202
5 Wave Evolution in Non-uniform Currents in Deep Water
Y
a)
Fig. 5.20. Trajectories of wave packet propagating against current velocity profile
(a) and (b); depth background (c) for different quadrants at points A and B; V(x)
-current velocity profile; H(x) -depth profile
The wave components can exist at the same point A in quadrant II if
they are reflected at the point x*: x < x* < Xm. This means that there is
a trajectory point x* being a turning point of the wave packet propagation
direction. The component of the group velocity Cgx is zero with kx = 0 at this
point. After having been reflected the wave packet can reach the given point x,
in the case of the current velocity value formally satisfying the inequality
V < V* < Vm,
(5.72)
where V is the current velocity at the given point x; V* is the velocity at the
turning point x; and Vm is the maximum current velocity.
5 Wave Evolution in Non-uniform Currents in Deep Water
Y
a)
Fig. 5.20. Trajectories of wave packet propagating against current velocity profile
(a) and (b); depth background (c) for different quadrants at points A and B; V(x)
-current velocity profile; H(x) -depth profile
The wave components can exist at the same point A in quadrant II if
they are reflected at the point x*: x < x* < Xm. This means that there is
a trajectory point x* being a turning point of the wave packet propagation
direction. The component of the group velocity Cgx is zero with kx = 0 at this
point. After having been reflected the wave packet can reach the given point x,
in the case of the current velocity value formally satisfying the inequality
V < V* < Vm,
(5.72)
where V is the current velocity at the given point x; V* is the velocity at the
turning point x; and Vm is the maximum current velocity.