[MITgcm-support] Surface waves relaxation without viscosity terms

Sun Feb 10 05:27:00 EST 2013

Dear MITgcm users and developers,

First of all I'd like to say thanks to Martin and Jean-Michel for
giving me the advice about the Crank-Nicholson scheme. It was very
helpful and surface waves aren't dissipated anymore with this setup.

But still I have some issues. Since the problem can be connected with
the topic I am writing to the same e-mail thread.
I've resetup my experiment as follows:
Depth = 0.194 m,
Length = 12.4 m.
It is 2D area with the flat bottom and the constant temperature (20
degrees of Celsius) and zero salinity. There is the constant
background flow 0.232 m/s from left to right hand side of the area.
There is no viscosity and diffusion in the area. I set the initial
surface elevation by the following formula:
eta = eta0*cos(k*x)*gap(x),
where
eta0 = 0.01 - initial wave amplitude (m),
k = -2*PI*3.271 - wave number (rad/m),
gap(x) - function of the argument X, which transforms the periodic
cosine to a wave-packet.

The initial setup can be found on the figure 1 (figure_1_ss.jpg). The
upper picture is the surface elevation, the middle picture is the
Fourier spectrum, and the lowest picture is the same Fourier spectrum
but for a less scale.
As you can see on that picture the Fourier analysis produces the exact
wave number, which I specified by the parameter "k" (3.271) in the
previous formula.

I don't setup any additional underwater velocities for the wave-packet
(except the constant background flow 0.232 m/s of course), which
obviously leads to the wave splitting into two anti-directional waves
(figure 2 - figure_2_ss.jpg).

So the both waves run with the same wave number (figure 2, 3 -
figure_3_ss.jpg - left hand side wave, 4 - figure_4_ss.jpg - right
hand side wave), which absolutely agrees with the theory. But since
there is the background flow they should travel with the different
group velocity. Therefore the time frequency of the waves must be
different and correspond to the following dispersion relation:

f = U*q + sqrt(q*g*tanh(2*PI*q*h) / (2*PI)),
where
f - time frequency (Hz = 1/s),
U - background flow velocity (m/s),
q - wave number (1/m),
g - gravity acceleration (m/(s^2)),
h - domain depth (m).

And here I get the mysticism. According to the formula above I shall
have f1 = 1.5 Hz and f2 = 3.01 Hz for the left and right hand side
traveling waves respectively. But as far as you can see on the figures
5 (figure_5_ts.jpg - left hand side wave) and 6 (figure_6_ts.jpg -
right hand side wave), the waves travel with frequencies ~ 2.0 Hz and
2.7 Hz respectively. The MITgcm underestimates the right hand side
wave and overestimate the left hand side wave by at most 30 %!

I tried the same experiment but without the background flow. And the
results were in compliance with the theory.
So to speak I think, that there is some inconsistency with the
background flow only. It leads to increasing of the left hand side
wave group velocity and decreasing of the right hand side group
velocity.

What do you feel about this? Are there any parameters, which I forget
to specify, or some trick, which I should consider?
You can find my setup in the attached archive (setup.zip). Any advice
would be very appreciated.

