An exact solution for equatorially trapped waves

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Some Nonlinear, Equatorially Trapped, Nonhydrostatic Internal Geophysical Waves (2014, background): “…periodic gravity water wave, where the particle paths are open loops in the absence of a current, and closed particle paths can only occur at a certain depth and only if there is a sufficiently strong adverse uniform current (see Constantin 2006; Henry 2008; Constantin and Strauss 2010).”
An Exact, Steady, Purely Azimuthal Equatorial Flow with a Free Surface (2016, background): “In these examples, and most others associated with exact solutions, it is possible to contrive a situation that comes close to the physical scenario relevant to the solution (see the discussion in Constantin 2012, 2014; Henry 2013; Hsu 2014).”
An Exact, Steady, Purely Azimuthal Flow as a Model for the Antarctic Circumpolar Current (2016, background): “approximation close to a fixed latitude (as in Pollard 1970; Mollo-Christensen 1979) or, for equatorial flows, the b-plane approximation (see Constantin 2012, 2014; Henry 2013; Hsu 2014; Ionescu-Kruse 2015). Recently, however, exact nonlinear solutions in spherical coordinates (so with a more precis”