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<p>Hi Ammar,<br>
<br>
as I am using a single deepwater wave with amplitude a = 0.01 and wavenumber k = 1 the steepness := k*a = 0.01 is quite low.<br>
Higher Order terms from Stokes Theory <a href="http://en.wikipedia.org/wiki/Stokes_wave">http://en.wikipedia.org/wiki/Stokes_wave</a> can be neglected as they are small<br>
For example the third order solution for deep water <a href="http://en.wikipedia.org/wiki/Stokes_wave#Third-order_Stokes_wave_on_deep_water">http://en.wikipedia.org/wiki/Stokes_wave#Third-order_Stokes_wave_on_deep_water</a> doesn't differ from the Airy Theory so the velocities are correct to order 3 in the pertubation series with respect to the steepness k*a<br>
Only the surface elevation differs in the order O( a²k +a³k) which should be neglectable as well.<br>
<br>
I want to simulate a simple wave and than goto steeper waves with higher nonlinearities (Stokes) in order to create a test case to see what resolution and parameters are needed in NEK5000<br>
and then step up to more complex sea states. I already simulated this wave with a pseudo-spectral method which stability strongly depends on accurate initial Conditions and could simulate many periods without problems.<br>
<br>
All the best, Arne<br>
<br>
PS: I'll let you know if 3rd Stokes made a difference<br>
<br>
Zitat von <a href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>:</p>
<blockquote style="border-left:2px solid blue;margin-left:8px;padding-left:8px;" type="cite">
<dl>
<dd>I am not an expert on surface waves but just wondering if</dd>
<dd>you are initializing with one wave component such as this?</dd>
<dd><img alt="\eta\, =\, a\, \cos\, ( k x\, -\, \omega t )." class="tex" src="http://upload.wikimedia.org/math/2/a/a/2aa55babc3913095e52a18b0738e8d61.png"></dd>
</dl>
<p>My understanding is you should have multiple components to see something interesting. This can be simply achieved by modulating the above<br>
form by a spatial localization function such as exp(-(x-x0)2) or add other components such as a1 cos(kx...)+ a2 cos(2kx...)+...etc<br>
<br>
Ammar<br>
<br>
<br>
<br>
<br>
</p>
<div class="gmail_quote">On Thu, Dec 6, 2012 at 6:38 AM, <span dir="ltr"><<a href="mailto:nek5000-users@lists.mcs.anl.gov" target="_blank">nek5000-users@lists.mcs.anl.gov</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<p>Hi Neks,<br>
<br>
I am trying to set up a traveling gravity wave and started from the<br>
std.wv example.<br>
<br>
- In the useric I prescribed the the Initial velocity by using linear<br>
wave theory (Airy)<br>
<br>
<a href="http://en.wikipedia.org/wiki/Airy_wave_theory#Solution_for_a_progressive_monochromatic_wave" target="_blank">http://en.wikipedia.org/wiki/Airy_wave_theory#Solution_for_a_progressive_monochromatic_wave</a><br>
wave amplitude<br>
- the initial mesh was generate with genbox with periodic sides, bottom<br>
wall and a free surface<br>
- the surface tension was excluded by setting sigma & We = 0<br>
- reverted density & viscosity to dimensional variables (SI Units) in<br>
the .rea to get correct velocities<br>
- set the gravitational force in userf ffy = -9.81*param(1)<br>
<br>
But instead of a traveling wave the system reverts to a sort of standing<br>
wave immediately<br>
<br>
Do I have set the initial velocity of the moving mesh as well? And if so<br>
are wx,wy the correct variables to do so?<br>
Did I apply the dimensions correctly?<br>
<br>
I attached the .rea & .usr, any help with my Problem would be greatly<br>
appreciated.<br>
<br>
Thanks<br>
Arne<br>
<br>
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</blockquote>
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<br>
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<a href="http://aelghany.googlepages.com/home">http://aelghany.googlepages.com/home</a></p>
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