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In fact, Biesel [Bi] performs a complete analysis of this situation. He finds that the following equations describe the motion of the surface waves:

y_x = x + r Asin(wt-	ó õ	k dx)+ar A₁ cos(wt-	ó õ	k dx)
y_y = r Bcos(wt-	ó õ	k dx)+ar B₁ sin(wt-	ó õ	k dx)

In this model a is the angle of incline of the beach and A,A₁,B,and B₁ are coefficients involving k and h. The motion described above is valid unless the wave reaches a breaking point.

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