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) a ...

, the wave height of a

surface wave In physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at ...

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 § ...

s of a crest and a neighboring trough. ''Wave height'' is a term used by mariners, as well as in coastal,

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 wor ...

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, an ...

. At sea, the term '' significant wave height'' 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 order and does not follow an intelligible pattern or combination. Individual ran ...

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 (ocean), swell—at a certain location and moment. A sea state is characterized by statistics, including the ...

'', including wind sea and swell. It is defined in such a way that it more or less corresponds to what a mariner 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 mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...

, 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 am ...

(i.e., the ''

peak-to-peak 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 ampl ...

''):

H = 2a.

*For a periodic wave, 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 r ...

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 r ...

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 exampl ...

(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 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 ...

, 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 languag ...

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. Ex ...

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