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Summary Article: WAVES, INTERNAL from Encyclopedias of the Natural World: Encyclopedia of Tidepools and Rocky Shores

Internal waves can be broadly defined as gravity waves occurring within density-stratified fluids. They are common in both the coastal and open oceans, potentially occurring anywhere that the local water column shows stable stratification with respect to density and where there are generating mechanisms such as, but not limited to, tidal currents flowing over abrupt topographic features. The interactions of internal waves with sea floor topography can have important physical and biological consequences, especially in near-shore environments. These consequences include enhanced near-bottom turbulence and mixing, redistribution of dissolved nutrients, and vertical and horizontal transport of sediments and biological particles such as plankton.


A useful conceptual model of ocean internal waves and their propagation can be motivated by considering discrete water parcels in a water column that is stratified with respect to density (see Fig. 1). Under conditions of stable density stratification—in which density increases either continuously or discretely with depth—any vertical displacement of a given water parcel either upward or downward will be opposed by a restoring force, due to gravity, that is proportional to the difference in density between the water parcel and its new surroundings. The restoring force will cause the parcel to move back toward its original position. The water parcel's momentum will tend to make it overshoot this original position, again setting up an opposing restoring force, with the result that a vertical oscillation is established that can propagate along lines of constant density (isopycnals) in the case of discrete stratification or at angles to the horizontal in cases of continuous stratification. In fact, the more familiar surface gravitational waves can be conceptualized as internal waves at the interface between two fluids (air and water) with a very large difference in densities. Because density gradients within the water column are very much smaller than that between the water and air, the wave periods of internal waves are typically much longer than those of surface waves, varying from minutes to multiple hours.

Schematic view of the generation of a propagating internal wave at the interface between two fluid layers of densities, pj and p2, where pj < p2 such that the vertical stratification is stable. In (1) an upward force, Fj, acts on water parcel V originally located at the density interface. The work of Fj acting on the water parcel moves V to a new location in (2). A gravitational restoring force, FR, acts to move V downward to a new location in (3). In the absence of energy loses to friction and mixing V will continue to oscillate vertically above and below the density interface. The frequency of the oscillation will be proportional to the magnitude of the difference between pj and p2.

The minimum wave period (highest frequency) of internal waves in a given setting is controlled by the degree of density stratification in the water column, and can be predicted by the Brunt—Väisälä buoyancy frequency:

where N is the frequency (in radians), g is the acceleration due to gravity, p is density, and z is depth. Typical values for the minimum Brunt-Väisälä period (i/BV frequency) in the ocean range from 2 to 20 minutes.

The maximum wave period (lowest frequency) for internal wave propagation is the local inertial period:

where f, the Coriolis parameter, is a function of latitude:

with ? being the earth's angular velocity about the local vertical and ? being latitude. The inertial period describes the time a body traveling in a rotating reference frame, with apparent deflection due to the Coriolis effect, takes to travel in a complete circle. Conceptually, a wave form with period longer than the local inertial period would be unable to propagate away from the location of generation. Maximum inertial period occurs at low latitudes, and minimum inertial period occurs near the poles. For example, at 10°N, T = 69 hours; at 30°N, T = 24 hours; and at 45°N, T = 16.9 hours. Thus, under typical ocean stratification at 30°N, internal waves can exist with periods varying between the Brunt—Väisälä periods (typically on the order of several minutes) up to the inertial period of 24 hours.


The speed at which the waveform of internal waves travels is also much smaller for internal waves than for surface waves, typically on the order of 10 to 30 centimeters per second. However, the vertical displacements, which are greatest when the vertical density gradient is strongest (the pycnocline), are typically quite large, on the order of 10 meters or more. Wave heights for internal waves at tidal periods can be very much larger, with reports as large as 200 meters. Whereas surface waves tend to occur during multiday bouts of intense activity (for example, associated with offshore storms) interspersed with relative calm, internal waves appear to be far more temporally persistent and are almost always present except for periods when stratification breaks down; for example, during strong or persistent wind mixing in winter. The most common mechanisms of internal wave generation in the coastal oceans and near the shelf break is the displacement of isopycnals associated with tidal currents flowing over abrupt topographic features. Tidal reversals of the currents lead to the generation of internal waves at the tidal frequency, termed internal tides.

