Wave–current interaction

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In fluid dynamics, wave–current interaction is the interaction between surface gravity waves and a mean flow. The interaction implies an exchange of energy, so after the start of the interaction both the waves and the mean flow are affected.

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics and hydrodynamics. Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation,

In fluid dynamics, the fluid flow is often decomposed into a mean flow – and deviations from the mean. The averaging can be done either in space or in time, or by ensemble averaging.

Contents

For depth-integrated and phase-averaged flows, the quantity of primary importance for the dynamics of the interaction is the wave radiation stress tensor.

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral

In physics and mathematics, the phase of a periodic function of some real variable is the relative value of that variable within the span of each full period.

In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.

Wave–current interaction is also one of the possible mechanisms for the occurrence of rogue waves, such as in the Agulhas Current. When a wave group encounters an opposing current, the waves in the group may pile up on top of each other which will propagate into a rogue wave. [1] [2]

Rogue waves are unusually large, unexpected and suddenly appearing surface waves that can be extremely dangerous, even to large ships such as ocean liners.

The Agulhas Current is the western boundary current of the southwest Indian Ocean. It flows down the east coast of Africa from 27°S to 40°S. It is narrow, swift and strong. It is suggested that it is the largest western boundary current in the world ocean, with an estimated net transport of 70 Sverdrups, as western boundary currents at comparable latitudes transport less — Brazil Current, Gulf Stream, Kuroshio.

Classification

Peregrine (1976) identifies five major sub-classes within wave–current interaction:

• interaction of waves with a large-scale current field, with slow – as compared to the wavelengthtwo-dimensional horizontal variations of the current fields;
• interaction of waves with small-scale current changes (in contrast with the case above), where the horizontal current varies suddenly, over a length scale comparable with the wavelength;
• the combined wave–current motion for currents varying (strongly) with depth below the free surface;
• interaction of waves with turbulence; and
• interaction of ship waves and currents, such as in the ship's wake.

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space-time. For example, on a weather map, the surface temperature is described by assigning a real number to each point on a map; the temperature can be considered at a fixed point in time or over some time interval, if one wants to study the dynamics of temperature change. A surface wind map, assigning a vector to each point on a map that describes the wind velocity at that point, would be an example of a 1 dimensional tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank 1 tensor field, and the full description of electrodynamics can be formulated in terms of two interacting vector fields at each point in space-time, or as a single rank 2 tensor field theory.

In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

In physics, length scale is a particular length or distance determined with the precision of one order of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group.

Footnotes

1. Dysthe, Kristian; Krogstad, Harald E.; Müller, Peter (2008), "Oceanic rogue waves", Annual Review of Fluid Mechanics, 40: 287–310, Bibcode:2008AnRFM..40..287D, doi:10.1146/annurev.fluid.40.111406.102203

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References

• Bretherton, F. P.; Garrett, C. J. R. (1968), "Wavetrains in inhomogeneous moving media", Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 302 (1471): 529–554, Bibcode:1968RSPSA.302..529B, doi:10.1098/rspa.1968.0034
• Bühler, O. (2014), Waves and mean flows (2nd ed.), Cambridge University Press, ISBN   978-1-107-66966-6
• Peregrine, D. H. (1976), "Interaction of water waves and currents", Advances in Applied Mechanics, 16, Academic Press, pp. 9–117, ISBN   978-0-12-002016-4
• Phillips, O. M. (1977), The dynamics of the upper ocean (2nd ed.), Cambridge University Press, ISBN   0-521-29801-6
• Craik, A. D. D. (1988), Wave interactions and fluid flows, Cambridge University Press, ISBN   0-521-36829-4
• Prandle, D. (1992), Dynamics and exchanges in estuaries and the coastal zone, Coastal and estuarine studies, 40, American Geophysical Union, ISBN   0-87590-254-5
• Jonsson, I. G. (1990), "Wave–current interactions", in B. Le Méhauté and D. M. Hanes, Ocean Engineering Science, The Sea, 9A, Wiley Interscience, pp. 65–120, ISBN   0-471-11543-6

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