Vertical kinetic energy density plots, E_z, plotted for the modes labeled in the top panel of Fig. 1, which corresponds to solutions of Eq. (8) with H = 5 and k = 2. Each corresponding vertical velocity eigenfunction w is normalized, such that . Shown here: a) low-order body modes m₁,m₂ (solid and dashed lines respectively); b) low-order body mode m₃; c) fastest growing surface modes, (solid and dashed lines respectively), and d) a high-order body mode, . The lowest order body mode, m₁ is the fundamental corrugation mode that dominates the energy density, contained in the high-order body modes and the surface modes by, at least a factor of 10³. The energy density contained in the fundamental breathing mode (m₂) is a factor 10 less than the mode m₁.