SCALING RELATIONSHIPS FOR SAND WAVE DEVELOPMENT IN UNIDIRECTIONAL FLOW

Sand wave development on an initially flat bottom under steady unidire ctional flow is examined on the basis of laboratory measurements. A co mmon scaling relationship P-0(t)/P-e = (t/T)(alpha) is proposed for th e length and height of waves [P-0(t) and P-e denote the average length or height of sand waves after time t and in an equilibrium state that is attained after time T]. A similar relationship sigma(z)(delta x, t )/sigma(z0) = (t/T)(alpha)f[(delta x/delta x(0))/(t/T)(alpha/H)] is pr oposed to describe the scaling behavior of the root-mean-square deviat ions sigma(z)(delta x, t) of bottom elevation Z(x, t). Here, sigma(z0) is sigma(z)(delta x, t) when delta x greater than or equal to delta x (0), and t greater than or equal to T, and delta x(0) is delta x(0) wh en the function sigma(z)(delta x, T) becomes saturated, i.e., during t he transition from the regime where sigma(z) proportional to delta x(H ) to the regime where sigma(z) = sigma(z0) scaling exponents alpha and H equaled 0.28 and 1.0, respectively, for the laboratory experiments.