The challenge of detecting asymptotic rotating convection in diffusion-free parameter space

Studying planetary fluid layers in laboratory and numerical settings requires bridging large gaps in the governing parameter values, making it difficult to tell whether experimental results can be reliably extrapolated. In rotating convection, scaling laws developed in the asymptotically-reduced, diffusion-free limit (Julien et al., Phys. Rev. Lett. 2012) provide an important reference point: if experiments demonstrate these asymptotic scalings, then the observed fluid physics should apply to planets and stars. However, establishing whether experimental data are truly asymptotic also poses a challenge. To combat this, geophysicists often express results in terms of parameters specially constructed to be independent of fluid diffusivities (Christensen and Aubert, Geophys. J. Int. 2006).

Here, we argue that diffusion-free parameters are an ineffective framework for examining heat transfer data. We show that the asymptotic scaling is, in fact, identical to the scaling of the onset of convection in diffusion-free space. Using synthetic data of various scaling slopes, parameter ranges, and noise levels, we show that this property greatly limits our ability to distinguish asymptotic heat transfer scalings from any other scaling in diffusion-free space. We test the effect of compensating data by the asymptotic scaling law, examining the degree to which this reverses the above limitations. Finally, we find that similar behaviors also manifest in plots of velocity and length scale data when cast in diffusion-free parameters. By tuning the amount of noise in our synthetic data in a variety of parameter spaces, we produce guidelines for the precision of experimental results necessary to confidently capture asymptotic rotating convection.