Models for damped water waves

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free bound- ary problems formulated in the works of Dias, Dyachenko and Zakharov (Physics Letters A, 2008 ), Jiang, Ting, Perlin and Schultz (Journal of Fluid Mechanics,1996 ) and Wu, Liu and Yue (Journal of Fluid Mechanics, 2006 )

Models for damped water wave

In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative effects and are obtained from the free boundary problems formulated in the works of Dias, Dyachenko, and Zakharov [Phys. Lett. A, 372 (2008), pp. 1297--1302], Jiang et al. [J. Fluid Mech., 329 (1996), pp. 275--307], and Wu, Liu and Yue [J. Fluid Mech., 556 (2006), pp. 45--54].The work of the second author was supported by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2017-0718 and through project MTM2017-82184-R funded by (AEI/FEDER, UE) and acronym “DESFLU.

On the motion of gravity-capillary waves with odd viscosity

We develop three asymptotic models of surface waves in a non-Newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves, while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional modelR.G-B was supported by the project “Mathematical Analysis of Fluids and Applications” Grant PID2019-109348GA-I00 funded by MCIN/AEI/ 10.13039/501100011033 and acronym “MAFyA.” This publication is part of the project PID2019-109348GA-I00 funded by MCIN/ AEI /10.13039/501100011033. R.G-B is also supported by a 2021 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation. The BBVA Foundation accepts no responsibility for the opinions, statements, and contents included in the project and/or the results thereof, which are entirely the responsibility of the authors

Traveling Waves In Deep Water with Gravity And Surface Tension

This paper is concerned with the simulation of periodic traveling deep-water freesurface water waves under the influence of gravity and surface tension in two and three dimensions. A variety of techniques is utilized, including the numerical simulation of a weakly nonlinear model, explicit solutions of low-order perturbation theories, and the direct numerical simulation of the full water wave equations. The weakly nonlinear models which we present are new and extend the work of Akers and Milewski [SIAM J. Appl. Math., 70 (2010), pp. 2390–2408] to arbitrary Bond number and fluid depth. The numerical scheme for the full water wave problem features a novel extension of the “Transformed Field Expansions” method of Nicholls and Reitich [Euro. J. Mech. B Fluids, 25 (2006), pp. 406–424] to accommodate capillary effects in a stable and rapid fashion. The purpose of this paper is apply the new numerical method, then compare small amplitude solutions of potential flow with those of the approximate model. Particular attention is paid to the behavior near quadratic resonances, an example of which is the Wilton ripple