Internal wave breaking

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Temporal evolution of internal wave breaking in the Rainbow Ridge, part of the Mid-Atlantic Ridge, North Atlantic Ocean. Measurements were taken by a single mooring deployed from June 28th till July 10th 2016. When the internal wave encounters the steep topography of the ridge, it breaks at around 1200 seconds and causes mixing and dissipation of heat. Modified from van Haren, et al. (2017) Internal wave breaking in the Rainbow Ridge.jpg
Temporal evolution of internal wave breaking in the Rainbow Ridge, part of the Mid-Atlantic Ridge, North Atlantic Ocean. Measurements were taken by a single mooring deployed from June 28th till July 10th 2016. When the internal wave encounters the steep topography of the ridge, it breaks at around 1200 seconds and causes mixing and dissipation of heat. Modified from van Haren, et al. (2017)

Internal wave breaking is a process during which internal gravity waves attain a large amplitude compared to their length scale, become nonlinearly unstable and finally break. This process is accompanied by turbulent dissipation and mixing. As internal gravity waves carry energy and momentum from the environment of their inception, breaking and subsequent turbulent mixing affects the fluid characteristics in locations of breaking. Consequently, internal wave breaking influences even the large scale flows and composition in both the ocean and the atmosphere. In the atmosphere, momentum deposition by internal wave breaking plays a key role in atmospheric phenomena such as the Quasi-Biennial Oscillation and the Brewer-Dobson Circulation. [2] In the deep ocean, mixing induced by internal wave breaking is an important driver of the meridional overturning circulation. [3] On smaller scales, breaking-induced mixing is important for sediment transport and for nutrient supply to the photic zone. [4] Most breaking of oceanic internal waves occurs in continental shelves, well below the ocean surface, which makes it a difficult phenomenon to observe.

Contents

The contribution of breaking internal waves to many atmospheric and ocean processes makes it important to parametrize their effects in weather and climate models.

Breaking mechanisms

Similar to what happens to surface gravity waves near a coastline, when internal waves enter shallow waters and encounter steep topography, they steepen and grow in amplitude in a nonlinear process known as shoaling. As the wave travels over topography with increasing height, bed friction leads to internal waves becoming asymmetrical with an increasing steepness. These nonlinear internal waves on a shallow slope are generally referred to as internal bores. [5] Wave height and energy increase until a critical steepness is reached, whereafter the wave breaks by convective, Kelvin-Helmholtz or parametric subharmonic instability. [6] Due to the relatively small density differences (and thus small restoring forces) over the ocean depth, ocean internal waves may reach amplitudes up to around 100 m. [5] Analogous to surface wave breaking in the region known as the surf zone, internal breaking waves dissipate energy in what is known as the internal surf zone. [7]

Internal tide breaking

Internal tidal waves are internal waves at tidal frequency in the ocean, which are generated by the interaction of the tide with the ocean topography. Alongside internal inertial waves, they constitute the majority of the ocean internal wavefield. The internal tides consist of so-called low modes and high modes with varying vertical wavelengths. As these waves propagate, the high modes tend to dissipate their energy quickly, leading to the low modes to dominate further away from the location of their generation. [5] Low mode internal waves, with wavelengths exceeding 100 km, generated by either tides or winds acting on the sea surface, can travel thousands of kilometers from their regions of generation, where they will eventually encounter sloping topography and break. [8] When this happens, isopycnals become steeper and steeper, where the wavefront is followed by a sharp temperature drop. This then leads to an unstable density profile that eventually overturns and breaks. [9] The magnitude of the topographic slope and the slope of the internal wave beam dictate where internal waves break.

The slope of an internal wave beam () can be expressed as the ratio between its horizontal () and vertical () wavenumbers: [5]

where is the buoyancy frequency (or Brunt-Väisälä frequency), is the Coriolis frequency and is the wave frequency in the dispersion relation that governs the propagation of internal waves in a continuously stratified and rotating medium:

.

