The following mathematical formula (Equation 1) explains how wave height and lake depth change the orbital velocity of the water, and hence the applied forces on the lake bottom due to wave action.
w = [(πH)/T]ekz sin(kx – ωt)(1)
where w = orbital velocity (m s–1), H = wave height (m), T = wave period (s), k = wave number (2π/L; m–1), L = wave length (m), z = depth of observation (negative in the column; m) and ω = radian wave frequency (2π/T; s–1), x is the point or place of observation of the wave (m) in the horizontal direction and t is time of observation(s).
If wave period and wave number variables remain constant, then the variables which affect the force of waves are: (1) H – wave height; (2) z – depth of lake; and (3) [ekz sin(kx – ωt)] – which is the periodic component of wave velocity and a function of the natural variability of forces within a wave. The periodic component has a (periodic) maximum at values of x equal to 0·25L and 0·75L, between crest and trough when the elevation of the water surface is zero. The periodic component has decreasing relative influence on orbital velocity as the water depth increases (Schutten et al., 2004).