Talk:Tide: Difference between revisions

Since astronomical nodal frequencies are very precise and stable (well the important ones are) the tidal initial-value problem may be reduced to an elliptical boundary-value problem, by separation of variables. This implies that (assuming linearity) that the u and v components of velocity form a tidal vector ellipse. u=Ucos(omega*t+-p1) and v=Vsin(omega*t-p1). This always traces an ellipse with eccentricity U/V and the major axis aligned along p1. Near boundaries one of U or V will be very small, and the flow is back and forth along a line. Away from boundaries, the Coriolis will cause the flow rotation to be clockwise in NH, and opposite in SH. Tidal vectors are usually quoted this way. (If non-linearity is to be included, such as modelling a storm surge at a flood tide, then it must be solved as an IV problem.) Heights are quoted by amp and phase, relative to UTC.

Laplace's great achievement of the cutoff latitude of the diurnal tides at the critical lat is not mentioned. All tides atwith periods shorter than a half pendulum day (12hrs/sin(lat)) are Poincare waves. Inertial oscillations in fact do have small height range due to Beta (Laplace'sthe zero-rangeLTE solution is on an f-plane). All tides with longer periods than the inertial period must be planetary (Rossby) waves; (Wunsch et al, progr oceanogr, 1997). This 1997 paper was the last "great leap forward" in the understanding of the tides.