Bottom drift due to periodic shallow water waves

Abstract

This paper deals with the transport of neutrally buoyant bottom particles suspended in fluid under the influence of periodic nonlinear surface waves. A comparison is made with existing solitary wave theory, and an explanation is given for discrepancies between theory and data.

Mass transport in the bottom boundary layer of cnoidal waves

“…These are, respectively, and Substitution of (4.6) and (4.7) in turn into (4.5) and simplification to maintain the present order of approximation gives (3.2) and (3.5) respectively. Thus the results of Spielvogel & Spielvogel(1974) are in agreement with those derived in 9 3.…”

“…Le M6hautA (1968) has used the cnoidal theory of Laitone (1960) to calculate the mass transport for cnoidal waves assuming an inviscid fluid, and he has found it to be invariant with depth. Using an alternative approach, Spielvogel & Spielvogel (1974) have derived an expression for the mass transport near the bed, but this does not correspond to Le M6hautB's results. Furthermore, these various expressions are somewhat arbitrary, depending on the definition of wave speed adopted for the irrotational flow.…”

“…This result was also obtained by Longuet-Higgins (1958, equation (20)), who showed, moreover, that it is independent of the vertical distribution of viscosity and so may apply to turbulent flow as well. Spielvogel & Spielvogel (1974) have derived an expression for the mass transport near the bed for cnoidal waves under the assumption of an inviscid fluid. In our notation, their expression is…”