How many waves in a wave group?

F10.largeEven though single waves are the most widely studied, waves predominantly come in groups in the open ocean.  One of the questions raised by Julian Hunt in his talk was the number of waves in a wave group.  It is folklore that the seventh wave arriving at a beach is the largest.  Observations worldwide seem to show that this is correct with a margin of error of +/- 1 wave.  These observations have some scientific basis due to the occurrence of wave groups at sea.  Peter Janssen sketched the following argument.  Suppose the spectral density has a single peak with peak frequency w, and let s be the peak width.  If the Benjamin-Feir index (BFI) is greater than 1, the field is unstable, and will moderate to BFI about 1.  When BFI=1, then s/w is approximately 1.414 A, where A is the wavefield amplitude.  In the open ocean A is about .1, giving s/w approximately .1414.  The inverse is the number of waves which is approximately 7!  A more refined analysis is given in the paper of Slunyaev & Shrira (2013).  They show that the number of waves in a group can vary between 2 and 20 for various sea states; see Section 3.1 in the above reference. The above figure comes from the paper Did the Draupner wave occur in a crossing sea? by Adcock, Taylor, Yan, Ma & Janssen, PRSLA (2011).

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