Where the tidal energy goes

The sun and moon put 3.5 TW of tidal power into the oceans, however, the total amount of energy present ocean-wide remains nearly constant from year to year. There must be a balance between the energy input and output, therefore tidal energy must go somewhere. The energy of the large-scale motions created by tides, along with energy from solar radiation and winds, is successively broken down to smaller scales and ultimately dissipated through viscous forces. This process doesn't happen evenly throughout the ocean, instead close proximity to structural hotspots such as continental shelves and sub-surface topography promote energy dissipation from basin-wide oscillations down to effects measured in millimeters. Complex internal flow dynamics are created at these hotspots which often support unique ecosystems.

Initially, tides are uniform with depth as the pull from the sun and moon act on the entire water column creating wavelengths on the order of thousands of kilometres. As the tide propagates it's molded by the shape of shorelines and roughness of the ocean floor. As it flows onto the shallower continental shelf, bottom friction slows the water down causing energy to accumulate in a smaller volume which acts to amplify the rise and fall of the water. Adding to the complexity of the dynamics, tidal flow over bottom topography produces internal tides (the discovery of which is an interesting tangent for another day). Shear instability, wave-wave interactions and topographical scattering all influence the rate of energy dissipation, and control whether internal tides dissipate near the generation site or far away. Ultimately, all tidal energy dissipates.

When the internal tide interacts with local existing internal waves, the kinetic energy is broken down to smaller scales. Waves are successively subdivided through non-linear processes and turbulence into smaller scale motion. Ultimately, a scale is reached that is small enough that viscosity dominates and the kinetic energy of the fluid motion is dissipated into heat. Effectively, there is an entire range of wave sizes that no longer directly receive energy from tides but are too large for viscosity effects to take hold; these mid-scale waves are called the 'internal subrange' (see my essay on turbulence for more info). In this range, the motion is completely determined by the rate energy enters at the large end of the scale and the rate it dissipates at the small end. In between, energy is transfered by inertial forces alone.

The 3.5 TW of tidal power is first dispersed into internal tides. Through wave-wave interactions and turbulence this energy is ultimately lost in small-scale diffusion. Turbulence is dissipative and irreversible by nature, resulting in kinetic energy lost to molecular viscosity acting on the smallest waves which reappears as thermal energy.

For more info:
Batchelor, G.K. (1953), The theory of homogeneous turbulence, 197pp.

Munk, W. and C. Wunsch (1998), Abyssal recipes II: energetics of tidal and wind mixing, Deep-Sea Research I, 45, 1977-2010.

St. Laurent, L., and C. Garrett (2002), The Role of Internal Tides in Mixing the Deep Ocean, J. Phys. Oceanogr, 32, 2882-2899.