3 Hydrodynamics
255
Fig. 3.80 G. de Vries, (1866–1934, Dutch mathematician)
cosine wave is generally used in shallow water, solitary wave is generally used
in nearshore shallow water and the peak energy of periodic wave accounts
for more than 90% of the total wave energy, and micro amplitude wave is
generally used in deepwater, However, for the limited water depth area, the
situation is more complex, and the application range of various wave theories
intersects here, so it is necessary to analyze according to the actual conditions
to select the appropriate wave theory.
(1) Potential wave equation
Micro amplitude wave theory is a linear wave theory which studies wave
motion from potential function. The basic assumption is that the water is
ideal and incompressible (most wave motion, this assumption is reasonable);
the mass force acting on the particle is only gravity (only to discuss the gravity
wave). When the free surface is in the equilibrium position, set it as xoy plane,
and Z is vertical upward, then the Euler equations representing the movement
of water particle are
∂u
∂t
+ u
∂u
∂ x
+ v
∂u
∂ y
+ w
∂u
∂z
= −
1
ρ
∂ p
∂ x