Excitation of inertial modes in a closed grid turbulence experiment under rotation

Abstract

We report an experimental study of the decay of grid-generated turbulence in a confined geometry submitted to a global rotation. Turbulence is generated by rapidly towing a grid in a parallelepipedic water tank. The velocity fields of a large number of independent decays are measured in a vertical plane parallel to the rotation axis using a corotating particle image velocimetry system. We first show that, when a "simple" grid is used, a significant amount of the kinetic energy (typically 50%) is stored in a reproducible flow composed of resonant inertial modes. The spatial structure of those inertial modes, extracted by band-pass filtering, is found compatible with the numerical results of L. R. M. Maas [Fluid Dyn. Res. 33, 373 (2003)]. The possible coupling between these modes and turbulence suggests that turbulence cannot be considered as freely decaying in this configuration. We demonstrate however that these inertial modes may be significantly reduced (down to 15% of the total energy) by adding a set of inner tanks attached to the grid. These results suggest that it is possible to produce an effectively freely decaying rotating turbulence in a confined geometry.

Discrete and continuous hamiltonian systems for wave modelling

“…either on convex (outer) or concave (inner) parts of spherical shells; in other studies by means of the Euler force (using libration). Experiments performed in square domains [14,54,15], seem to show that inviscid eigenmodes derived above are relevant in the sense that energy spectra display peaks at inviscid eigenfrequencies of some of the larger scale eigenmodes. In two experiments [14,54] forcing arises by pulling a grid through the fluid, leaving a set of waves behind.…”

“…Experiments performed in square domains [14,54,15], seem to show that inviscid eigenmodes derived above are relevant in the sense that energy spectra display peaks at inviscid eigenfrequencies of some of the larger scale eigenmodes. In two experiments [14,54] forcing arises by pulling a grid through the fluid, leaving a set of waves behind. In another experiment with a libration ( [15]), forcing occurs through Ekman-layer convergence, lending the spatial structure of the response much more of a beam-like character.…”

“…In experiments like those in [34,73,65,67,53,102,4,64,106,12,14,54,15,69], a variety of forcing mechanisms and geometries have been applied. In some cases forcing occurs by pumping through viscous boundary layers, e.g.…”

“…While some of the eigenfrequencies have indeed been obtained experimentally [14,54], validating the precise shape of the corresponding eigenmodes has been more cumbersome [15]. This may of course be partially due to viscous boundary layers modifying the flow field near the boundaries, but may also partly be due to this convergence problem.…”

“…Inertial waves were identified in a rotating axial cylinder [34,73,65,67,53], in a slightly tilted free surface cylinder [102], in a sphere [4], in a tilted spheroid (tilt of its axis of rotation with respect to the axis of the cavity) [64,106], in a (truncated) cone [12], in a rectangular parallelepiped [14,54,15] and in a trapezoid [61,69].…”