Review of Selected Literature

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the interaction between currents and waves and the modeling of the roller in

the surf zone are of central interest. Also, a summary is given of studies that

involved laboratory and field data collection on nearshore currents.

Kraus and Larson (1991) and Larson and Kraus (1991) provide a detailed

theoretical background to NMLong, including a comprehensive verification

of the model. The literature to 1991 was comprehensively reviewed. The

references in those publications may be consulted for a more general

discussion of the basic equations employed in the modeling of the cross-shore

distribution of waves, mean water level, and longshore current.

Wave-Current Interaction and Its Modeling

Bretherton and Garrett (1969) showed that, for waves propagating on a

current, it is the wave action, defined as the wave energy divided by the

intrinsic (relative) frequency, that is conserved and not wave energy. The

wave action equation that they derived is the starting point for modeling

wave transformation in the presence of a current. Jonsson, Skovgaard, and

Wang (1970) studied waves propagating on a steady current and derived the

linear dispersion relation for waves on a current. Conditions for wave

blocking, that is, when an opposing current prevents the waves from traveling

further, were established. Jonsson (1978) further discussed the wave action

equation, and Jonsson and Skovgaard (1978) included energy dissipation

(e.g., due to breaking or friction in the bottom boundary layer) in this

equation. Furthermore, Jonsson and Skovgaard (1978) studied wave

refraction across a shearing current, and Jonsson and Christoffersen (1984)

expanded this study to encompass varying depth. Jonsson (1990) made a

comprehensive review of the interaction between waves and a current. In the

next chapter, the theoretical foundation for NMLong-CW is discussed, and a

significant amount of the material was adapted from or inspired by the

Jonsson (1990) review.

A few engineering numerical models that employ the wave action

equation to simulate wave transformation in the presence of a current have

previously been presented. Southgate (1987, 1989) developed a one-

dimensional computational model to simulate waves, wave-induced currents,

and tidal currents in coastal regions. The wave action equation was solved to

obtain the cross-shore distribution of wave heights, including energy dissipa-

tion due to wave breaking and bottom friction. The method proposed by

Chapter 2 Brief Literature Review