# Experimental internal gravity wave turbulence

^{1}Laboratoire des Ecoulements Géophysiques et Industriels, Université Grenoble Alpes, CNRS, Grenoble-INP, Grenoble, France (geraldine.davis@univ-grenoble-alpes.fr)^{2}Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France^{3}Institut Universitaire de France (IUF)

Stratified fluids may develop simultaneously turbulence and internal wave turbulence, the latter describing a set of a large number of dispersive and weakly nonlinear interacting waves. The description and understanding of this regime for internal gravity waves (IGW) is really an open subject, in particular due to their very unusual dispersion relation. In this presentation, I will show experimental signatures of a large set of weakly interacting IGW obtained in a 2D trapezoidal tank.

Due to the peculiar linear reflexion law of IGW on inclined slopes, this setup - for given excitation frequencies - focuses all the input energy on a closed loop called attractor. If the forcing is large enough, this attractor destabilizes and the system eventually achieves a nonlinear cascade in frequencies and wavevectors via triadic resonant interactions, which results at large forcing amplitudes in a k^-3 spatial energy spectrum. I will also show some results obtained in a much larger set-up -the Coriolis facility in Grenoble- with signature of 3D internal wave turbulence.

**How to cite:**
Davis, G., Dauxois, T., Joubaud, S., Jamin, T., Mordant, N., and Savaro, C.: Experimental internal gravity wave turbulence, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-18419, https://doi.org/10.5194/egusphere-egu2020-18419, 2020

## Comments on the display material

AC: Author Comment |CC: Community Comment | Report abuseDisplay material version 1– uploaded on 05 May 2020CC1: Questions / Comment on EGU2020-18419, Georg Sebastian Voelker, 06 May 2020Good morning Ms. Davis,

first of all thanks for uploading the interesting research. When the forcing amplitude is increased the waves become naturally more non-linear. You report that when you increase the forcing amplitude of the experiment xour spectrum approaches the k^-3 slope. As an explanation you suggest triadic interactions, i.e. wave turbulence reshaping the spectrum. I was wondering what the effect of other non-linear mechanisms are on the spectral shape. Do you observe non-negligible wave-mean flow interactions leading to increased wave modulation? When you project your flow field on IGW polarization relations, how large is the residual, i.e. non gravity wave motion, with respect to the gravity wave signal? Do you observe any instabilities other then triadic interaction?

Best, Georg Sebastian Voelker

AC1: Reply to CC1, Géraldine Davis, 06 May 2020Thank you very much for your interest and questions. I just prepared an answer with some figures but unfortunatly I do not manage to upload the figures... So here is my answer anyway, hope I will be able to post the figures afterwards.

Indeed we observe a mean flow which is due to boundary streaming : the forced wave (ie the attractor) deposites its horizontal momentum in the viscous boundary layers near the two horizontal walls (in (x,z) planes), which --via a recirculation-- results in the central vertical plane (where the velocity field is measured) in a mean flow of the opposite direction (see the figure "mean_flow").

However this mean flow is quite small (around 3% of the total energy), as you can see on the attached figure of evolution of energies. But yes the energy density is indeed a little bit shifted due to Doppler shift, as you can see on the slide n°14 where the maxima of energy appear to be slightly "to the left" of the dispersion relation (visible for waves a,b,c).

On the figure displaying the evlolution of energy densities, "E\omega_0" is the energy of the attractor, E_in is the energy relying on the dispersion relation (with a 10% criteria on the frequency) exept the one at \omega_0.E(w=0) is the measured mean flow and E_out is the remaining energy. You can see that Eout is following Ein because of the widening of the "observed dispersion relation" due to non linearities, widening that is bigger than the 10% criteria (see figure "dispersion_relation", please do not take into account the dashed blue lines).

We can extract from this width a non linear time scale (just by T_NL = 1/ width in frequency), which was found to be of the order of 1 linear time to 10 linear times (see figure "non_linear_time").

So it seems that even if the system is not really *weakly* non linear, it is still well described by an assembly of interacting waves. [Some of these interactions are non resonant, leading to bound waves, as it is visible on slide 14 where some energy relies outside the dispersion relation. But as the amplitude of forcing is increased these bound waves tend to be less present (see figure "dispersion_relation").]

So to conclude exept for the (small) mean flow generation it seems to us that we only oberved triadic interactions.

CC2: Reply to AC1, Georg Sebastian Voelker, 06 May 2020Thanks. That is indeed very intersting. I am looking forward to the chat on Friday!

CC3: Reply to CC2, Paul PUKITE, 15 May 2020This plot is interesting, which I have annotated below

This mirror folding about 1/2 the primary frequency is known as double-sideband suppressed-carrier modulation, and is closely related to a triad.

What one can do with the well-known ENSO signal is to perform the same folding about the annual carrier (annual because ENSO has an annual spring predicability barrier). Then you get the following plot, which clearly shows the symmetric sidebands.

The upper inset is the frequencies on the right half of the panel folded onto the left half. The alignment is very good, indicating DSSC modulation is occurring for ENSO. (BTW this continues for the next annual harmonic but not as clear)