fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, the wave height of a surface wave is the difference between the

elevation The elevation of a geographic location (geography), ''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 equipotenti ...

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

ocean The ocean is the body of salt water that covers approximately 70.8% of Earth. The ocean is conventionally divided into large bodies of water, which are also referred to as ''oceans'' (the Pacific, Atlantic, Indian Ocean, Indian, Southern Ocean ...

and naval engineering. 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 (physics), trough to crest (physics), crest) of the highest third of the ocean surface wave, waves (''H''1/ ...

'' is used as a means to introduce a well-defined and standardized statistic to denote the characteristic height of the random waves in a '' sea state'', 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 sinusoid (symbol: ∿) is a periodic function, periodic wave whose waveform (shape) is the trigonometric function, trigonometric sine, sine function. In mechanics, as a linear motion over time, this is ''simple ...

, the wave height ''H'' is twice the amplitude (i.e., the '' peak-to-peak amplitude''):

H = 2a.

*For a periodic wave, it is simply the difference between the maximum and minimum of the surface elevation :

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

with ''c''_p the phase speed (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 (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

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. ...

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 colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by ...

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