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- W2078941439 abstract "The efficacy of perturbation approaches for short–long wave interactions is examined by considering a simple case of two interacting wave trains with different wavelengths. Frequency-domain solutions are derived up to third order in wave steepness using two different formulations: one employing conventional wave-mode functions only, and the other introducing a modulated wave-mode representation for the short-wavelength wave. For long-wavelength wave steepness and short-to-long wavelength ratio ε 1 and ε 3 respectively, the two results are shown to be identical for ε 1 [Lt ] ε 3 < 0.5. As ε 1 approaches ε 3 , the conventional wave-mode approach converges slowly and eventually diverges for ε 1 [Gt ] ε 3 . The loss of convergence is because the linear phase of conventional wave-mode functions is ineffective for modelling the modulated phase of the short wave. As expected, this difficulty can be removed by using a modulated wave-mode function for the short wave. On the other hand, for relatively large ε 3 ∼O(1), the conventional wave-mode approach converges rapidly while the slowly varying interaction between the two waves cannot be accurately predicted by the present modulated wave-mode approach. These findings have important implications to (time-domain) numerical simulations of the nonlinear evolution of ocean wave fields, and suggest that a hybrid wave model employing both conventional (for large-ε 3 interactions) and modulated (for small-ε 3 interactions) wave-mode functions should be particularly effective." @default.
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- W2078941439 date "1993-03-01" @default.
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- W2078941439 title "Effects of wavelength ratio on wave modelling" @default.
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- W2078941439 doi "https://doi.org/10.1017/s0022112093000709" @default.
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