschneider and Collins model and calibrated it for- various reaches along the Texas coast by using three hurricanes
of record, and also made parametric studies of hypo-hurricane surges for
the entire coast of Texas.
In some cases the underlying assumptions made in the development of
this theory are not satisfied. Thus, as a conséquence of assuming that
the onshore wind stresses cause an instantaneous change of the water level,
i.e., u = 0, the traverse line (the line over the Continental Shelf along
which computations are carried out) must (zLwoye be taken perpendicular to
3-101
This method for determining open-coast storm surge is based on theoretical
approximations of the governing hydrodynamic équations originally proposed
by Freeman, Baer, and Jung (1957). The term quasi-static method is used
here to emphasize that this method should be restricted to slow-moviug,
large-scale storm Systems. This method is called the Bathystrophic Storm
Tide Theory and, unlike earlier one-dimensional théories, some of the
effects of longshore flow and the apparent Coriolis force are considered.
Such an approximation of the theory can be described as a quasi-static
method in which a numerical solution is obtained by successively integrating wind stresses over the Continental Shelf from its seaward edge to the
shore for a predetermined interval of time.
This simplified method assumes that storm surge responds instantaneously to the onshore wind stresses, advection of momentum can be ignored,
longshore sea surface is uniform, and no flow is assumed normal to the
shore which is treated as a seawall. Barometric effects and précipitation also can be neglected. Setup due to atmospheric pressure différence
can be estimated from another source, and added to the final design water
level. Based on the preceding assumptions, Equations 3-50 and 3-51 reduce
to
as
gD — =
ôx
~
SX
fV + —
P
dV _ rsy Tby
dt
P
(3-53)
(3-54)
Conservation of mass is not considered because, (1) there is no flow
perpendicular to shore, (2) the longshore flow is assumed independent of
y and, (3) the water level is assumed slowly changing. The forces (expressed in mass times accélération per unit area) involved and the corresponding response of the sea for the bathystrophic approximation are shown
in Figure 3-45. As indicated in the figure, the surface shear force acting in the x-direction tqa. and the apparent Coriolis force is balanced
by the hydrostatic pressure force pgA(9S/3x). Moreover, the surface shear
force acting in the y-direction
is balanced by the bottom shear
force
and the inertial force p(3V/3t).
Bretschneider and Collins (1963) developed a computational model
based on this Bathystrophic Theory and applied it to open-coast surge
Problems for the région around Corpus Christi, Texas. Marinos and
Woodward (1968) modified the Bretschneider and Collins model and calibrated it for- various reaches along the Texas coast by using three hurricanes
of record, and also made parametric studies of hypo-hurricane surges for
the entire coast of Texas.
In some cases the underlying assumptions made in the development of
this theory are not satisfied. Thus, as a conséquence of assuming that
the onshore wind stresses cause an instantaneous change of the water level,
i.e., u = 0, the traverse line (the line over the Continental Shelf along
which computations are carried out) must (zLwoye be taken perpendicular to
3-101