3 Wave Model
Enhancements of the wave model in the original NMLong involved
introducing the full interaction between currents and waves, and describing
the action of the roller formed by breaking waves on the momentum transport
in the surf zone. This section documents these enhancements, in particular,
the wave-current interaction. For additional treatment on the wave
transformation calculations, reference is made to Kraus and Larson (1991).
The presence of a steady-state current may modify the waves propagating
on it in several ways:
. Basic properties
of the waves change
. Wave transformation changes (e.g.,
c. Waves may be blocked by the current.
d. Waves may break because of excessive steepening due to shoaling.
For example, the wavelength will be shorter and longer for opposing and
following currents, respectively, as compared to the situation commonly
calculated of no current. The presence of gradients in a current field will
cause propagating waves to refract and shoal, sometimes inducing wave
breaking or even blocking of the waves. It is not only the waves that are
modified by the current, but typically the current is also modified by the
waves. This is obvious in the case of wave-generated currents in the surf
zone, but also currents of other types (e.g., wind and tide) are influenced by
the waves through increased friction and mixing of momentum.
In describing wave propagating on a current, it is convenient to employ
two different frames of reference, an absolute frame where an observer
remains fixed with respect to the current and wave motion, and a relative
frame where the observer travels with the waves. In the following theoretical
discussion, the subscript "a" denoted quantities in the absolute frame, and the
subscript "r" denoted quantities in the relative frame. Much of the discussion
here is extracted from work by Jonsson and his colleagues, and their work
can be consulted for a more general and extensive treatments on the topic of
interaction between currents and waves (Jonsson, Skovgaard, and Wang
1970; Jonsson 1978; Jonsson and Skovgaard 1978; Jonsson and
Christoffersen 1984; Jonsson 1990).
Chapter 3 Wave Model