This paper considers the description of a two dimensional wave tram propagating on an arbitrary current The bi-linear numerical model, first proposed by Dalrymple (1974), has been extended to incorporate a fire layered description of the flow field. This model allows an accurate representation of a strongly sheared current, and at the same time minimises the discontinuity In the vorticity profile A variety of wave current combinations are investigated, and it is shown that the time-averaged vorticity profile is an Important parameter In determining the non-linearity of the wave form In particular, the presence of a strongly sheared current at the water surface is shown to produce a significant increase In both the crest elevation and the wave induced velocity field. These changes cannot be predicted by a simple Doppler shifted solution based on an "equivalent" uniform current.

1. INTRODUCTION

The interaction between waves and currents is an important feature of most marine environments, and should be taken into account when describing the combined flow field Even In the simplest of situations, involving a linear wave and a uniform current, the combined kinematics cannot be represented by the linear sum of the wave and the current components. In all cases the wave form travels on top of the current profile. This creates an apparent Doppler shift which produces a change In the dispersive characteristics of the wave form. If the current profile is non-uniform (or depth varying) then the interactive process may become highly nonlinear and lead to the formation of a rotational wave component. Under these conditions the fluid velocity In the vicinity of a strongly sheared current may be much larger than the linear sum of the wave and the current components. This may have important implications for the structural design of an individual member subject to increased local velocities

If the current profile is sheared In the vicinity of the water surface the total overturning moment experienced by a structure can only be determined after the inclusion of the wave-current interaction Furthermore, the water surface elevation is dependent upon the non-linearity of the wave motion. The interaction with a current profile may therefore produce an increase In the crest elevation (for a given wave height) and a corresponding reduction In the "air gap" separating the lowest layers of the structure and the water surf ace.

The present paper will consider the equilibrium conditions resulting from the combination of waves and currents. The nonlinearity of the interaction will be described together with the characteristics of the combined flow field. This paper will not consider the initial propagation of the wave onto the current profile. This forms part of a transient condition In which there is a transfer of energy between the various components of the flow field This problem has already been considered by a number of authors including Longuet-Higgins and Stewart (1960, 1961), Rretherton and Garrett (1968), Brink-kjaer and Jonsson (1975) and Skop (1987a). A full discussion of these matters is given In the review articles by Feregrine (1976) and Jonsson (1990)

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