[Nek5000-users] Traveling gravity waves

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

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
>>
>>      _______________________________________________
>>      Nek5000-users mailing list
>> Nek5000-users at lists.mcs.anl.gov
>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
>>       
>>
>
>
>
>
>
>    --
> http://aelghany.googlepages.com/home
>
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