fluid dynamics 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'' (the study of air and other gases in motion) an ...

, the wave height of a

surface wave In physics, a surface wave is a mechanical wave that propagates along the Interface (chemistry), interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occu ...

is the difference between the

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vert ...

s of a

crest Crest or CREST may refer to: Buildings *The Crest (Huntington, New York), a historic house in Suffolk County, New York *"The Crest", an alternate name for 63 Wall Street, in Manhattan, New York *Crest Castle (Château Du Crest), Jussy, Switzerla ...

and a neighboring

trough Trough may refer to: In science * Trough (geology), a long depression less steep than a trench * Trough (meteorology), an elongated region of low atmospheric pressure * Trough (physics), the lowest point on a wave * Trough level (medicine), the l ...

. ''Wave height'' is a term used by

mariner A sailor, seaman, mariner, or seafarer is a person who works aboard a watercraft as part of its crew, and may work in any one of a number of different fields that are related to the operation and maintenance of a ship. The profession of the s ...

s, as well as in

coastal The coast, also known as the coastline or seashore, is defined as the area where land meets the ocean, or as a line that forms the boundary between the land and the coastline. The Earth has around of coastline. Coasts are important zones in n ...

ocean The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...

and

naval engineering Naval architecture, or naval engineering, is an engineering discipline incorporating elements of mechanical, electrical, electronic, software and safety engineering as applied to the engineering design process, shipbuilding, maintenance, and o ...

. At sea, the term ''

significant wave height In physical oceanography, the significant wave height (SWH, HTSGW or ''H''s) is defined traditionally as the mean ''wave height'' ( trough to crest) of the highest third of the waves (''H''1/3). Nowadays it is usually defined as four times the ...

'' is used as a means to introduce a well-defined and standardized

statistic A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypo ...

to denote the characteristic height of the

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...

waves in a ''

sea state In oceanography, sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, p ...

'', including wind sea and swell. It is defined in such a way that it more or less corresponds to what a

observes when estimating visually the average wave height.

Definitions

Depending on context, wave height may be defined in different ways: *For a

sine wave A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...

, the wave height ''H'' is twice the

amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...

(i.e., the '' peak-to-peak amplitude''):

H = 2a.

*For a

periodic wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

, it is simply the difference between the

maximum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ran ...

and

minimum In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ran ...

of the surface elevation :

H = \max\left\ - \min\left\,

with ''c''_p the

phase speed The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...

(or propagation speed) of the wave. The sine wave is a specific case of a periodic wave. *In random waves at sea, when the surface elevations are measured with a wave buoy, the individual wave height ''H''_m of each individual wave—with an

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

label ''m'', running from 1 to ''N'', to denote its position in a sequence of ''N'' waves—is the difference in elevation between a wave crest and trough in that wave. For this to be possible, it is necessary to first split the measured

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...

of the surface elevation into individual waves. Commonly, an individual wave is denoted as the

time interval Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to c ...

between two successive downward-crossings through the

average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...

surface elevation (upward crossings might also be used). Then the individual wave height of each wave is again the difference between maximum and minimum elevation in the time interval of the wave under consideration.

Significant wave height

RMS wave height

Another wave-height statistic in common usage is the

root-mean-square In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...

(or RMS) wave height ''H''_rms, defined as:

H_\text = \sqrt,

with ''H''_m again denoting the individual wave heights in a certain

Notes

References

*, 387 pages. *, 704 pages. *, viii & 336 pages. {{physical oceanography Water waves Physical oceanography

Definitions

Significant wave height

RMS wave height

See also

Notes

References