DOMAINS OF VALIDITY FOR WAVE THEORIES
77
there is some overlapping with the higher-order Stokes theory domains and the
cnoidal theory domain. LeMehaute’s graph is particularly useful during preliminary engineering calculations since it indicates the possibility of employing
simple théories easily solvable on hand-held calculators.
The following numerical examples illustrate the utility of these graphs by
Dean and LeMehaute.
0.01
0.1
10
1
the free stream function fifth order theory is encompassed by the bold boundary Unes
(Le Mehaute, 1969).
Example Problem 3.1.
Find the maximum horizontal and vertical water
particle velocity at an élévation of 10 ft below the still waterline, in a wave that
has a period of 8 sec, a height peak to trough of 2 ft, and is propagating in a
constant water depth of 200 ft.
1. Deduce the appropriate theory by first computing the following flow
parameters:
d/T2 = 200/82 = 3.125 ft/sec2
77
there is some overlapping with the higher-order Stokes theory domains and the
cnoidal theory domain. LeMehaute’s graph is particularly useful during preliminary engineering calculations since it indicates the possibility of employing
simple théories easily solvable on hand-held calculators.
The following numerical examples illustrate the utility of these graphs by
Dean and LeMehaute.
0.01
0.1
10
1
the free stream function fifth order theory is encompassed by the bold boundary Unes
(Le Mehaute, 1969).
Example Problem 3.1.
Find the maximum horizontal and vertical water
particle velocity at an élévation of 10 ft below the still waterline, in a wave that
has a period of 8 sec, a height peak to trough of 2 ft, and is propagating in a
constant water depth of 200 ft.
1. Deduce the appropriate theory by first computing the following flow
parameters:
d/T2 = 200/82 = 3.125 ft/sec2