Sincerely,
Sergey Semin

On Wed, Jan 23, 2013 at 11:54 PM, fancer lancer <fancer.lancer at gmail.com> wrote:
> Martin, Jean-Michel,
>
> Thank you very much for the helping me with such specific issues.
>
> Concerning the 1st question.
> I corrected my setup of the model to use the Crank-Nicholson scheme.
> I have now:
> implicSurfPress=0.5,
> implicDiv2Dflow=0.5,
> By default, implicitNHPress = implicSurfPress.
> So I hope it help. I shall write about the results of the simulation here.
>
> Concerning the 2nd question.
> Martin, you are absolutely right. Since the environment in the
> experiments is a bit different, they have the different dispersion
> relations:
> 1st experiment: w^2 = k*g*tanh(k*h)
> 2nd experiment: (w - k*U) = k*g*tanh(k*h)
> As you can see if frequency (w) is the same in the both experiments,
> the wave-number (k) is different (if the 1st exp. does have the
> non-zero background flow (U)). It doesn't matter what sign of the
> wave-number is specified in the first experiment, because the graphic
> is symmetric relatively OY axis. I setup the following parameters for
> the wave-maker:
> 1st experiment: frequency  w=2*PI*1.5, wave-number k=2*PI*1.515
> 2nd experiment: frequency  w=2*PI*1.5, wave-number k=2*PI*3.271
>
> In the first experiment it gives appropriate surface sinusoidal wave,
> but in the second case we have the high-frequency patters on the
> background of the vertical velocity. In addition the space Fourier
> specter of the surface wave doesn't fit the initial wave-number at all
> for the second experiment. I setup k/(2*PI)=3.271 1/m, but the Fourier
> analysis gives k/(2*PI) = 1.9 1/m. Any suggestion what else can be
> wrong?
>
> Best regards,
> Sergey V. Semin
> Post graduate course student
> Department of Mathematics,
> Nizhny Novgorod State Technical University n.a. R.E.Alekseeva
> http://www.nntu.ru/
> 117-24 ulitsa Minina, Nizhny Novgorod, 603950, Russia
> e-mail: fancer.lancer at gmail.com
>
> On Wed, Jan 23, 2013 at 8:03 PM, Jean-Michel Campin <jmc at ocean.mit.edu> wrote:
>> Hi Sergey,
>>
>> Just a comment regarding this:
>>> it says, that this is not yet possible with non-hydrostatic code, so you'd have to try to implement that.
>> I think the documentation is not up to date. Crank-Nicholson type time
>> stepping has also been implemented for the non-hydrostatic pressure gradient
>> (parameter: implicitNHPress, which default to implicSurfPress)
>> and is tested in the verification experiment "short_surf_wave".
>>
>> Cheers,
>> Jean-Michel
>>
>> On Wed, Jan 23, 2013 at 11:19:00AM +0100, Martin Losch wrote:
>>> Sergey,
>>>
>>> for your first question, you might want to consider turning off the implicit free surface, which will have a damping effect, and use an explicit Crank-Nicholson scheme instead. Unfortunately, here: <http://mitgcm.org/public/r2_manual/latest/online_documents/node41.html>
>>> it says, that this is not yet possible with non-hydrostatic code, so you'd have to try to implement that.
>>> Without any dissipation, the code will blow up sooner or later
>>>
>>> question 2: I cannot look at all the details, but from comparing obcs_calc.F in both setups I see that your "wn" is twice as large as (and has a differen sign) in your second case.
>>>
>>> Martin
>>>
>>>
>>> On Jan 22, 2013, at 6:07 PM, fancer lancer <fancer.lancer at gmail.com> wrote:
>>>
>>> > Hello dear MITgcm developers and users.
>>> >
>>> > I am trying to create the MITgcm setup, which could describe the
>>> > following two laboratory experiment cases:
>>> > 1) There is 2D tank with depth 0.196 m and length 12.4 m, bottom is
>>> > plain. Left boundary is solid, but the right boundary is opened. The
>>> > open boundary represents a wave-producer, which generates a sinusoidal
>>> > surface wave with frequency 1.5 Gz.
>>> > 2) The same experiment as above, but the left boundary is also opened
>>> > and the background flow runs from left to right with velocity 0.232
>>> > m/s.
>>> >
>>> > Both setups are attached to the e-mail. The modeling works pretty well
>>> > except the following issues:
>>> > 1. I turned off all the dissipation (horizontal - viscAh=0, vertical -
>>> > viscAr=0, biharmonic - viscA4=0, even the viscosity term in the
>>> > momentum equation - momViscosity=.true.), but the surface waves keep
>>> > dissipating (picture 02_U.jpg, blue line under the 0 vertical level is
>>> > the surface elevation). Of course, the reason can be in the numerical
>>> > viscosity (diffusion), but the dissipation is too intensive. It can be
>>> > possible, that I miss something and there is another term of
>>> > dissipation, which I haven't tuned off. Can anybody check whether I
>>> > miss something or not?
>>> > If the reason still is the numerical viscosity what can I do to
>>> > decrease such the annoying effect?
>>> >
>>> > 2. The second issue is a bit more complex. We use the formulas of the
>>> > vertical and horizontal waves velocities in the basin with the finite
>>> > depth (see the obcs_calc.F file) to create the harmonic on the right
>>> > boundary (some kind of wave-maker). That formulas work pretty well in
>>> > case of the zero background flow (see 01_U.jpg, 01_W.jpg). But if the
>>> > background flow exists then the high-frequency patterns appear on the
>>> > picture of the vertical velocity (see 02_W.jpg, 02_U.jpg).
>>> >
>>> > The attached files:
>>> > 01_U.jpg - horizontal velocity and surface displacement (t ~ 17 s), no
>>> > background flow
>>> > 01_W.jpg - vertical velocity and surface displacement (t ~ 17 s), no
>>> > background flow
>>> > 02_U.jpg - horizontal velocity and surface displacement (t ~ 25 s),
>>> > with background flow
>>> > 02_W.jpg - vertical velocity and surface displacement (t ~ 25 s), with
>>> > background flow
>>> >
>>> > Does anybody have any suggestion what can be the reason of the
>>> > patterns? I am quite sure, that the formulas of the wave-maker are
>>> > correct.
>>> >
>>> > In addition here are my projects:
>>> > 1.zip - experiment without the background flow,
>>> > 2.zip - experiment with the background flow.
>>> >
>>> > Any help would be highly appreciated.
>>> >
>>> > Best regards,
>>> > Sergey V. Semin
>>> > Post graduate course student
>>> > Department of Mathematics,
>>> > Nizhny Novgorod State Technical University n.a. R.E.Alekseeva
>>> > http://www.nntu.ru/
>>> > 117-24 ulitsa Minina, Nizhny Novgorod, 603950, Russia
>>> > e-mail: fancer.lancer at gmail.com
>>> > <1.zip><01_U.jpg><01_W.jpg><2.zip><02_U.jpg><02_W.jpg>_______________________________________________
>>> > MITgcm-support mailing list
>>> > MITgcm-support at mitgcm.org
>>> > http://mitgcm.org/mailman/listinfo/mitgcm-support
>>>
>>>
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>>> MITgcm-support at mitgcm.org
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>>
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