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These are corrections known so far. If you have a question or find an apparent error, please email the author.

44.563This argument for strictly barotropic flow far from shore requires both that 1) the wind stress far from shore does not vary in the cross-shelf direction, and 2) that the Coriolis parameter f is a constant. If f is not constant, baroclinic Rossby waves can extend far from the coast. These two conditions should have been stated at the outset of this argument.
55.2, equ. 5.2.8a,b71This expression for the phase velocity is derived by projecting the scalar phase speed ω/(k2 + l2)1/2 onto the direction of the vector wavenumber (k, l). This is the definition used, for example, by Whitham (1974) and by Wunsch (2015). It has several pleasing properties such as the phase velocity equaling the group velocity in the nondispersive (high frequency for Poincaré waves) limit.

However, the problem with this definition is that it is not consistent with the verbal definition of the phase velocity in the text immediately following eqns. 5.2.8: phase velocity describes the rate at which wave crests (for example) propagate in the x and y directions. Carefully tracking the wave crests (e.g., Pedlosky, 1979) leads to

c_p^x= ω/k , c_p^y= ω/l (5.2.8c, d)

The applicability of this consistent definition can be readily appreciated by considering a wave that propagates almost exactly in the x direction. In this case, the y wavenumber approaches zero and the wave crests move very rapidly in the y direction. In the limit of propagation exactly in the x direction (l = 0), the y component of phase velocity is infinite: wave crests arrive everywhere in y at the same time. One difficulty with this definition is that it lacks vector properties such as the ability to undergo coordinate rotation sensibly.

Whitham, G.B., 1974. Linear and Nonlinear Waves. John Wiley & Sons, New York, 636pp.

5Line 15102"In" should be "in"