6.6. Breaking Progressive Waves

Both theoretical and empirical estimates for breaking waves are available. Reid and Bretschneider (1953) combine both theoretical and empirical breaking wave estimates to form a breaking index curve over three decades of dimensional water depth from deep- to shallow-water on the dimensional H _b /gT ² ?hb/gT ² dissection plane illustrated in Fig. 6.11. Separate theoretical wave breaking estimates are required for deep- and shallow-water as illustrated in Fig. 6.11, where the deep-water estimates are identified as Michell theory and are independent of the water depth h, and where the shallow-water estimates are identified as Solitary wave theory and vary linearly on the logarithmic axes with the depth of breaking h _b . Empirical estimates connect these two theoretical estimates in deep- and shallow-water over one decade of the dimensional breaking depth h _b /T ² between 0.3< hb/T ² <3.0.

Fig. 6.11: Wave breaking index dissection plane (Reid and Bretschneider, 1953).

Theoretical Wave Breaking Criteria

Two theoretical criterion have been identified to determine wave breaking; viz., kinematic and dynamic. Dean (1974) tabulates the relative error between the Dean Stream Function Theory and linear wave theory for each criterion.

Kinematic Wave Breaking Parameter ? _K

The kinematic wave breaking parameter is the ratio of the maximum horizontal water particle velocity u _C at the wave crest ? _C to the wave celerity C given by

Dynamic Wave Breaking Parameter ? _D

The dynamic wave breaking parameter is...