In the case that the slope of a downgoing incident internal wave beam is larger than the topographic slope (supercritical slope), waves will be reflected downward. In the case that the slope of a downgoing incident internal wave beam is smaller than the topographic slope (subcritical slope), however, waves will be reflected upward with reduced wavelength and lower group velocity. Because the energy flux is conserved during reflection, energy density and therefore wave amplitude in the reflected wave must increase with respect to the incident wave. [10] This increase in amplitude and wave steepness results in the waves being subject to breaking. These effects are increased the closer the slope of the internal wave beam is to the magnitude of the topographic slope. When the slope of the beam of the incoming internal wave is equal to the topographic slope, the slope of the topography is referred to as the critical slope. Critical slopes and near-critical slopes are important locations for both wave breaking and wave generation via tide-topography interactions. [11]

Internal solitary wave breaking

Owing to the generally long distances traveled by internal tidal waves, they may steepen and form trains of internal solitary waves, or internal solitons. [5] These internal solitons have much shorter wavelengths, on the order of hundreds of meters, making them much steeper than internal tides. The ratio of the topographic slope to the wave steepness can be characterized by the internal Iribarren number:

where is the topographical slope, the internal wave amplitude and the wavelength of the internal wave. The internal Iribarren number can be used to classify internal bores into two categories: canonical bores and non-canonical bores. For a gentle slope, as is typical for the continental shelf and nearshore areas, the internal Iribarren number is low () such that canonical bores occur. In this case, an incoming internal solitary wave can convert to a packet of solitary waves or boluses as it travels up the slope in a process referred to as fission. This is also called a fission breaker. Canonical bores are generally accompanied by an intense drop in temperature as the wavefront passes by, followed by a gradual increase over time. [5]

In rarer cases, non-canonical () bores may occur. In these cases, for an increasing internal Iribarren number (that is, steeper waves or steeper topographic slope), wave breaking can be classified successively as surging, collapsing and plunging breakers (see Breaking wave). [12] Contrary to canonical bores, temperature gradually decreases as the wavefront passes by, followed by a sharp increase in temperature. Due to the steeper topographic slopes associated with non-canonical bores, a larger part of the wave energy is reflected back, meaning there is less turbulent energy that leads to mixing. [5]

Mixing

Breaking internal waves are regarded to play an important role on mixing of the ocean based on lab experiments and remote sensing. The effect of internal waves on mixing is also studied extensively in direct numerical simulations. Even though research indicates that internal wave breaking is important for local turbulence, there remains uncertainty in global estimates. [13] [14] [15] [16]

Breaking internal tidal waves can result in turbulent water columns of several hundred meters high and the turbulent kinetic energy may reach levels up to 10.000 times higher than in the open ocean. [5] [13]

Quantifying mixing efficiency

The intensity of the turbulence caused by breaking internal waves depends mainly on the ratio between topographical steepness and the wave steepness, known as the internal Iribarren number. A smaller internal Iribarren number correlates with a larger intensity of the resulting turbulence due to internal wave breaking. That means that a small internal Iribarren number predicts that a lot of the wave energy will be transferred to mixing and turbulence, while a large internal Iribarren number predicts that the wave energy will reflect offshore. [5]

Studies express the mixing efficiency as the ratio between the total amount of mixing and the total irreversible energy loss. In other words, the mixing efficiency can generally be defined as the following ratio:

,

where is the mixing efficiency, the change in background potential energy due to mixing and the total energy expended. Because and are not directly observable, studies use different definitions to determine the mixing efficiency.

It is notoriously hard to estimate the mixing efficiency in the ocean, due to practical limitations in measuring ocean dynamics. Besides measurements of ocean dynamics, the mixing efficiency can also be obtained from lab experiments and numerical simulations, but they also have their limitations. Therefore, these three different approaches have slightly different definitions of mixing efficiency. In theory these three approaches should give the same estimates for the mixing efficiency, but there remain discrepancies between them. Therefore, there are varying estimates and disagreements on mixing efficiency and comparisons are difficult due to the different definitions. [17]

Studies that quantify the mixing properties of breaking internal solitary waves have split estimates of the mixing efficiency range, with values between 5% and 25% for laboratory experiments [18] or between 13% and 21% for numerical simulations [14] depending on the Internal Iribarren number.

