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Experimental and theoretical study of internal gravity waves
J. Sommeria, C. Staquet, L. Gostiaux, H. Didelle, S. Viboud (CORIOLIS-LEGI, Grenoble, France),
D. Martinand (MSMN-GP, Marseille, France)
O. Eiff (IMFT, Toulouse, France)
A. Paci, J.C. Canonici (Météo France)
L. Maas, T. Gerkema (NIOZ, Texel, The Netherlands)
T. Peacock (MIT, Boston, USA)
W.R. Young (Scripps, San Diego, USA)
Internal gravity waves are unusual waves propagating within continuously stratified fluids. The dispersion relation &omega = N sin&theta links the wave's frequency &omega to its
angle of propagation &theta, with N being the Brünt-Väisälä's frequency (typical of the density gradient). Thus there is no wavelength
selection, and the angle between gravity and the direction of propagation is conserved.
more info on these waves (in french)
The emission and reflection of internal gravity waves in the oceans are fundamental mechanisms to explain the conversion of the barotropic tide
into the baroclinic one, and the mixing process observed near the seafloors and within the oceans.
In our laboratory, theoretical description of this kind of phenomena and experimental investigations of simple setups are coupled, according to the
following research fields.
At small scale, we study waves in a two-dimensional stratified fluid (tanks of 80x42.5x17cm3 and 300x40x10.5cm3).
Visualization is obtained using 'synthetic schlieren', giving a quantitative measurement of the density's gradient field.
At larger scale, experiments are done at the Coriolis turntable, Grenoble.
Emission of internal waves
- Internal plane waves generator: We have designed with the Coriolis team a new kind of internal waves wave-maker (left-hand picture).
Thanks to a system of oscillating plates with a tunable profile, the wave generator can force a specific oscillating boundary condition
corresponding to different types of internal waves.
Experiments have shown that this source can emit internal plane waves (right-hand picture) which are spatially and temporally monochromatic (Exp.Fluids 2007).
This is very interesting because it generates a plane wave used for theoretical developments but never done before.
The wavemaker can also be used to generate internal tides which correspond to vertically standing modes associated to
the ducting of internal waves in a finite depth stratified fluid. Finally, it is possible to emit intense and localized
internal wave beams described by the self-similar viscous solution introduced by Thomas & Stevenson (JFM 1972).
- Oscillating cylinder: The study of internal waves generated by a vertically oscillating cylinder and the comparison with Hurley & Keady theory
(L.Gostiaux PhD Thesis 2006) has provided a precise analysis of the spatial structure of the
emitted wave, and more specifically the difference between a classic beam (left-hand picture) and a bimodal one (right-hand picture).
- Internal tide (principle on left-hand picture): An oscillating fluid motion over a topography is similar to an oscillating body in a fluid
at rest. We have demonstrated experimentally that internal waves are emitted at an amphidromic point which position relies on the excitation's
frequency and the topography's shape. The mechanism involved explains the typical size of the waves generated. The beam has a structure very closed to
the one of an oscillating cylinder of which the radius fits the local curvature's radius of the topography in the emission area (right-hand picture)
- Theory: While reflecting on a slope, the angle of propagation of an internal wave with gravity is preserved. This property
leads to an increase of the spatial density of the energy of the reflected internal wave, thus to the creation of nonlinear structures (left-hand side).
The theoretical description of such phenomenon is unrealistic: the reflected wave's amplitude is infinite when the angle &beta of the incident wave beam
is equal to the one of the slope γ. Taking into account the nonlinear terms, we have shown how to solve this paradoxical results and described the
near-critical case too (JFM 1999), the right-hand side picture describes
the velocity field.
- Small scale experiments: A look-up at isodensity lines near a slope has permited the caracterization of an overturning instability
triggering the boundary-mixing process (vidéo,
Phys.Fluids 2004). Quantitative measurements have provided more
precise details on the evolution of the density gradient. Nevertheless, the laboratory's experiments are at too small scales in order to reach an
oceanographic type of turbulence. Furthermore, neither experiment nor simulation includes rotation. These are the reasons why we have chosen the Coriolis
turntable to perform experiments at larger scales.
- Large scale experiments: The Coriolis turntable is a cylinder tank (13m large, 1m deep) which can rotate and can be filled with stratified
salty water (left-hand side). Internal waves are generated by the plane waves generator described above. During the 2005 and 2006 experimental
campaigns, critical reflection has been studied using PIV technique. The reflected beam (right-hand side) and solibores at the slope with and without
rotation of the tank were observed (Phys.Fluids 2005).
In particular, second order and third order harmonics have been observed. The three-dimensional structure of the reflected beam still remains unclear.
Internal tide scattering at topographies
Large scale experiments:
The dissipation of internal tides within the ocean plays an important part to
understand the global energetic ocean budget. Internal tide scattering
is a linear mechanism converting large scales motions (low modes) into smaller
scales (high modes) which are damped faster. This is due to internal tide interaction
with finite amplitude topographies, with spatial scales comparable to the ones
of the internal tide. Under these assumptions, linear theoretical model cannot describe
the evolution of the internal wavefield.
We realized the experiment described in the left-hand side figure ((a) side view and (b) top view).
We follow the evolution of an incoming mode 1 internal tide whose associated velocity field
is shown in the right-hand side top figure (vectors + intensity in cm/s), with a 27cm tall gaussian
seamount. Experiments were done at the Coriolis turntable and confirm that
higher modes (modes 2 to 5 mainly) compose the transmitted wavefield, as can be seen
in the right-hand side bottom figure of the velocity field after the gaussian bump
(vectors + intensity in cm/s). This is in agreement with numerical predictions
(Johnston & Merrifield, JGR 2003). Nevertheless, the linear process is not
sufficient to describe the complete phenomenon since nonlinearites were also
observed (Phys. of Fluids Letters 2009).
Experiments at the Coriolis turntable did not allow three-dimensional study of internal waves reflection. Moreover the nonlinear structures developing
at the slopes have not been quantified. Fundamental issues remain on the interaction of internal waves with a thermocline (strong density gradient at the
The interaction of internal waves with flows (current, vortex) is a burning issue to understand the fate of internal waves
propagating in the ocean and the atmosphere.