A note on some nonlinear water-wave experiments and the comparison of data with theory

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Abstract
The problem of the instability of a uniform, nonlinear, deep-water wave train to infinitesimal long-wave perturbations, first studied by Benjamin ' Feir (1967) and Benjamin (1967), is re-examined. It is found that the apparent discrepancy between the experimental and theoretical growth rates of the instability is associated with the experimental generation of waves which do not have the Stokes wave profiles assumed in the theory. Experimental and theoretical results relating the initial wave steepness and the most unstable long-wave perturbation are used to obtain a correction factor, which is found to account for the mismatch in wave forms and which resolves the discrepancy in growth rates. The results illustrate that, when theory is compared with experiments in which the values of certain higher-order (nonlinear) quantities must be deduced from measurements of first-order quantities, great care must be taken to ascertain that the experimental conditions and the theoretical assumptions are indeed compatible to the required order.

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