Scaling laws for planetary dynamos

We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed by Christensen and Aubert. The main difference is that, in view of the small value of the Rossby number in planetary cores, we insist that the non-linear inertial term, uu, is negligible. This changes the exponents in the power-laws which relate the various properties of the fluid dynamo to the planetary dipole moment and rotation rate. Our scaling laws are consistent with the available numerical evidence. © The Authors 2013 Published by Oxford University Press on behalf of The Royal Astronomical Society.

Scaling of velocity fluctuations in off-wall boundary conditions for turbulent flows

A model for off-wall boundary conditions for turbulent flow is investigated. The objective of such a model is to circumvent the need to resolve the buffer layer near the wall, by providing conditions in the logarithmic layer for the overlying flow. The model is based on the self-similarity of the flow at different heights in the logarithmic layer. It was first proposed by Mizuno and Jiménez (2013), imposing at the boundary plane a velocity field obtained on-the-fly from an overlying region. The key feature of the model was that the lengthscales of the field were rescaled to account for the self-similarity law. The model was successful at sustaining a turbulent logarithmic layer, but resulted in some disagreements in the flow statistics, compared to fully-resolved flows. These disagreements needed to be addressed for the model to be of practical application. In the present paper, a more refined, wavelength-dependent rescaling law is proposed, based on the wavelength-dependent dynamics in fully-resolved flows. Results for channel flow show that the new model eliminates the large artificial pressure fluctuations found in the previous one, and a better agreement is obtained in the bulk properties, the flow fluctuations, and their spectral distribution across the whole domain. © Published under licence by IOP Publishing Ltd.

Scaling the iHMM: Parallelization versus Hadoop

This paper compares parallel and distributed implementations of an iterative, Gibbs sampling, machine learning algorithm. Distributed implementations run under Hadoop on facility computing clouds. The probabilistic model under study is the infinite HMM [1], in which parameters are learnt using an instance blocked Gibbs sampling, with a step consisting of a dynamic program. We apply this model to learn part-of-speech tags from newswire text in an unsupervised fashion. However our focus here is on runtime performance, as opposed to NLP-relevant scores, embodied by iteration duration, ease of development, deployment and debugging. © 2010 IEEE.