Effects of bottom topography on the spin-up in a cylinder

Abstract

Motivated by better understanding the long-standing issue of the role of topography on the transport of angular momentum in rapidly rotating fluids, we conducted spin-up experiments in a straight cylinder with a regular pavement of rectangular blocks at the bottom. We perform particle image velocimetry measurements to monitor the decay of the initial differential motion generated by the sudden increase of the container rotation rate. We observe that the re-synchronization time, the so-called spin-up time, is shorter in the presence of topography with a minimum at a particular length scale of the topography pattern. We show evidence of energy transport by inertial waves as well as non-linear mechanisms leading to a scaling of the spin-up time significantly different from the classical E−1/2 in the absence of topography.

Mean zonal flows induced by weak mechanical forcings in rotating spheroids

“…Finally, the core-mantle boundary of most planets exhibits roughness (Narteau et al 2001;Le Mouël et al 2006), but scant attention has been given to the flow dynamics in the presence of small-scale topography (e.g. Burmann & Noir 2018). However, our asymptotic theory could be used to get further physical insights into topographic effects for planetary applications.…”

Transition between advection and inertial wave propagation in rotating turbulence

“…In the absence of rotation effects, the jet develops as U(z)/U 0 ∼ d/z (Pope 2000, p. 100), so z T must scale as z T ∼ (U 0 d/2Ω) 1/2 , or equivalently, z T /L ∼ Ro 1/2 Q , as in (4.1). A similar criterion was put forward by Burmann & Noir (2018) to explain the breakdown of inertial wave propagation in a spun up cylinder where the waves were emitted by a topography of the bottom wall. When turbulence is forced by an oscillating grid, Dickinson & Long (1983) similarly observe that the progression of the front is not affected by rotation in the early stages up to a critical distance, which these authors express (in our notations) as z T 0.36( f S 2 /Ω) 1/2 , in terms of the frequency f and stroke S of the grid.…”

“…In statistically steady turbulence, jet experiments (Yarom & Sharon (2014), 0.006 Ro 0.2), and experiments with a two-dimensional mechanical forcing (Campagne et al 2015) confirmed that some of the fluctuations of frequency lower than 2Ω, the maximum frequency of inertial waves, satisfied the dispersion relation for inertial waves (but for the sweeping effect at high wavenumbers identified by Campagne et al (2015)). The recent experiments of Burmann & Noir (2018) showed that inertial waves of a wide range of length scales emitted by a topography near an Ekman wall could speed up momentum transfer along the rotation axis and lead to an accelerated spin-up time following a step change in the rotation of a cylindrical vessel.…”

Fluid Dynamics Experiments for Planetary Interiors

“…A comparison between theoretical and/or numerical predictions yields a semiquantitative agreement, and it is concluded that thermal Rossby waves may significantly influence the core convection close to the tangent cylinder. Motivated by the challenge to better characterize the transport of energy and angular momentum from the topography to the fluid flow, Burmann and Noir (2018) carried out a study of the spin-up of a rapidly rotating fluid with bottom topography. The experimental setup consists of a rotating straight circular cylinder with a chessboard like arrangement of rectangular blocks at the bottom (Fig.…”

“…10Investigation of meso-scale topography. Spin-up experiments in a cylinder with bottom topography(Burmann and Noir 2018): a experimental setup; b kinetic energy as a function of time. The decay of the kinetic energy depends on the length scale of the bottom topography s (ratio between the block size and the radius of the cylindrical container).…”