. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography Electric and magnetic fields 53 Hydrodynamic equations. The linearized equations of motion for free barotropic water waves (Lamb 1945) are and duy dC, ct cy and the continuity equation is at ox cy where u^ and Uy are the horizontal particle velocities in the directions x and y respectively, C is the wave height and / is the Coriolis parameter assumed constant. Kelvin wave solution. The Kelvin wave solution (Lamb 1945) is "-m ,-(//(u) Ay pi(*x-c
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography Electric and magnetic fields 53 Hydrodynamic equations. The linearized equations of motion for free barotropic water waves (Lamb 1945) are and duy dC, ct cy and the continuity equation is at ox cy where u^ and Uy are the horizontal particle velocities in the directions x and y respectively, C is the wave height and / is the Coriolis parameter assumed constant. Kelvin wave solution. The Kelvin wave solution (Lamb 1945) is "-m ,-(//(u) Ay pi(*x-cor) and Wy = 0, where /=(—1)*, k is the longshore wave number, co the frequency, and co/k = (gli)^ > 0. For the northern hemisphere these waves propagate only in the positive -Y direction. One sees that the particle motion is always parallel to the coastline and dies away exponentially from the coast. Also, the vertical motion at the surface compared with the horizontal motion is —ikh so that the vertical motion, for low frequencies, can be ignored. Comparison of Kelvin nave with lunar tidal observations along western North America. The Mj tidal amplitudes and phases for exposed coastal tide stations along western North America are given in Fig. 5. The values are plotted as a function of distance south from Vancouver, B. C. From the 6th point (San Francisco) to the 14th point (central Baja California) the Mj amplitude is nearly constant at 0-50 m and the phase changes almost uniformly as the tide sweeps northward along the coast. The magnitude and direction of the longshore phase velocity is consistent 300 200-. J± 200 m/s 0 f Voncojver Avilo Beoch'°°° Nouiicol miles -T- rlO 0 5 -J 2 Mazotlon •-0 2000 Fig. 5. Lunar Mi tide along western North America as a function of distance south from Vancouver, along the rumb line, 148 °T, parallel to the central Cali- fornia coast. Open circles are amplitudes and solid circles arc phase leads relative to zero hour, 1965 Januar
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