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When gravity is the only restoring force, Eqn. 41, after taking the dot product with k and with , and some rearrangement becomes,

(44) 
where k_{z} is the component of k along z, and which further simplifies to,

(45) 
where θ_{z} is the angle between k and z, and ω_{BV} is the BruntVäisälä frequency,

(46) 
It is clear from Eqn. 45 that gravity waves are dispersive (v_{p} varies with wavelength), and anisotropic (v_{p} varies with k). In addition gravity waves can only propagate with angular frequencies less than ω_{BV} and cannot propagate vertically (θ_{z} ≠ 0). The group velocity is also perpendicular to the phase velocity such that when waves are upwardlypropagating, energy is downwardlypropagating.
James McAteer
20040114