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- W2802973071 abstract "In high-order analysis and simulation of long–short surface wave interaction using mode decomposition, ‘divergent’ terms of the form $k_{S}a_{L}=O(unicode[STIX]{x1D6FE}unicode[STIX]{x1D716})gg 1$ appear in the high-order expansions, where $k_{L,S}$ , $a_{L,S}$ are respectively the long, short modal wavenumbers and amplitudes, with $unicode[STIX]{x1D6FE}equiv k_{S}/k_{L}gg 1$ and $k_{L}a_{L}sim k_{S}a_{S}=O(unicode[STIX]{x1D716})$ finite. We address the effect of these terms on the numerical scheme, showing numerical cancellation at all orders $m$ ; but increasing ill-conditioning of the numerics with $unicode[STIX]{x1D6FE}$ and $m$ , which we quantify. In the context of mode decomposition, we show theoretical exact cancellation of the divergent terms up to $m=3$ , extending the existing result of Brueckner & West ( J. Fluid Mech. , vol. 196, 1988, pp. 585–592) and supporting the conjecture that this is obtained for all orders $m$ . We show the latter by developing a theoretical proof for any $m$ using a Dirichlet–Neumann operator and mathematical induction. The implication of the theoretical proof on the numerical simulation of long–short wave interaction is discussed." @default.
- W2802973071 created "2018-05-17" @default.
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- W2802973071 date "2018-05-11" @default.
- W2802973071 modified "2023-10-18" @default.
- W2802973071 title "On high-order perturbation expansion for the study of long–short wave interactions" @default.
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- W2802973071 doi "https://doi.org/10.1017/jfm.2018.296" @default.
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