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.

Tides

The truth of the matter is that local topography is all-important in determining the features that our minds make ‘the tide’

– Rachel Carson “The Sea Around Us”

With each ebb and flow the shoreline changes. Rocks and sand are exposed only to be hidden again a few hours later. Tides are rhythmic and predictable – a look at a tide chart will tell you when a beach will be exposed. What makes tides predictable is how they are created, yet how the tide manifests at a specific location is shaped by the local topography.

The sun and moon’s gravities pull at the earth, and since the oceans are a fluid they are free to respond to this pull in a very observable way. Tides start out uniform with depth since the pull from the sun and moon act on the entire water column at once. The wave created is thousands of kilometres long – the true tidal wave, but it won’t look like a wave to an observer like lapping wind driven waves do instead tides raise and lower the sea level, exposing more or less of the beach. Since tides are a type of wave, they take time to propagate. This means that low tide (or high tide) occurs at different times at different locations. How the tides propagate is determined by the shape of shorelines and roughness of the ocean floor. As tides flow onto the shallower continental shelf, they slow down and their energy builds up in a smaller volume, amplifying the rise and fall of the water.

Anyone living near a sea shore can observe tides on a daily basis and there are tidal records extending back to antiquity. To build our modern understanding, Lord Kelvin led the first systematic effort to resolve the fundamental frequencies in 1867 and much of this work still holds today. There are semi-diurnal (twice-a-day), diurnal (once-a-day) and longer period components measured in days, months, and up to just over 18 years. To add complexity, these constituents can interact with each other, amplifying or damping local tides, however, the semi-diurnal lunar tides dominate other tidal frequencies at most locations.

The maximum height a tide reaches varies greatly depending on location. On Hawaii tides are tiny, reaching only 30 cm, while in the Bay of Fundy tides reach up to 12 m. The Bay of Fundy is often cited as having the highest tide in the world, however it has a competitor; Ungava Bay in northern Quebec, and it is still not determined which has the higher tides.

Strong tidal currents are typically the result of a constriction on the flow. Consider a garden hose: if you turn it on the water comes out at a certain rate, if you cover part of the opening with your finger, water will come out faster. The same amount of water is coming out, just the opening has changed. Even though the Islands of Hawaii have tiny tides, there are huge currents in the area. The islands are actually part of a mountain chain with a height comparable to the Himalayas. Tidal waters are pushed up the slopes and between the islands, forcing them to speed up.

Tides are an important factor in ocean mixing, which is a ongoing area of investigation for physical oceanographers. In a coastal environment, tides keep the water mixed, bringing up nutrient- rich water from the depths and removing waste.