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Inertial waves in rotating fluids

Members: M. Brunet, P.-P. Cortet

Former members: J. Boisson, C. Lamriben, N. Machicoane, F. Moisy, C. Morize, M. Rabaud

Collaborations: T. Dauxois (ENS Lyon), L.R.M. Maas (Univ. Utrecht), B. Voisin (LEGI)

Propagation of a plane inertial wave

Fig. 1: Propagation of a plane inertial wave excited by a wavemaker made of stacked plates oscillating around a helical camshaft. Particle Image Velocimetry (PIV) measurements are performed in a plane parallel to the rotation axis using a corotating PIV system. [Read the paper]

A fluid rotating at constant angular velocity supports a specific and unusual class of waves, called inertial waves, which propagate in the interior of the fluid. These waves are of primary importance in geophysical and astrophysical flows (in ocean, atmosphere and liquid core of planets, in rotating stars,...), in which cases they are often coupled with density stratification effects. Pure inertial waves are also relevant to industrial flows, such as spacecrafts fuel tanks or liquid-filled ballistics. The most striking properties of these waves arise from their anisotropic dispersion, leading to a number of non-intuitive geometrical behaviors: an energy propagation normal to the phase propagation (see fig. 1), a wavelength independent of the wave frequency leading, for example, to anomalous reflection on solid boundaries.

In our experiments, inertial waves are generated either by oscillating wavemakers leading to propagative wave beams (fig. 1) or wave attractors in closed domains [see the paper], moving objects leading to wake of inertial waves (fig. 2), or by harmonic perturbations of the fluid container rotation, which mimic planets harmonic motions, leading to both propagative wave beams and resonant modes (fig. 3). These experiments are performed on the specifically designed "Gyroflow" rotating platform. Velocity fields are measured in the rotating frame by means of a corotating particle image velocimetry system.

A inertial mode excited in a cube under libration

Fig. 2: We have studied the wake of inertial waves produced by a horizontal cylinder translated horizontally in a fluid rotating about the vertical. We have shown that, owing to the horizontal invariance of the object, a boundary condition using a slender-body approximation leads to a quantitative description of the wake, even for non-slender bodies.
[Read the paper]

In these experiments, we study how the waves are excited and how their amplitude decays under the action of viscosity. We also study the non-linear instabilities and interactions which can affect the inertial waves. Such processes can be at the origin of permanent "zonal" winds in the atmosphere, ocean or liquid core of planets. The non-linear interactions between inertial waves is also a fundamental ingredient of the modification of turbulence by global rotation, leading notably to an inhibition of energy transfers between spatial scales.

A inertial mode excited in a cube under libration

Fig. 3: A resonant inertial mode excited in a cube under libration, i.e. under a modulated rotation, at two different phases. PIV measurements are performed in a plane parallel to the rotation axis.
[Read the paper|See movies]


  • Linear and nonlinear regimes of an inertial wave attractor
    M. Brunet, T. Dauxois, P.-P. Cortet, Physical Review Fluids 4 034801 (2019) [PDF]
    Selected as an "Editors' suggestion"
  • Wake of inertial waves of a horizontal cylinder in horizontal translation
    N. Machicoane, V. Labarre, B. Voisin, F. Moisy, P.-P. Cortet, Physical Review Fluids 3 034801 (2018) [PDF]
  • Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid, N. Machicoane, F. Moisy, P.-P. Cortet, Physical Review Fluids 1 073701 (2016) [PDF]
  • Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid
    N. Machicoane, P.-P. Cortet, B. Voisin, F. Moisy, Physics of Fluids 27 066602 (2015) [PDF]
  • Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment
    A. Campagne, B. Gallet, F. Moisy, P.-P. Cortet , Physical Review E 91 043016 (2015) [PDF]
  • Inertial waves and modes excited by the libration of a rotating cube
    J. Boisson, C. Lamriben, L.R.M. Maas, P.-P. Cortet, F. Moisy, Physics of Fluids 24 076602 (2012) [PDF|movies]
  • Earth rotation prevents exact solid body rotation of fluids in the laboratory
    J. Boisson, D. Cébron, F. Moisy, P.-P. Cortet, EPL 98 59002 (2012) [PDF]
    Selected in "EPL Highlights 2012"
  • Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid
    G. Bordes, F. Moisy, T. Dauxois, P.-P. Cortet, Physics of Fluids 24 014105 (2012) [PDF]
  • Excitation of inertial modes in a closed grid turbulence experiment under rotation
    C. Lamriben, P.-P. Cortet, F. Moisy, L. R. M. Maas, Physics of Fluids 23 015102 (2011) [PDF]
  • Viscous spreading of an inertial wave beam in a rotating fluid
    P.-P. Cortet, C. Lamriben, F. Moisy, Physics of Fluids 22 086603 (2010) [PDF]
  • Experimental observation using particle image velocimetry of inertial waves in a rotating fluid
    L. Messio, C. Morize, M. Rabaud, F. Moisy, Exp. in Fluids 44, 519–528 (2008) [PDF]

Last modification: July 17 2019, 21:45:00.