Planetary energy balance for tidal dissipation

Abstract

Dissipation of tidal energy is expressed here as an integral on the surface of a sphere that encloses the mass of the planet. When developed in constituent form, this surface integral depends linearly on the secondary potential that arises from the tidal disturbance; it can therefore be expressed as the sum of one part due to the body tide and another due to the fluid tides. The body tide part depends only on the anelastic response of the solid earth to the primary potential. The fluid tide part depends mainly on the elastic solid earth response to tidal loading and on the sum of the ocean tide and atmospheric tide mass disturbances. The atmosphere's contribution can be evaluated reliably from published analyses of the observed barometric tide. Tide gage data, on the other hand, do not suffice for a comparably reliable analysis of the observed ocean tide and must therefore be supplemented by dynamical interpolation through numerical integration of Laplace's tidal equations. Dissipation obtained from ocean tide models published during the past 5 years has a range of at least ±15% from the average value. The main cause of this uncertainty is the difficulty of modeling dissipation, but there are other uncertain aspects of existing models, notably the lack of provision for absorption of energy into baroclinic motions and for the anelastic response of the solid earth to tidal loading.

Constraints on energy dissipation in the Earth's body tide from satellite tracking and altimetry

“…There will thus be an adjustment to both the in-phase and out-of-phase components. This estimate of D sin y for the ocean implies (Platzman 1984;Cartwright & Ray 1991) an oceanic tidal dissipation of 2.421t0.015 TW. The tracking coef®cients (eq.…”

“…The anelasticity that induces the lag e in the Earth's body tide implies a certain loss of tidal energy. Platzman (1984) has shown that the energy dissipation rate in given by P~101:4 TW|k 2 sin e ,…”

“…This depends on the lag in k n k for all n, and thus also depends on all spherical harmonics of the ocean tide. Platzman (1984) estimated this load-tide contribution to tidal dissipation and concluded that it is an order of magnitude smaller than the dissipation in the body tide. His results, of course, are dependent on his adopted k n k .…”

Lunar and solar torques on the oceanic tides

“…Table 2 As is well known, the dominant tide in •, responsible for about 70% of the total acceleration, is M2. The next largest tide is S2, but its oceanic effect is partly canceled by the S2 atmospheric tide, which tends to accelerate the Earth's rotation rate by roughly +55" cy -2 (based on spherical harmonic coefficients listed in Haurwitz and Cowley [1973]; see also Platzman [1984] and Cartwright and Ray [1991]; Volland [ 1990] gives an estimate of +80" cy -2 but without the factor (1 + k[).). The totals listed in Table 2 are misleadingly close, a coincidence of favorable cancellations.…”

Interior Structure, Composition, and Mineralogy of the Terrestrial Planets

“…The combined effect of the torques exerted by the tiny Martian moons, Phobos and Deimos, is much less than the torque exerted on Mars by the Sun . The torque applied to the Earth by the Moon decelerates the Earth's rotation due to tidal friction in the oceans and, to a minor extent, in the solid Earth (Platzman, 1984;Zharkov et al, 1996). In turn, the Moon is accelerated in its orbit and recedes from the Earth at a rate of a few centimeters per year.…”