the wave orthogonals. This condition, in fact, corresponds to wave blocking,

discussed in the following paragraphs.

As can be seen from Equation 6, the wave angle α must be known before

the wave properties can be calculated. Here, Snell's law is employed to

between two locations with different depth and current characteristics,

denoted with index 1 and 2, Snell's law may be expressed as (Jonsson and

Skovgaard 1978):

sin α1 sin α2

=

(11)

In calculating the wave properties at location 2, assuming all quantities are

known at location 1, Equations 6 and 11 are solved simultaneously because

both α and *L *are unknown at the new location.

In Equation 1, the wave energy dissipation must be estimated before the

wave transformation can be calculated. As previously stated, only the

is normally much larger than the dissipation due to friction in the bottom

boundary layer *P*f. Wave breaking occurs because the wave form is not

stable for the existing hydrodynamic and topographic conditions. In shallow

water, the topography typically induces the breaking (called depth-limited

breaking). However, in the presence of a current, the hydrodynamic

conditions may cause the waves to break because the wave steepness exceeds

a critical limit (steepness-limited breaking). Typically, for depth-limited

breaking a criterion on the maximum wave height to water depth is employed

(e.g., *H*/*d *= 0.78, where *H *is the wave height), whereas for steepness-limited

breaking the maximum wave steepness is used (e.g., *H*/*L *= 1/7).

The Miche criterion (Miche 1951), as modified by Battjes and Janssen

(1978), provides a reliable estimate of the maximum wave height before

breaking, including both hydrodynamic and topographic controls on the

waves (i.e., includes both steepness- and depth-limited breaking). This

maximum wave height is given by,

(12)

where γb is the maximum ratio between wave height and water depth in

shallow water (depth-limited breaking), typically taken to be 0.78 (done here

also). Thus, the asymptotes of Equation 12 for shallow and deep water are

depend on wave steepness (e.g., Kaminsky and Kraus 1994), but introduction

of such a dependence would require yet another iteration between waves and

for a database comprising more than 400 measurements from a variety of

15

Chapter 3 Wave Model

Integrated Publishing, Inc. |