Regimes and scaling laws for convection with and without rotation

The geodynamo is maintained by turbulent rotating convection in Earth's liquid iron outer
core. Core dynamics are inaccessible to direct measurement and our understanding comes
from a combination of observations, theoretical arguments, laboratory experiments and
numerical simulations. The vast range of spatial and temporal scales present prevent
numerical or physical experiments from being able to reproduce the convective state of
Earth's core exactly. This motivates systematic studies in which we attempt to understand
the fundamentals of convection over the broad range of accessible parameter space with a
view to identifying asymptotic behaviour; if such behaviour is found, then this could allow
extrapolation to Earth's core values.
We present a combined numerical-laboratory survey of hydrodynamic convection to elucidate
the role of different boundary conditions, geometries and the influence of rotation
over a wide range of parameter space. We focus on transitions in thermal convection with
a particular interest in the constraining effects of rotation.
The transition from rapidly rotating to weakly rotating convection is hypothesised to be
controlled by the thermal boundary layers. Using plane-layer Rayleigh-Benard convection
simulations we determine a robust definition of the thermal boundary layer which can be
used for non-rotating or rotating convection with different thermal boundary conditions.
Different physical regimes of convection are identified in a rotating spherical shell by
correlating changes in both local and global flow diagnostics. We identify a regime of
quasi-geostrophic turbulence which may be relevant to describing the dynamics of Earth's
core.
Laboratory experiments and local plane-layer simulations are thought to be analogues
for convection in the polar region of a spherical shell and unsurprisingly these modelling
approaches do not agree with full spherical shell calculations. In an attempt to unify
these different modelling approaches we harvest a
fluid region at high latitude and are
able to explicitly show good agreement between experiments and local simulations with
polar convection. Ultimately this work provides a platform to investigate convection in a
regime which bridges that of Earth's core.