[Nek5000-users] Traveling gravity waves

[nek5000-users at lists.mcs.anl.gov]

I understand H.O.T. do not make big difference in the displacement amplitude, but how can you have dispersion without having at least two components such as cos(theta) and cos(2*theta)
you can estimate how much run time you need to see significant dispersion based on the phase speed of each component. 

I also had a lot of problems in the past with pseudospectral codes where there are small inconsistencies/errors in the initial conditions. 

Ammar


On Dec 6, 2012, at 4:05 PM, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Ammar,
> 
> 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.
> Higher Order terms from Stokes Theory http://en.wikipedia.org/wiki/Stokes_wave can be neglected as they are small
> For example the third order solution for deep water http://en.wikipedia.org/wiki/Stokes_wave#Third-order_Stokes_wave_on_deep_water 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
> Only the surface elevation differs in the order O( a²k +a³k) which should be neglectable as well.
> 
> 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
> 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.
> 
> All the best, Arne
> 
> PS: I'll let you know if 3rd Stokes made a difference
> 
> Zitat von nek5000-users at lists.mcs.anl.gov:
> 
>> I am not an expert on surface waves but just wondering if
>> you are initializing with one wave component such as this?
>> 
>> My understanding is you should have multiple components to see something interesting. This can be simply achieved by modulating the above
>> 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
>> 
>> Ammar
>> 
>> 
>> 
>> 
>>  
>> 
>> On Thu, Dec 6, 2012 at 6:38 AM, <nek5000-users at lists.mcs.anl.gov> wrote:
>> Hi Neks,
>> 
>> I am trying to set up a traveling gravity wave and started from the
>> std.wv example.
>> 
>> - In the useric I prescribed the the Initial velocity by using linear
>> wave theory (Airy)
>> 
>> http://en.wikipedia.org/wiki/Airy_wave_theory#Solution_for_a_progressive_monochromatic_wave
>>   wave amplitude
>> - the initial mesh was generate with genbox with periodic sides, bottom
>> wall and a free surface
>> - the surface tension was excluded by setting sigma & We = 0
>> - reverted density & viscosity to dimensional  variables (SI Units) in
>> the .rea to get correct velocities
>> - set the gravitational force in userf ffy = -9.81*param(1)
>> 
>> But instead of a traveling wave the system reverts to a sort of standing
>> wave immediately
>> 
>> Do I have set the initial velocity of the moving mesh as well? And if so
>> are wx,wy the correct variables to do so?
>> Did I apply the dimensions correctly?
>> 
>> I attached the .rea & .usr, any help with my Problem would be greatly
>> appreciated.
>> 
>> Thanks
>> Arne
>> 
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>> 
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> 
> 
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