File:Stokes3 amplitude double frequency.svg
Summary
Ratio of the <a href="https://en.wikipedia.org/wiki/amplitude" class="extiw" title="en:amplitude">amplitude</a> a2 of the <a href="https://en.wikipedia.org/wiki/harmonic" class="extiw" title="en:harmonic">harmonic</a> with twice the <a href="https://en.wikipedia.org/wiki/wavenumber" class="extiw" title="en:wavenumber">wavenumber</a> (2 k) to the amplitude a of the <a href="https://en.wikipedia.org/wiki/fundamental_frequency" class="extiw" title="en:fundamental frequency">fundamental</a>, according to <a href="https://en.wikipedia.org/wiki/George_Gabriel_Stokes" class="extiw" title="en:George Gabriel Stokes">Stokes</a>' second-order theory for <a href="https://en.wikipedia.org/wiki/surface_gravity_wave" class="extiw" title="en:surface gravity wave">surface gravity waves</a>. On the horizontal axis is the relative water depth h / λ, with h the mean depth and λ the <a href="https://en.wikipedia.org/wiki/wavelength" class="extiw" title="en:wavelength">wavelength</a>, while the vertical axis is the ratio a2 / a, divided by the wave steepness ka (with k = 2π / λ).
The blue line is valid for arbitrary water depth, while the dashed red line is the shallow-water limit (water depth small compared to the wavelength), and the dash-dot green line is the asymptotic limit for deep water waves.
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:52, 7 January 2017 | | 677 × 373 (82 KB) | 127.0.0.1 (talk) | Ratio of the <a href="https://en.wikipedia.org/wiki/amplitude" class="extiw" title="en:amplitude">amplitude</a> <i>a</i><sub>2</sub> of the <a href="https://en.wikipedia.org/wiki/harmonic" class="extiw" title="en:harmonic">harmonic</a> with twice the <a href="https://en.wikipedia.org/wiki/wavenumber" class="extiw" title="en:wavenumber">wavenumber</a> (2 <i>k</i>) to the amplitude <i>a</i> of the <a href="https://en.wikipedia.org/wiki/fundamental_frequency" class="extiw" title="en:fundamental frequency">fundamental</a>, according to <a href="https://en.wikipedia.org/wiki/George_Gabriel_Stokes" class="extiw" title="en:George Gabriel Stokes">Stokes</a>' second-order theory for <a href="https://en.wikipedia.org/wiki/surface_gravity_wave" class="extiw" title="en:surface gravity wave">surface gravity waves</a>. On the horizontal axis is the relative water depth <i>h</i> / λ, with <i>h</i> the mean depth and λ the <a href="https://en.wikipedia.org/wiki/wavelength" class="extiw" title="en:wavelength">wavelength</a>, while the vertical axis is the ratio <i>a</i><sub>2</sub> / a, divided by the wave steepness <i>ka</i> (with <i>k</i> = 2π / λ).<br>The blue line is valid for arbitrary water depth, while the dashed red line is the shallow-water limit (water depth small compared to the wavelength), and the dash-dot green line is the asymptotic limit for deep water waves. |
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