Ice-coupled waves in weakly random, inhomogeneous sea ice

The passage of ice-coupled flexural waves is modelled in an ice sheet that has a weak random variation about its mean thickness. To do this, small changes in thickness are synthesized into a parameter mu(x) that captures spatial change in the sea ice, where mu(x) is a normalized centred Gaussian random variable that varies in the direction of propagation. By defining a deep water velocity potential phi(x, y) proportional to X(x)e(k(1+epsilon mu(x))y) where epsilon is a small quantity, x is the propagation direction and y is the vertical coordinate, we obtain to first order an equation for the x-component d(2)X(x)/dx(2) + k(2)(1 + epsilon mu(x))X(x) = 0 This equation is solved formally in this paper.