Effects of compressibility on driving zonal flow in gas giants

The banded structures observed on the surfaces of the gas giants are associated with strong zonal winds alternating in direction with latitude. We use three-dimensional numerical simulations of compressible convection in the anelastic approximation to explore the properties of zonal winds in rapidly rotating spherical shells. Since the model is restricted to the electrically insulating outer envelope, we therefore neglect magnetic effects. A systematic parametric study for various density scaleheights and Rayleigh numbers allows to explore the dependence of convection and zonal jets on these parameters and to derive scaling laws. While the density stratification affects the local flow amplitude and the convective scales, global quantities and zonal jets properties remain fairly independent of the density stratification. The zonal jets are maintained by Reynolds stresses, which rely on the correlation between zonal and cylindrically radial flow components. The gradual loss of this correlation with increasing supercriticality hampers all our simulations and explains why the additional compressional source of vorticity hardly affects zonal flows. All these common features may explain why previous Boussinesq models were already successful in reproducing the morphology of zonal jets in gas giants.Comment: 17 pages, 15 figures, 2 tables, accepted for publication in Icaru

Glue spin and helicity in proton from lattice QCD

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin $S_{G}$ in the Coulomb gauge in the $\overline{\text{MS}}$ scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of $S_G$ in the range $0\leq |\vec{p}| < 1.5$ GeV is very mild, and we determine it in the large momentum limit to be $S_{G}=0.251(47)(16)$ at the physical pion mass in the $\overline{\text{MS}}$ scheme at $\mu^2=10$ GeV$^2$. If the matching procedure in large momentum effective theory is neglected, $S_G$ is equal to the glue helicity measured in high-energy scattering experiments.Comment: Version accepted for publication in Physical Review Letters, 4 pages, 4 figures, supplemental materials are attached after the conten

Can the Earth's dynamo run on heat alone?

The power required to drive the geodynamo places significant constraints on the heat passing across the core-mantle boundary and the Earth's thermal history. Calculations to date have been limited by inaccuracies in the properties of liquid iron mixtures at core pressures and temperatures. Here we re-examine the problem of core energetics in the light of new first-principles calculations for the properties of liquid iron. There is disagreement on the fate of gravitational energy released by contraction on cooling. We show that only a small fraction of this energy, that associated with heating resulting from changes in pressure, is available to drive convection and the dynamo. This leaves two very simple equations in the cooling rate and radioactive heating, one yielding the heat flux out of the core and the other the entropy gain of electrical and thermal dissipation, the two main dissipative processes. This paper is restricted to thermal convection in a pure iron core; compositional convection in a liquid iron mixture is considered in a companion paper. We show that heat sources alone are unlikely to be adequate to power the geodynamo because they require a rapid secular cooling rate, which implies a very young inner core, or a combination of cooling and substantial radioactive heating, which requires a very large heat flux across the core-mantle boundary. A simple calculation with no inner core shows even higher heat fluxes are required in the absence of latent heat before the inner core formed

An analysis of the fluctuations of the geomagnetic dipole

The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 13 to 33 kyr, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(x/x0)^2]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core.Comment: 11 pages, 6 figure

Remarks on the stability of the Navier-Stokes equations supplemented with stress-free boundary conditions

The purpose of this note is to analyze the long term stability of the Navier-Stokes equations supplemented with the Coriolis force and the stress-free boundary condition. It is shown that, if the flow domain is axisymmetric, spurious stability behaviors can occur depending whether the Coriolis force is active or not

Physical processes leading to surface inhomogeneities: the case of rotation

In this lecture I discuss the bulk surface heterogeneity of rotating stars, namely gravity darkening. I especially detail the derivation of the omega-model of Espinosa Lara & Rieutord (2011), which gives the gravity darkening in early-type stars. I also discuss the problem of deriving gravity darkening in stars owning a convective envelope and in those that are members of a binary system.Comment: 23 pages, 11 figure, Lecture given to the school on the cartography of the Sun and the stars (May 2014 in Besan\c{c}on), to appear in LNP, Neiner and Rozelot edts V2: typos correcte

A Lattice Study of Quark and Glue Momenta and Angular Momenta in the Nucleon

We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with $Z_4$ noise, and the signal-to-noise is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a $16^3 \times 24$ quenched lattice at $\beta = 6.0$ for Wilson fermions with $\kappa=0.154, 0.155$, and $0.1555$ which correspond to pion masses at $650, 538$, and $478$~MeV, respectively. The chirally extrapolated $u$ and $d$ quark momentum/angular momentum fraction is found to be $0.64(5)/0.70(5)$, the strange momentum/angular momentum fraction is $0.024(6)/0.023(7)$, and that of the glue is $0.33(6)/0.28(8)$. The previous study of quark spin on the same lattice revealed that it carries a fraction of $0.25(12)$ of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes $0.47(13)$ of the proton spin with almost all of it coming from the disconnected insertions.Comment: Renormalization section is expanded to include more details. There are slight changes in the final numbers. A few modification and corrections are made in the rest of the tex