Page 128 - Fundamentals of Ocean Renewable Energy Generating Electricity From The Sea

Wave Energy Chapter | 5 119

FIG. 5.4 Range of validity of various wave theories. The controlling factors are water depth (x
axis), wave height (y axis), and wave breaking. (Based on a figure first presented by B. Le Méhauté,
An Introduction to Hydrodynamics and Water Waves, Springer, New York, NY, 1976.)

Miche’s breaking limit criterion, which was proposed in 1944, can approxi-
mately predict wave breaking in deep or shallow waters [7]. It can be written as
follows,
kH b
= 1 (5.41)
γ tanh kd
where H b is the breaking wave height and γ is a constant parameter. In shallow
water, wave breaking occurs due to a decrease in water depth and shoaling (see
Section 5.2.1). Looking at Fig. 5.2, in shallow waters, tanh kd ≈ kd, which
results in the following breaking limit criterion:
kH b H b
= 1 → = γ ≈ 0.7−0.8 (5.42)
γ kd d
In deep waters (see Fig. 5.2), tanh kd ≈ 1; therefore, Miche’s formula leads to
the following relation: