Wave friction factor rediscovered

Abstract

The wave friction factor is commonly expressed as a function of the horizontal water particle semi-excursion (Awb) at the top of the boundary layer. Awb, in turn, is normally derived from linear wave theory by UwbTw 2p , where Uwb is the maximum water particle velocity measured at the top of the boundary layer and Tw is the wave period. However, it is shown here that Awb determined in this way deviates drastically from its real value under both linear and non-linear waves. Three equations for smooth, transitional and rough boundary conditions, respectively, are proposed to solve this problem, all three being a function of Uwb, Tw, and δ, the thickness of the boundary layer. Because these variables can be determined theoretically for any bottom slope and water depth using the deepwater wave conditions, there is no need to physically measure them. Although differing substantially from many modern attempts to define the wave friction factor, the results coincide with equations proposed in the 1960s for either smooth or rough boundary conditions. The findings also confirm that the long-held notion of circular water particle motion down to the bottom in deepwater conditions is erroneous, the motion in fact being circular at the surface and elliptical at depth in both deep and shallow water conditions, with only horizontal motion at the top of the boundary layer. The new equations are incorporated in an updated version (WAVECALC II) of the Excel program published earlier in this journal by Le Roux et al. Geo-Mar Lett 30(5): 549– 560, (2010).