Internal ISVA report on fifth-order Stokes wave shoaling
Jonsson and Arneborg (1995) combined energy flux and set-down in order to
make shoaling predictions for fourth-order Stokes waves with and without
a net volume flux. As the authors also present the governing equations
for fifth-order theory (the only difference lying in the wave number
equation), it is straightforward and tempting to investigate the effect
of introducing this higher order in the calculations. The fourth-order
results were recalculated and compared with those of Jonsson and Arneborg
and no deviations were found. The fifth-order results were compared with
the fourth-order results and the effects of introducing fifth-order
theory were in general found to be small. As expected, the deviation
increased with increasing wave steepness and decreasing depth. Also as
expected, an opposing current increased the deviations, whereas a
following current reduced the deviations. As a novelty, also, the
evolution with depth of the wave steepness was calculated.