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So on land, I believe that one factor in their formation is due to inhomogeneities in surface heating between land and ocean (and also inhomogeneities in surface heating due to terrain effects like the Rocky Mountains).
But what about in the ocean, where we don't see such inhomogeneities? How is the formation and movement of Rossby Waves in ocean different from that of land?
First, inhomogeneities in the ocean are in fact quite common. There are density gradients in both horizontal and vertical directions and those gradients result in the baroclinic circulation of the ocean. The density gradients in the ocean are caused by salinity and temperature differences.
Rossby waves are common in the ocean. They propagate along lines of latitude with the waves traveling along the Equator being the most obvious example and the most thoroughly studied. As in the case of atmospheric Rossby waves, their formation and propagation is related to the conservation of (potential) vorticity (rotational movement, angular momentum). A parcel of water has two sources of vorticity: its own spin and the planetary spin. When a parcel of water moves across a latitudinal line, its planetary spin (planetary vorticity) changes (as the Coriolis effect is latitudinally dependent) and, in order to conserve vorticity, it changes its own spin (relative vorticity). The water parcel tends to swing back and forth around the original latitude resulting in a wave-like motion. A Rossby wave is characterized by a westward phase velocity (that of the wave crests).
To add to the excellent answer by aretxabaleta:
This is what happens for eastward flow over a step change in depth. Note that the wavy pattern is seen from above, and it veers right due to the step and the conservation of potential vorticity (and the fact it is in the Northern Hemisphere). Similar to a particle displaced from its equilibrium in a buoyancy field, the particle veers right towards the latitude that is its new equilibrium point. However, due to its momentum it overshoots the equilibrium latitude. When it returns, the same happens and so on forever (in linear terms), thus giving origin to the wave.
(from kundu)
First of all, Rossby wave forms not only in the ocean, but also in the atmosphere (even in magma). It is a feature of fluids on rotating planets.
Maybe you can try to understand Rossby wave by appreciating the analogy between (internal) gravity wave and Rossby wave.
Two distinct features of geofluid are stratification and (differential) rotation. Stratification, or vertical variation of density, produces internal gravity wave. Similarly, differential rotation (or variation of rotation), gives rise to (barotropic) Rossby wave. Their difference can not be easily identified by observing the tracer (temperature, density etc.) field in the figure below, without knowing the coordinates.
Vertical decreasing density with altitude gives a fluid parcel a restore force when it is displaced upward/downward; Likewise, meridionally increasing rotation also gives a restore force when a parcel is displaced northward/southward. Therefore, a fluid parcel cannot move freely in the vertical and meridional directions due to these restore forces (you probably already notice that the contours of many things on rotating planets are horizontal lines or zonal lines). Such restoring forces actually generates respectively the internal gravity wave and Rossby wave. The gradient of potential temperature (density of mass), as well as the gradient of potential vorticity (density of rotation) here is a measurement of the restoring force.
