Mean flow modeling in high-order nonlinear Schrödinger equations

• Published in: Physics of fluids (1994) 2023-08, Vol.35 (8)
• Main Authors: Gomel, Alexis, Montessuit, Corentin, Armaroli, Andrea, Eeltink, Debbie, Chabchoub, Amin, Kasparian, Jérôme, Brunetti, Maura
• Format: Article
• Language: English
• Subjects: Evolution; Fluid dynamics; Flumes; Intermediate water; Mathematical models; Modelling; Ocean currents; Particle trajectories; Physics; Pollution transport; Schrodinger equation; Slopes; Water depth; Water waves; Wave groups; Wave propagation
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/5.0164784

The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of pollutants in the ocean to the estimation of energy and momentum exchanges between the waves at small scales and the ocean circulation at large scale. We derive an expression of the mean flow at a finite water depth, which, in contrast to other approximations in the literature, accurately accords with the deep-water limit at third order in steepness and is equivalent to second-order formulations in intermediate water. We also provide envelope evolution equations at fourth order in steepness for the propagation of unidirectional wave groups either in time or space that include the respective mean flow term. The latter, in particular, is required for accurately modeling experiments in water wave flumes in arbitrary depths.