Mass and sediment transport

Breaking and shoaling of internal waves have been shown to cause the transport of mass and energy in the form of sediment and heat, but also of nutrients, plankton and other forms of marine life.

Sediment transport

Wave breaking causes mass and sediment transport that is important for the ocean biology and shaping of the continental shelves due to erosion. [19] The erosion caused by internal wave breaking can result in sediment to be suspended and transported off-shore. This off-shore sediment transport may give rise to the emergence of nepheloid layers, which are in turn important for the ocean biology. [15] [5] Direct numerical simulations show that breaking internal waves are also responsible for on-shore sediment transport, after which sediment can be deposited or transported elsewhere. [20]

Although many studies show that internal wave breaking leads to sediment transport, their traces in the geologic record remain uncertain. Their sedimentary structures may coexist in turbidites on continental slopes and canyons. [19]

Transport of nutrients

The mixing and transport of nutrients in the ocean is affected largely by internal wave breaking. The arrival of internal tidal bores has been shown to cause a 10 to 40 fold increase of nutrients on Conch Reef. [21] Here it has been shown that the appearance of internal bores provide a predictable and periodic source of transport that can be important for a diversity of marine life. [22] Large amplitude tidal internal tidal waves can cause sediments to be resuspended for as long as 5 hours each tidal wave [23] and internal bores have shown to play a vital role in the onshore transportation of planktonic larvae. [24]

Internal wave breaking may also cause ecological hazards, such as red tides [4] and low dissolved oxygen levels. [25]

Related Research Articles

<span class="mw-page-title-main">Tide</span> Rise and fall of the sea level under astronomical gravitational influences

Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon and are also caused by the Earth and Moon orbiting one another.

<span class="mw-page-title-main">Estuary</span> Partially enclosed coastal body of brackish water

An estuary is a partially enclosed coastal body of brackish water with one or more rivers or streams flowing into it, and with a free connection to the open sea. Estuaries form a transition zone between river environments and maritime environments and are an example of an ecotone. Estuaries are subject both to marine influences such as tides, waves, and the influx of saline water, and to fluvial influences such as flows of freshwater and sediment. The mixing of seawater and freshwater provides high levels of nutrients both in the water column and in sediment, making estuaries among the most productive natural habitats in the world.

<span class="mw-page-title-main">River delta</span> Silt deposition landform at the mouth of a river

A river delta is a landform shaped like a triangle, created by the deposition of sediment that is carried by a river and enters slower-moving or stagnant water. This occurs at a river mouth, when it enters an ocean, sea, estuary, lake, reservoir, or another river that cannot carry away the supplied sediment. It is so named because its triangle shape resembles the uppercase Greek letter delta, Δ. The size and shape of a delta are controlled by the balance between watershed processes that supply sediment, and receiving basin processes that redistribute, sequester, and export that sediment. The size, geometry, and location of the receiving basin also plays an important role in delta evolution.

<span class="mw-page-title-main">Tidal resonance</span> Enhanced tide due to ocean resonance

In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean. The effect is most striking when a continental shelf is about a quarter wavelength wide. Then an incident tidal wave can be reinforced by reflections between the coast and the shelf edge, the result producing a much higher tidal range at the coast.

<span class="mw-page-title-main">Amphidromic point</span> Location at which there is little or no tide

An amphidromic point, also called a tidal node, is a geographical location which has zero tidal amplitude for one harmonic constituent of the tide. The tidal range for that harmonic constituent increases with distance from this point, though not uniformly. As such, the concept of amphidromic points is crucial to understanding tidal behaviour. The term derives from the Greek words amphi ("around") and dromos ("running"), referring to the rotary tides which circulate around amphidromic points. It was first discovered by William Whewell, who extrapolated the cotidal lines from the coast of the North Sea and found that the lines must meet at some point.

