An equatorially trapped wave that behaves like a mixture of gravity and Rossby waves. Yanai waves exhibit an eastward group velocity at all wave numbers k, although for large positive k is behaves like a Rossby wave and for large negative k like a gravity wave. For the case k=0 it is a standing wave for which the surface moves sinusoidally up and down with opposite sign on opposite sides of the equator. Fluid particles move anticyclonically around elliptical orbits. with eastward motion when the surface is elevated and westward motion when it is depressed. To be completed.