Transitions in turbulent rotating Rayleigh-B\'enard convection

Numerical simulations of rotating Rayleigh-B\'enard convection are presented for both no slip and free slip boundaries. The goal is to find a criterion distinguishing convective flows dominated by the Coriolis force from those nearly unaffected by rotation. If one uses heat transport as an indicator of which regime the flow is in, one finds that the transition between the flow regimes always occurs at the same value of a certain combination of Reynolds, Prandtl and Ekman numbers for both boundary conditions. If on the other hand one uses the helicity of the velocity field to identify flows nearly independent of rotation, one finds the transition at a different location in parameter space

Heat transport in rotating convection without Ekman layers

Numerical simulation of rotating convection in plane layers with free slip boundaries show that the convective flows can be classified according to a quantity constructed from the Reynolds, Prandtl and Ekman numbers. Three different flow regimes appear: Laminar flow close to the onset of convection, turbulent flow in which the heat flow approaches the heat flow of non-rotating convection, and an intermediate regime in which the heat flow scales according to a power law independent of thermal diffusivity and kinematic viscosity.Comment: 4 pages, 4 figure

Rapidly rotating plane layer convection with zonal flow

The onset of convection in a rapidly rotating layer in which a thermal wind is present is studied. Diffusive effects are included. The main motivation is from convection in planetary interiors, where thermal winds are expected due to temperature variations on the core-mantle boundary. The system admits both convective instability and baroclinic instability. We find a smooth transition between the two types of modes, and investigate where the transition region between the two types of instability occurs in parameter space. The thermal wind helps to destabilise the convective modes. Baroclinic instability can occur when the applied vertical temperature gradient is stable, and the critical Rayleigh number is then negative. Long wavelength modes are the first to become unstable. Asymptotic analysis is possible for the transition region and also for long wavelength instabilities, and the results agree well with our numerical solutions. We also investigate how the instabilities in this system relate to the classical baroclinic instability in the Eady problem. We conclude by noting that baroclinic instabilities in the Earth's core arising from heterogeneity in the lower mantle could possibly drive a dynamo even if the Earth's core were stably stratified and so not convecting.Comment: 20 pages, 7 figure

Global fluctuations in magnetohydrodynamic dynamos

The spectrum of temporal fluctuations of total magnetic energy for several dynamo models is different from white noise at frequencies smaller than the inverse of the turnover time of the underlying turbulent velocity field. Examples for this phenomenon are known from previous work and we add in this paper simulations of the G.O. Roberts dynamo and of convectively driven dynamos in rotating spherical shells. The appearance of colored noise in the magnetic energy is explained by simple phenomenological models. The Kolmogorov theory of turbulence is used to predict the spectrum of kinetic and magnetic energy fluctuations in the inertial range

A spherical shell numerical dynamo benchmark with pseudo vacuum magnetic boundary conditions

It is frequently considered that many planetary magnetic fields originate as a result of convection within planetary cores. Buoyancy forces responsible for driving the convection generate a fluid flow that is able to induce magnetic fields; numerous sophisticated computer codes are able to simulate the dynamic behaviour of such systems. This paper reports the results of a community activity aimed at comparing numerical results of several different types of computer codes that are capable of solving the equations of momentum transfer, magnetic field generation and heat transfer in the setting of a spherical shell, namely a sphere containing an inner core. The electrically conducting fluid is incompressible and rapidly rotating and the forcing of the flow is thermal convection under the Boussinesq approximation. We follow the original specifications and results reported in Harder & Hansen to construct a specific benchmark in which the boundaries of the fluid are taken to be impenetrable, non-slip and isothermal, with the added boundary condition for the magnetic field <b>B</b> that the field must be entirely radial there; this type of boundary condition for <b>B</b> is frequently referred to as ‘pseudo-vacuum’. This latter condition should be compared with the more frequently used insulating boundary condition. This benchmark is so-defined in order that computer codes based on local methods, such as finite element, finite volume or finite differences, can handle the boundary condition with ease. The defined benchmark, governed by specific choices of the Roberts, magnetic Rossby, Rayleigh and Ekman numbers, possesses a simple solution that is steady in an azimuthally drifting frame of reference, thus allowing easy comparison among results. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier-finite element code. There is good agreement among codes

Towards an experimental von Karman dynamo: numerical studies for an optimized design

