Simple hydrodynamic treatment of ocean tides

A dynamical picture of the oceanic tides

“…Let q 1 (t) be the normal coordinate describing the first forced oscillation whose elliptical shape is characterized by a major axis oriented along the earth-sun line ͑and in the perpendicular direction after a half period͒, and let q 2 (t) be the normal coordinate describing the second oscillation with the axis inclined 45°to the earth-sun line. A disturbance of the water surface caused by the first oscillation can be described by ⌬r 1 (,t)ϭq 1 (t)cos (2), which gives the small vertical displacement of the surface at an arbitrary point (r 0 ,) of the equator. Similarly, the second oscillation causes a distortion of the surface described by ⌬r 2 (,t)ϭq 2 (t)sin (2).…”

“…A disturbance of the water surface caused by the first oscillation can be described by ⌬r 1 (,t)ϭq 1 (t)cos (2), which gives the small vertical displacement of the surface at an arbitrary point (r 0 ,) of the equator. Similarly, the second oscillation causes a distortion of the surface described by ⌬r 2 (,t)ϭq 2 (t)sin (2). The forced oscillations experienced by the normal coordinates q 1 (t) and q 2 (t) are periodic ͑steady-state͒ partial solutions of the two differential equations:…”