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P. Liu
the seafloor. The water particle is on a vertical plane, with a uniform circular
motion. The center of the circle is a certain distance above the position of
the particle at rest. Water particles located on the same horizontal plane at
rest forms the wave surface during waving. Water particles on the same wave
surface have equal radius r of circular motion and at the water surface r =
h/2. But in the vertical direction, the r decreases sharply from the water
surface. When the water particle moves in a circle, the angle between the
radial line and the upward vertical line is the phase angle θ. At the same time
particle, on any wave surface, the phase angle decreases along with the direction of the wave as the distance increases. At the same time particle, the phase
angles of the water particles with the center of the circle on the same vertical
line are equal. This is shown in Fig. 3.86.
As shown in Fig. 3.87, we take the midline of the wave as x-axis, the positive direction is the wave propulsion direction. The positive direction of the
vertical axis z is along the downside. The center of the water mass particle
A is (x 0 , z 0 ). A moves at a constant speed around the center particle with
radius r, and its trajectory is
x = x 0 + r sin θ
z = z 0 − r cos θ
Fig. 3.86 The wave shape of circle trochoid curve with different water depth
Fig. 3.87 The establishment of trochoid curve
P. Liu
the seafloor. The water particle is on a vertical plane, with a uniform circular
motion. The center of the circle is a certain distance above the position of
the particle at rest. Water particles located on the same horizontal plane at
rest forms the wave surface during waving. Water particles on the same wave
surface have equal radius r of circular motion and at the water surface r =
h/2. But in the vertical direction, the r decreases sharply from the water
surface. When the water particle moves in a circle, the angle between the
radial line and the upward vertical line is the phase angle θ. At the same time
particle, on any wave surface, the phase angle decreases along with the direction of the wave as the distance increases. At the same time particle, the phase
angles of the water particles with the center of the circle on the same vertical
line are equal. This is shown in Fig. 3.86.
As shown in Fig. 3.87, we take the midline of the wave as x-axis, the positive direction is the wave propulsion direction. The positive direction of the
vertical axis z is along the downside. The center of the water mass particle
A is (x 0 , z 0 ). A moves at a constant speed around the center particle with
radius r, and its trajectory is
x = x 0 + r sin θ
z = z 0 − r cos θ
Fig. 3.86 The wave shape of circle trochoid curve with different water depth
Fig. 3.87 The establishment of trochoid curve