Angular momentum and energy

The gravitational torque between the Moon and the tidal bulge of the Earth causes the Moon to be constantly promoted to a slightly higher orbit and the Earth to be decelerated in its rotation. As in any physical process within an isolated system, total energy and angular momentum are conserved. Effectively, energy and angular momentum are transferred from the rotation of the Earth to the orbital motion of the Moon (however, most of the energy lost by the Earth (-3.321 TW) is converted to heat by frictional losses in the oceans and their interaction with the solid Earth, and only about 1/30th (+0.121 TW) is transferred to the Moon). The Moon moves farther away from the Earth (+38.247±0.004 mm/y), so its potential energy (in the Earth's gravity well) increases. It stays in orbit, and from Kepler's 3rd law it follows that its angular velocity actually decreases, so the tidal action on the Moon actually causes an angular deceleration, i.e. a negative acceleration (-25.858±0.003 "/cy?) of its rotation around the Earth. Although its kinetic energy decreases, its potential energy increases by a larger amount. The rotational angular momentum of the Earth decreases and consequently the length of the day increases. The net tide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. Tidal friction is required to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exch nge of rotational and orbital energy between the Earth and Moon as heat. If the friction and heat dissipation were not present, the Moon's gravitational force on the tidal bulge would rapidly (within two days) bring the tide back into synchronization with the Moon, and the Moon would no longer recede. Most of the dissipation occurs in a turbulent bottom boundary layer in shallow seas such as the European shelf around the British Isles, the Patagonian shelf off Argentina, and the Bering Sea.[11] The dissipation of energy by tidal friction averages about 3.75 terawatts, of which 2.5 terawatts are from the principal M2 lunar component and the remainder from other components, both lunar and solar.[12] An equilibrium tidal bulge does not really exist on Earth because the continents do not allow this mathematical solution to take place. Oceanic tides actually rotate around the oceans basin as vast gyres around several amphidromic points where no tide exists. The Moon pulls on each individual undulation as Earth rotates—some undulations are ahead of the Moon, others are behind it, while still others are on either side. The "bulges" that actually do exist for the Moon to pull on (and which pull on the Moon) are the net result of integrating the actual undulations over all the world's oceans. Earth's net (or equivalent) equilibrium tide has an amplitude of only 3.23 cm, which is totally swamped by oceanic tides that can exceed one metre.