File:Stokes wave energy deep water.svg
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Summary
| Description |
English: Several integral properties of Stokes waves on deep water as a function of wave steepness. The wave steepness is defined as the ratio of wave height H to the wavelength λ. These properties of surface gravity waves are made dimensionless using the wavenumber k = 2π / λ, gravitational acceleration g and the fluid density ρ.
Shown are the kinetic energy density T, the potential energy density V, the total energy density E = T + V, the horizontal wave momentum density I, and the relative enhancement of the phase speed c. Wave energy densities T, V and E are integrated over depth and averaged over one wavelength, so they are energies per unit of horizontal area; the wave momentum density I is similar. The dashed black lines show 1/16 (kH)2 and 1/8 (kH)2, being the values of the integral properties as derived from (linear) Airy wave theory. The maximum wave height occurs for a wave steepness H / λ of 0.1412, above which no periodic surface gravity waves exist. Note that the shown wave properties have a maximum for a wave height less than the maximum wave height (see e.g. E.D. Cokelet (1977) "Steep gravity waves in water of arbitrary uniform depth", Philosophical Transactions of the Royal Society of London, A 286(1335), pp. 183–230, doi:10.1098/rsta.1977.0113). This figure is a remake and adaptation of Figure 1 in: L.W. Schwartz and J.D. Fenton (1982) "Strongly nonlinear waves", Annual Review of Fluid Mechanics 14, pp 39–60, doi:10.1146/annurev.fl.14.010182.000351. |
| Date | |
| Source | Own work |
| Author | Kraaiennest |
| Background | The wave physics are computed with the Rienecker & Fenton streamfunction theory; for a computer code to compute these see: J.D. Fenton (1988) "The numerical solution of steady water wave problems". Computers & Geosciences 14(3), pp. 357–368, doi:10.1016/0098-3004(88)90066-0. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:11, 4 March 2012 | | 963 × 529 (293 KB) | Kraaiennest | Linear horizontal scale, in terms of ''kH'' instead of its square. Added several other wave properties |
| 07:35, 2 March 2012 |  | 401 × 347 (94 KB) | Kraaiennest | {{Information |Description={{en|1=Energy – the sum of kinetic and potential energy – of Stokes waves on deep water as a function of wave height. For these [[:en:surface gravity wav... |
