Topographical effects
Fluid layers are a common feature of celestial bodies, for example in the form of liquid metal cores or subsurface oceans. These large scale fluid layers contribute to angular momentum exchange and in some cases contribute to the self-generation of magnetic fields. The dynamics in these layers are strongly influenced by the planetary rotation, but also the forced orbital perturbations of the celestial body, such as precession, libration or nutation. Fluid layers have been addressed in various experimental, numerical and theoretical studies mostly in idealized spherical geometries, but the case of boundary topography has received less attention. Therefore, we investigate experimentally the effects of topography in planetary fluid layers.
Investigating the drag force due to inertial waves generated by topography
Observations of the rotation rates of rapidly rotating astral bodies, such as the Moon and the Earth, reveal energy dissipation between their liquid cores and solid shells. This dissipation cannot be explained solely by viscous energy transfer and is thought to arise from magnetic, convective, and pressure forces within the fluid. This study investigates the impact of the inertial wave pressure drag caused by topographic features at the fluid-solid boundary.
In the absence of forces other than the Coriolis acceleration, pressure dissipation arises due to the topography at the boundary generating inertial waves. These waves transport energy away and dissipate it through viscous processes in the fluid volume. To best examine this effect, two distinct approaches were employed to study rotating topographies submerged in a neutrally buoyant, non-conductive fluid with a constant mean flow.
The first approach, conducted numerically using Nek5000 in a periodic box, revealed that the drag force scales as \(h^2\) for slender topographies. For steeper slopes exceeding unity, the drag force becomes wavelength-dependent. These were carried out for Rossby number between \(10^{-5}\) and 3, and slopes between 0.1 and 10.
The second approach combined physical measurements and numerical modelling in a rotating cylinder with differential rotation between the topography and the fluid. This validated the analytical torque predictions derived from periodic box results when integrated over a cylinder.
These findings demonstrate that the periodic box framework can be generalized to a planetary spherical shell, providing a foundation for estimating energy dissipation caused by inner topographies in planetary bodies. By highlighting the role of inertial wave drag, this work offers valuable insights into the mechanisms driving rotational evolution in celestial bodies and the dynamics of flows within their liquid layers.
People involved: Vadim Giraud, Jerome Noir, Fabian Burmann, Remy Monville, David Cebron
Grant: Funded through ETH Zurich Research Grant ETH-0422-1
Effects of topography on the Spin-up of a fluid
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.
People involved: Fabian Burmann, Jerome Noir
Grants: Funded through ETH ZURICH Research Grant No. ETH-26 15-1