wavedim2dimless#

[dimlessValue] = wavedim2dimless(windvel, dimValue, ValueType)

Description#

Calculate dimensionless numbers from dimensional numbers

Inputs#

windvel: Wind velocity in (m/s)
dimValue: Dimensional value to be converted to dimensionless value
ValueType=’waveheight’;: Type of the dimensional value

‘fetch’: Wind fetch in (m)

‘depth’: Water depth in (m)

‘frequency’: Wave frequency in (Hz)

‘energy’: Zero-moment of surface elevation power spectral density in (m^2)

‘waveheight’: Wave height in (m)

‘period’: Wave period in (s)

‘wavelength’: Wave length in (m)

‘wavenumber’: Wave number in (1/m) or (Radian/m)

‘time’: Time in (s)

‘length’: Length in (m)

Outputs#

dimlessValue: Dimensionless value calculated from dimensional value

For ValueType=’fecth’: dimlessValue is dimensionless wind fetch (Fetchhat): Fetchhat=g*Fetch/U10^2

For ValueType=’depth’: dimlessValue is dimensionless depth (hhat): hhat=g*h/U10^2

For ValueType=’frequency’: dimlessValue is dimensionless wave frequency (fhat): fhat=f*U10/9.81

For ValueType=’energy’: dimlessValue is dimensionless wave energy (Ehat): Ehat=g^2*m0/U10^4

For ValueType=’waveheight’: dimlessValue is dimensionless wave height (Hhat): Hhat=g*H/U10^2

For ValueType=’period’: dimlessValue is dimensionless wave period (That): That=g*T/U10

For ValueType=’wavelength’: dimlessValue is dimensionless wave length (Lhat): Lhat=g*L/U10^2

For ValueType=’wavenumber’: dimlessValue is dimensionless wave number (khat): khat=k*U10^2/g

For ValueType=’time’: dimlessValue is dimensionless time (that): that=g*t/U10

For ValueType=’length’: dimlessValue is dimensionless time (that): that=g*t/U10

Note, g=9.81: gravitational acceleration

U10: wind velocity

Fetch: Wind fetch in (m)

h: Water depth in (m)

f: Wave frequency in (Hz)

m0: Zero-moment of water surface elevation power spectral density in (m^2)

H: Wave height in (m)

T: Wave period in (s)

L: Wave length in (m)

k: Wave number in (1/m) or (Radian/m)

t: Time in (s)

Examples#

windvel(:,1)=10.*rand(100,1);
Fetch(:,1)=10000.*rand(100,1);
dimValue=Fetch;
[dimlessValue]=wavedim2dimless(windvel,dimValue,'fetch');

References#

Sverdrup, H. U., & Munk, W. H. (1947). Wind, sea, and swell: theory of relations for forecasting. U.S. Navy Department, Hydrographic Office, Publication No. 601, 44 pp.

wavedim2dimless

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