68
Figure 5.3: Non-dimensional longshore velocities vresus the non-dimensional distance off
shore from the analytical solution of Longuet-Higgins. Reprinted from Longuet-Higgins
(1970b), Journal of Geophysical Research, vol. 75(33) page 6793, copyright by the Ameri
can Geophysical Union.
from the various frequency components once breaking is initiated.
5.2 Longshore Currents
Longuet-Higgins (1970b) gives an analytical solution for the longshore current generated
by obliquely incident waves on a plane beach. The solution involves a spilling breaker
assumption and assumptions concerning the form of the bottom friction and the lateral
mixing. For steady state conditions the y equation of motion reduces to a balance between
the gradient of the Sxy term and the bottom friction with the lateral mixing serving to
distribute the current. Details of the solution can be found in the cited paper.
Figure 5.3 gives the results of the analytical solution of Longuet-Higgins. In the figure
the ordinate V is the non-dimensional velocity v/v0, where t; is the actual velocity and v0
is the velocity at the breaking point obtained for the case of no lateral mixing.
5jt. .isinfl .
v0 =--(fffis)i (5.6)
O C
The abscissa X is the non-dimensional distance z/n, where ij is the distance from the