Numerical studies of a kinematic dynamo based on von Karman type flows between two counterrotating disks in a finite cylinder are reported. The flow has been optimized using a water model experiment, varying the driving impellers configuration. A solution leading to dynamo action for the mean flow has been found. This solution may be achieved in VKS2, the new sodium experiment to be performed in Cadarache, France. The optimization process is described and discussed, then the effects of adding a stationary conducting layer around the flow on the threshold, on the shape of the neutral mode and on the magnetic energy balance are studied. Finally, the possible processes involved into kinematic dynamo action in a von Karman flow are reviewed and discussed. Among the possible processes we highlight the joint effect of the boundary-layer radial velocity shear and of the Ohmic dissipation localized at the flow/outer-shell boundary

Full sphere hydrodynamic and dynamo benchmarks

Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamic behaviour of such systems. We report on the first community activity to compare numerical results of computer codes designed to calculate fluid flow within a whole sphere. The flows are incompressible and rapidly rotating and the forcing of the flow is either due to thermal convection or due to moving boundaries. All problems defined have solutions that allow easy comparison, since they are either steady, slowly drifting or perfectly periodic. The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for the flow. Benchmark 1 is purely hydrodynamic, and has a drifting solution. Benchmark 2 is a magnetohydrodynamic benchmark that can generate oscillatory, purely periodic, flows and magnetic fields. In contrast, Benchmark 3 is a hydrodynamic rotating bubble benchmark using no slip boundary conditions that has a stationary solution. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier–finite element code. There is good agreement between codes. It is found that in Benchmarks 1 and 2, the approximation of a whole sphere problem by a domain that is a spherical shell (a sphere possessing an inner core) does not represent an adequate approximation to the system, since the results differ from whole sphere results

Poloidal-toroidal decomposition in a finite cylinder. II. Discretization, regularization and validation

The Navier-Stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility. Regularity of the solutions is ensured in several ways: First, the potentials are represented using a spectral basis which is analytic at the cylindrical axis. Second, the non-physical discontinuous boundary conditions at the cylindrical corners are smoothed using a polynomial approximation to a steep exponential profile. Third, the nonlinear term is evaluated in such a way as to eliminate singularities. The resulting pseudo-spectral code is tested using exact polynomial solutions and the spectral convergence of the coefficients is demonstrated. Our solutions are shown to agree with exact polynomial solutions and with previous axisymmetric calculations of vortex breakdown and of nonaxisymmetric calculations of onset of helical spirals. Parallelization by azimuthal wavenumber is shown to be highly effective

The influence of clouds on radical concentrations: observations and modelling studies of HOx during the Hill Cap Cloud Thuringia (HCCT) campaign in 2010

The potential for chemistry occurring in cloud droplets to impact atmospheric composition has been known for some time. However, the lack of direct observations and uncertainty in the magnitude of these reactions led to this area being overlooked in most chemistry transport models. Here we present observations from Mt Schmücke, Germany, of the HO2 radical made alongside a suite of cloud measurements. HO2 concentrations were depleted in-cloud by up to 90% with the rate of heterogeneous loss of HO2 to clouds necessary to bring model and measurements into agreement, demonstrating a dependence on droplet surface area and pH. This provides the first observationally derived assessment for the uptake coefficient of HO2 to cloud droplets and was found to be in good agreement with theoretically derived parameterisations. Global model simulations, including this cloud uptake, showed impacts on the oxidising capacity of the troposphere that depended critically on whether the HO2 uptake leads to production of H2O2 or H2O

The influence of clouds on radical concentrations: Observations and modelling studies of HOx during the Hill Cap Cloud Thuringia (HCCT) campaign in 2010

The potential for chemistry occurring in cloud droplets to impact atmospheric composition has been known for some time. However, the lack of direct observations and uncertainty in the magnitude of these reactions led to this area being overlooked in most chemistry transport models. Here we present observations from Mt Schmücke, Germany, of the HO2 radical made alongside a suite of cloud measurements. HO2 concentrations were depleted in-cloud by up to 90% with the rate of heterogeneous loss of HO2 to clouds necessary to bring model and measurements into agreement, demonstrating a dependence on droplet surface area and pH. This provides the first observationally derived assessment for the uptake coefficient of HO2 to cloud droplets and was found to be in good agreement with theoretically derived parameterisations. Global model simulations, including this cloud uptake, showed impacts on the oxidising capacity of the troposphere that depended critically on whether the HO2 uptake leads to production of H2O2 or H2O