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<p>Analytical and numerical solutions of the Linearized Rotating Shallow Water Equations are combined to study the geostrophic adjustment on the mid-latitude <em>β</em>-plane. The adjustment is examined in zonal periodic channels of width <em>Lᵧ</em> = 4<em>R<sub>d</sub></em> (‘narrow’ channel, where <em>R<sub>d</sub></em> is the radius of deformation) and <em>Lᵧ</em>=60<em>R<sub>d</sub></em> (‘wide’ channel) for the particular initial conditions of a resting fluid with a step-like height distribution, <em>η</em>₀. In the one-dimensional case, where <em>η</em>₀ = <em>η</em>₀(<em>y</em>) we find that: (i) <em>β</em> affects the geostrophic state (determined from the conservation of the meridional vorticity gradient) only when <em>b </em>= cot (<em>Φ</em>₀) <em>R<sub>d </sub></em>/<em>R</em> ≥ 0.5 (where <em>Φ</em>₀ is the channel’s central latitude and <em>R</em> is Earth’s radius); (ii) The energy conversion ratio varies by less than 10 % when <em>b</em> increases from 0 to 1; (iii) In ‘wide’ channels, <em>β</em> affects the waves significantly even for small <em>b</em> (e.g. <em>b</em> = 0.005). (iv) For <em>b</em> = 0.005, harmonic waves approximate the waves in ‘narrow’ channels, and trapped waves approximate the waves in ‘wide’ channels. In the two-dimensional case, where <em>η</em>₀ = <em>η</em>₀(<em>x</em>) we find that: (i) At short times the spatial structure of the steady solution is similar to that on the <em>f</em>-plane, while at long times the steady state drifts westward at the speed of Rossby waves – harmonic Rossby waves in ‘narrow’ channels and trapped Rossby waves in ‘wide’ channels; (ii) In ‘wide’ channels, trapped wave dispersion causes the equatorward segment of the wavefront to move faster than the northern segment; (iii) The energy of Rossby waves on the <em>β</em>-plane approaches that of the steady-state on the <em>f</em>-plane; (iv) The results outlined in (iii) and (iv) of the one-dimensional case also hold in the two-dimensional case.</p>