<span class="mw-page-title-main">Continental shelf</span> Coastal and oceanic landform

A continental shelf is a portion of a continent that is submerged under an area of relatively shallow water, known as a shelf sea. Much of these shelves were exposed by drops in sea level during glacial periods. The shelf surrounding an island is known as an insular shelf.

<span class="mw-page-title-main">Seiche</span> Standing wave in an enclosed or partially enclosed body of water

A seiche is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbors, caves and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

<span class="mw-page-title-main">Inlet</span> Indentation of a shoreline

An inlet is a indentation of a shoreline, such as a small arm, bay, sound, fjord, lagoon or marsh, that leads to an enclosed larger body of water such as a lake, estuary, gulf or marginal sea.

<span class="mw-page-title-main">Surface layer</span> Layer of a turbulent fluid affected by interaction with a surface

The surface layer is the layer of a turbulent fluid most affected by interaction with a solid surface or the surface separating a gas and a liquid where the characteristics of the turbulence depend on distance from the interface. Surface layers are characterized by large normal gradients of tangential velocity and large concentration gradients of any substances transported to or from the interface.

<span class="mw-page-title-main">Wind wave</span> Surface waves generated by wind on open water

In fluid dynamics, a wind wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result of the wind blowing over the water's surface. The contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometers before reaching land. Wind waves on Earth range in size from small ripples to waves over 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.

<span class="mw-page-title-main">Internal wave</span> Type of gravity waves that oscillate within a fluid medium

Internal waves are gravity waves that oscillate within a fluid medium, rather than on its surface. To exist, the fluid must be stratified: the density must change with depth/height due to changes, for example, in temperature and/or salinity. If the density changes over a small vertical distance, the waves propagate horizontally like surface waves, but do so at slower speeds as determined by the density difference of the fluid below and above the interface. If the density changes continuously, the waves can propagate vertically as well as horizontally through the fluid.

<span class="mw-page-title-main">Carbonate platform</span> Sedimentary body with topographic relief composed of autochthonous calcareous deposits

A carbonate platform is a sedimentary body which possesses topographic relief, and is composed of autochthonic calcareous deposits. Platform growth is mediated by sessile organisms whose skeletons build up the reef or by organisms which induce carbonate precipitation through their metabolism. Therefore, carbonate platforms can not grow up everywhere: they are not present in places where limiting factors to the life of reef-building organisms exist. Such limiting factors are, among others: light, water temperature, transparency and pH-Value. For example, carbonate sedimentation along the Atlantic South American coasts takes place everywhere but at the mouth of the Amazon River, because of the intense turbidity of the water there. Spectacular examples of present-day carbonate platforms are the Bahama Banks under which the platform is roughly 8 km thick, the Yucatan Peninsula which is up to 2 km thick, the Florida platform, the platform on which the Great Barrier Reef is growing, and the Maldive atolls. All these carbonate platforms and their associated reefs are confined to tropical latitudes. Today's reefs are built mainly by scleractinian corals, but in the distant past other organisms, like archaeocyatha or extinct cnidaria were important reef builders.

Internal tides are generated as the surface tides move stratified water up and down sloping topography, which produces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other major source of internal waves is the wind which produces internal waves near the inertial frequency. When a small water parcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due to buoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off an internal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as waves at the sea surface-perhaps even more so, for no one has ever reported an interior calm."

A mouth bar is an element of a deltaic system, which refers to the typically mid-channel deposition of the sediment transported by the river channel at the river mouth.

In physical oceanography, undertow is the undercurrent that moves offshore while waves approach the shore. Undertow is a natural and universal feature for almost any large body of water; it is a return flow compensating for the onshore-directed average transport of water by the waves in the zone above the wave troughs. The undertow's flow velocities are generally strongest in the surf zone, where the water is shallow and the waves are high due to shoaling.