The leading edge of an internal tide is often accompanied by packets of higher frequency, nonlinear, internal waves, and horizontal current velocities associated with internal tides can be comparable to or larger than those associated with surface tides. Propagating internal waves can also take on the form of half waves of depression or elevation only, sometimes termed solitary waves or solitons. The dynamics of solitons are highly nonlinear (meaning they cannot be accurately described by the equations of linear wave theory), and net horizontal water velocities can be large, especially in shallow water. Internal waves generated at or near the shelf break tend to travel inshore, and as they progress into shallow water over a gradually sloping bottom, the waves tend to steepen and shoal. Shear at the leading edge of the traveling wave can lead to instability and breaking, with the resulting turbulent bores of water from below the pycnocline continuing to travel inshore if the bottom angle is less than a critical angle for wave reflection. The resulting mixing across isopycnal surfaces may be an important source of nutrients to the euphotic zone. The shear associated with currents generated by internal tides is thought to be a major source of vertical mixing within the interior of the oceans.


Although ocean internal waves are a subsurface phenomenon, manifestations at the surface such as slicks, where water is converging over traveling internal waves, are observed frequently by remote sensing from airplanes and satellites (see Fig. 2). Surface slicks are caused by damping of surface gravity and capillary waves in the convergence zone over traveling internal waves. Understanding of the biological and ecological effects of internal waves for nearshore communities is limited, but they likely extend to both the subtidal and intertidal communities, including tidepool communities along rocky shores. These effects likely include both direct consequences of rapid thermal variability and transport of materials such as nutrients and zooplankton, and indirect effects associated with mixing and enhanced biological production. Vertical oscillations and mixing within the water column can concentrate and redistribute phytoplankton and zooplankton. It has been suggested that onshore transport of zooplankton at the surface can occur in slicks over nonlinear internal waves. Onshore transport of fronts associated with surface warm bores associated with internal waves very near shore has been shown for the coast of Southern California and may contribute to pulses of barnacle larvae arriving on shore. Oscillations of the pycnocline have been described as a mechanism of nutrient transport to kelp forests and coral reefs. The downward transport of subsurface layers of high chlorophyll concentration may be important in rockysubtidal habitats. The temporal variability associated with internal waves in near-shore communities can also be accompanied by strong spatial variability associated with the interaction of waves with rough topographic features such as the spur and groove formations on coral reefs. Internal tides can be a major source of sediment resuspension near the bottom, and their interaction with the continental shelves is thought to play a major role in determining the angle of the shelf slopes.

Surface slicks formed over internal waves propagating into shallow water near shore in Southern California. Slicks result from dampening of surface gravity and capillary waves in the convergence zone over traveling internal waves. Linear slicks formed offshore become deformed as the underlying internal waves refract around bottom features and break in shallow water. Photograph by J. Leichter.


There are a number of open and significant research questions associated with the mechanisms and effects of internal waves. The dissipation of energy in the subtidal and consequences of mixing are likely to have an impact on the distribution of nutrients and zooplankton in a variety of habitats, but these processes are poorly understood. Modulation of the amplitude of internal waves by mechanisms, such as alongshore currents, that affect the mean depth of thermocline may produce synchronized, episodic variability at multiple sites alongshore at scales of tens of kilometers or more. Understanding the sources of spatial variability in the impact of internal waves offers a context for experimental work to understand the biological consequences of internal waves at kilometer to regional scales.


Near-Shore Physical Processes, Effects of / Nutrients / Ocean Waves / Tides / Turbulence

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  • Garrett, C. 2001. Internal waves, in Encyclopedia ofocean sciences. Steel, J. H.,.
  • Thorpe, S. A., and Turekian, K. K. eds. San Diego: Academic Press. Haury, L. R., Briscoe, M. G., and Orr, M. H.. 1979. Tidally generated internal wave packets in Massachusetts Bay. Nature 278: 312-317.
  • Leichter, J. J., Stewart, H. L., and Miller, S. L.. 2003. Episodic nutrient transport to Florida coral reefs. Limnology and Oceanography 48: 1394-1407.
  • Pineda, J. 1999. Circulation and larval distribution in internal tidal bore warm fronts. Limnology and OOceanography 44: 1400-1414.
  • Pond, S., and Pickard, G. L.. 1983. Introductory dynamical oceanography, 2nd ed. Oxford: Pergamon Press.
  • Shanks, A. L. 1995. Mechanisms of cross-shelf dispersal of larvale invertebrates and fish, in Ecology of marine invertebrate larvae L. McEdward, ed. Boca Raton, FL: CRC Press, 323-367,.
  • Wolanski, E. 1994. Physical oceanographic processes of the Great Barrier Reef Boca Raton, FL: CRC Press.
Scripps Institution of Oceanography
© 2007 by the Regents of the University of California

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