Long-period lunar fortnightly and monthly ocean tides

Long-period lunar fortnightly (Mf) and monthly (Mm) tides in the global oceans are of particular interest to geophysicists because of their impact on the Earth's rotation, and they are of interest to oceanographers from the point of view of the response characteristics of the global oceans to low-frequency forcing. Long-period tides have long been quite controversial,but precision altimetry is providing an accurate means of measuring and modeling them in the global oceans. Here we describe Mf and Mm tides in the global oceans extracted from a 1 degrees barotropic global hydrodynamic tidal model, which assimilates ocean tides estimated from cycles 10-130 of TOPEX altimetric data by an empirical tide model. The model results enable a better understanding of the energetics of these tides. Compared to the short-period ocean tides, which dissipate a total of roughly 3490 GW of lunisolar gravitational energy, the dissipation rates for Mf and Mm, 0.369 and 0.023 GW, respectively, are quite insignificant from the point of view of the dissipation of tidal energy in the global oceans. Their energy content is also low, 0.381 and 0.049 PJ respectively (compared to 580 PJ in short-period tides). Also compared to the high quality factor Q values for short-period tides (similar to 23 for semidiurnal and similar to 13 for diurnal), the Q values for these tides are 5.9 and 6.2 for Mf and Mm, respectively. The corresponding unassimilated model Q value is 5.8 for both. These Q values correspond to a decay timescale of the order of a period and hence indicate that unlike its response to short-period tidal forcing, the oceanic response to barotropic forcing at these low frequencies is like a heavily damped system. They are also consistent with the low values of Q (similar to 5.5) observed in the global oceans on timescales of several days. The relative potential energy to kinetic energy ratios for Mf and Mm tides (0.59 and 2.91 for assimilated and 0.83 and 3.20 for unassimilated, for Mf and Mm, respectively) are consistent with the dynamics of long-wavelength Rossby waves. At amplitudes of similar to 0.115 ms in universal time, UT1, for both Mf and Mm, the impact of these long-period tides on the length of day fluctuations of the Earth is considerable.