<span class="mw-page-title-main">River plume</span> Mix of fresh river water and seawater

A river plume is a freshened water mass that is formed in the sea as a result of mixing of river discharge and saline seawater. River plumes are formed in coastal sea areas at many regions in the World. River plumes generally occupy wide, but shallow sea surface layer bounded by sharp density gradient. The area of a river plume is 3-5 orders of magnitude greater than its depth, therefore, even small rivers with discharge rates ~1–10 m/s form river plumes with horizontal spatial extents ~10–100 m. Areas of river plumes formed by the largest World rivers are ~100–1000 km2. Despite relatively small volume of total freshwater runoff to the World Ocean, river plumes occupy up to 21% of shelf areas of the World Ocean, i.e., several million square kilometers.

<span class="mw-page-title-main">Mediterranean outflow</span>

The Mediterranean Outflow is a current flowing from the Mediterranean Sea towards the Atlantic Ocean through the Strait of Gibraltar. Once it has reached the western side of the Strait of Gibraltar, it divides into two branches, one flowing westward following the Iberian continental slope, and another returning to the Strait of Gibraltar circulating cyclonically. In the Strait of Gibraltar and in the Gulf of Cádiz, the Mediterranean Outflow core has a width of a few tens of km. Through its nonlinear interactions with tides and topography, as it flows out of the Mediterranean basin it undergoes such strong mixing that the water masses composing this current become indistinguishable upon reaching the western side of the strait.

Tides in marginal seas are tides affected by their location in semi-enclosed areas along the margins of continents and differ from tides in the open oceans. Tides are water level variations caused by the gravitational interaction between the Moon, the Sun and the Earth. The resulting tidal force is a secondary effect of gravity: it is the difference between the actual gravitational force and the centrifugal force. While the centrifugal force is constant across the Earth, the gravitational force is dependent on the distance between the two bodies and is therefore not constant across the Earth. The tidal force is thus the difference between these two forces on each location on the Earth.

The nonlinearity of surface gravity waves refers to their deviations from a sinusoidal shape. In the fields of physical oceanography and coastal engineering, the two categories of nonlinearity are skewness and asymmetry. Wave skewness and asymmetry occur when waves encounter an opposing current or a shallow area. As waves shoal in the nearshore zone, in addition to their wavelength and height changing, their asymmetry and skewness also change. Wave skewness and asymmetry are often implicated in ocean engineering and coastal engineering for the modelling of random sea states, in particular regarding the distribution of wave height, wavelength and crest length. For practical engineering purposes, it is important to know the probability of these wave characteristics in seas and oceans at a given place and time. This knowledge is crucial for the prediction of extreme waves, which are a danger for ships and offshore structures. Satellite altimeter Envisat RA-2 data shows geographically coherent skewness fields in the ocean and from the data has been concluded that large values of skewness occur primarily in regions of large significant wave height.

<span class="mw-page-title-main">Seismic oceanography</span>

Seismic oceanography is a form of acoustic oceanography, in which sound waves are used to study the physical properties and dynamics of the ocean. It provides images of changes in the temperature and salinity of seawater. Unlike most oceanographic acoustic imaging methods, which use sound waves with frequencies greater than 10,000 Hz, seismic oceanography uses sound waves with frequencies lower than 500 Hz. Use of low-frequency sound means that seismic oceanography is unique in its ability to provide highly detailed images of oceanographic structure that span horizontal distances of hundreds of kilometres and which extend from the sea surface to the seabed. Since its inception in 2003, seismic oceanography has been used to image a wide variety of oceanographic phenomena, including fronts, eddies, thermohaline staircases, turbid layers and cold methane seeps. In addition to providing spectacular images, seismic oceanographic data have given quantitative insight into processes such as movement of internal waves and turbulent mixing of seawater.

References

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