{{Short description|Difference between the elevations of a crest and a neighbouring trough}} thumb|upright=1.2|Wave characteristics

In fluid dynamics, the '''wave height''' of a surface wave is the difference between the elevations of a crest and a neighboring trough.<ref name=Kinsman_38>{{harvtxt|Kinsman|1984|page=38}}</ref> ''Wave height'' is a term used by mariners, as well as in coastal, ocean and naval engineering.

At sea, the term ''significant wave height'' 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, the wave height ''H'' is twice the amplitude (i.e., the ''peak-to-peak amplitude''):<ref name=Kinsman_38/> <math display="block">H = 2a. </math> *For a periodic wave, it is simply the difference between the maximum and minimum of the surface elevation {{math|1=''z'' = ''η''(''x'' – ''c''<sub>p</sub> ''t'')}}:<ref name=Kinsman_38/> <math display="block">H = \max\left\{ \eta(x\,-\,c_p\,t) \right\} - \min\left\{ \eta(x - c_p\,t) \right\}, </math> with ''c''<sub>p</sub> 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''<sub>m</sub> of each individual wave—with an integer 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 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 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.<ref name=Holt_24_28>{{harvtxt|Holthuijsen|2007|pages=24–28}}</ref>

===Significant wave height=== {{excerpt|Significant wave height}}

===RMS wave height=== Another wave-height statistic in common usage is the root-mean-square (or RMS) wave height ''H''<sub>rms</sub>, defined as:<ref name=Holt_24_28/> <math display="block">H_\text{rms} = \sqrt{ \frac{1}{N} \sum_{m=1}^N H_m^2}, </math> with ''H''<sub>m</sub> again denoting the individual wave heights in a certain time series.

== See also == *Sea state *Wind wave

== Notes ==

{{reflist}}

== References == {{ref begin}} *{{Citation | title=Waves in Oceanic and Coastal Waters | first=Leo H. | last=Holthuijsen | publisher=Cambridge University Press | year=2007 | isbn=978-0-521-86028-4 }}, 387 pages. *{{Citation | last=Kinsman | first=Blair | title=Wind waves: their generation and propagation on the ocean surface | year=1984 | publisher=Dover Publications | isbn=0-486-49511-6 }}, 704 pages. *{{Citation | first=Owen M. | last=Phillips | author-link=Owen Martin Phillips |title=The dynamics of the upper ocean | publisher=Cambridge University Press | year=1977 | edition=2nd | isbn=0-521-29801-6 }}, viii & 336 pages. {{ref end}}

{{physical oceanography}}

Category:Water waves Category:Physical oceanography