Capturing the flow beneath water waves

Abstract

Recently, the authors presented two numerical studies for capturing the flow structure beneath water waves (Nachbin and Ribeiro-Junior 2014 , 3135-3153 (doi:10.3934/dcds.2014.34.3135); Ribeiro-Junior 2017 , 792-814 (doi:10.1017/jfm.2016.820)). Closed orbits for irrotational waves with an opposing current and stagnation points for rotational waves were some of the issues addressed. This paper summarizes the numerical strategies adopted for capturing the flow beneath irrotational and rotational water waves. It also presents new preliminary results for particle trajectories, due to irrotational waves, in the presence of a bottom topography.This article is part of the theme issue 'Nonlinear water waves'.

Surface waves over currents and uneven bottom

“…In some parts of the ocean, due to volcanic activity, the seabed is not even a stationary structure. Numerous studies are dedicated to the wave motion over an uneven bottom (Johnson, 1973a(Johnson, ,b, 1997Nachbin, 2003;Craig et al,2005a;Dejak and Sigal, 2006;de Bouard et al, 2008;Compelli et al, 2017;Nachbin and Ribeiro-Jr., 2018). In the majority of the existing publications however, the fluid is irrotational, i.e.…”

Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

“…[17][18][19][20]. The effect of the topography on the flow structure beneath the surface of a water wave has been investigated in [21].…”

Dispersion relations for steady periodic water waves of fixed mean-depth with two rotational layers

“…Following the ground-breaking papers of Constantin and Strauss [3,12], the study of rotational water flows with a fixed mass-flux received significant attention-evidentiated by an abundance of works on issues like symmetry [1,2,5,33,52], stability [6], regularity [11,13,21,22,24,25], stratification [20,27,30,32,34,59,60], the presence of stagnation points and critical layers [13,17,19,20,48,53,58]-much less has been done in the scenario of the fixed mean-depth. The fixedness of the meandepth is a perspective, of physical relevance, proposed by Henry, cf.…”