NAME: 3) There is a class of long-period water waves known as "Edge Waves" or "Infragravity Waves" which propagate parallel to the shoreline and are "trapped", i.e. they cannot propagate into deep water (see picture below). a) Formulate the linearized 3-D boundary value problem for edge waves on a planar beach. b) Show that the following velocity potential satisfies the formulation: p(x, y, z, t) = A cos (y) exp{-[(x cosB) - (z sin)]} elat where A is a constant, b is the longshore wave length, and is the bottom slope. c) Develop an expression for the free surface displacement, n(x,y,t). d) Develop the dispersion relation for the solution. If = 90, how does it compare to the "usual" dispersion relation developed in Chapter 3 of the book. INFRAGRAVITY WAVE - MODE O Y b 3