Internal equatorial water waves and wave–current interactions in the f-plane

Geophysical Equatorial Edge Wave with Underlying Currents in the f-Plane Approximation

“…From (20) and (21), we understand that the crest (and the troughs) lines are orthogonal to the shoreline and parallel each other. We can also see that the crest and the trough lines are monotonic curves.…”

“…Recently, Gerstner-type solutions have been derived and adapted to model a number of different physical and geophysical fluid dynamics [14][15][16]. These solutions were shown to incorporate constant underlying currents [17][18][19][20][21], with an analysis of the effects of the mathematical modification on the resulting physical flow properties. Constantin [22] presented an explicit edge wave solution.…”

On three-dimensional Gerstner-like equatorial water waves

“…recent work initiated by Constantin & Johnson [24][25][26][27] which is surveyed in this issue in [28]. Secondly, with regard to Gerstner-like (that is, explicit and exact) solutions, we refer to [29][30][31] for a discussion of geophysical edge-wave solutions; we do not discuss the restriction of β-plane solutions to the f -plane, which follows upon setting β = 0, and essentially reduces solutions from being three-dimensional to twodimensional in nature [32] (although an interesting exception are the fully three-dimensional solutions derived in [33][34][35][36] which exist solely in the f -plane setting). Finally, we refer to [11] for a recent extension of Pollard's nonlinear geophysical wave solution [37] which exists at all latitudes, whereby the authors accommodate a depth-invariant current and in the process generate a…”

Particle paths in equatorial flows

“…However, in one case we show that it is possible to recover a free-boundary flow in the form of trochoidal waves. Such trochoidal waves have been used extensively to model a wide variety of geophysical phenomena, (see [20,21,24,34] for various applications of trochoidal waves in the f -plane approximation).…”