F. J. Robinson

Three-dimensional convection simulations of the outer layers of the Sun using realistic physics

This paper describes a series of 3D simulations of shallow inefficient convection in the outer layers of the Sun. The computational domain is a closed box containing the convection-radiation transition layer, located at the top of the solar convection zone. The most salient features of the simulations are that: i)The position of the lower boundary can have a major effect on the characteristics of solar surface convection (thermal structure, kinetic energy and turbulent pressure). ii)The width of the box has only a minor effect on the thermal structure, but a more significant effect on the dynamics (rms velocities). iii)Between the surface and a depth of 1 Mm, even though the density and pressure increase by an order of magnitude, the vertical correlation length of vertical velocity is always close to 600 km. iv) In this region the vertical velocity cannot be scaled by the pressure or the density scale height. This casts doubt on the applicability of the mixing length theory, not only in the superadiabatic layer, but also in the adjacent underlying layers. v) The final statistically steady state is not strictly dependent on the initial atmospheric stratification.

INCLUSION OF TURBULENCE IN SOLAR MODELING

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer (SAL) of the Sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass and the effective ratio of specific heats owing to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g., pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in three-dimensional simulations and produces a p-mode frequency correction an order of magnitude better than the first method.

On Dissipation inside Turbulent Convection Zones from Three-dimensional Simulations of Solar Convection

The development of two-dimensional and three-dimensional simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We investigate the impact of this changed structure on the dissipation properties of the convection zone, parameterized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh, applied to a numerical model of solar convection, to calculate effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of Kolmogorov turbulence. The results quite closely match a linear scaling with period, even though this same formalism applied to a Kolmogorov spectrum of eddies gives a scaling with a power-law index of 5/3.

Global Parameter and Helioseismic Tests of Solar Variability Models

We construct models of the structure and evolution of the Sun which include variable magnetic fields and turbulence. The magnetic effects are (1) magnetic pressure, (2) magnetic energy, and (3) magnetic modulation to turbulence. The effects of turbulence are (1) turbulent pressure, (2) turbulent kinetic energy, and (3) turbulent inhibition of the radiative energy loss of a convective eddy, and (4) turbulent generation of magnetic fields. Using these ingredients we construct five types of solar variability models (including the standard solar model) with magnetic effects. These models are in part based on three-dimensional numerical simulations of the superadiabatic layers near the surface of the Sun. The models are tested with several sets of observational data, namely, the changes of (1) the total solar irradiance, (2) the photospheric temperature, (3) radius, (4) the position of the convection zone base, and (5) low- and medium-degree solar oscillation frequencies. We find that turbulence plays a major role in solar variability, and only a model that includes a magnetically modulated turbulent mechanism can agree with all the current available observational data. We find that because of the somewhat poor quality of all observations (other than the helioseismological ones), we need all data sets in order to restrict the range of models.

Resonant Response of Deep Convection to Surface Hot Spots

Abstract Observations show substantial variations of the intensity of tropical and/or summertime deep convection on land that are not explained by standard measures of convective instability. One feature that distinguishes land surfaces is their heterogeneity. The possible importance of this is investigated here by calculating the response of a nonrotating atmosphere to localized, transient surface heating using both the linearized equations of motion and a cloud-resolving configuration of the Weather Research and Forecasting (WRF) numerical model with moist physics, each in 2D. Both models predict that the depth of the resulting surface heat low near storm center will be greatest for a particular horizontal scale of heating. The linear model reveals that this is a resonant scale determined by the product of the environmental buoyancy frequency, characteristic heating time scale, and thickness of the thermal boundary layer, and the resonance occurs when the aspect ratio of the applied heating matches the ...

Exploring the land-ocean contrast in convective vigor using Islands

Moist convection is well known to be generally more intense over continental than maritime regions, with larger updraft velocities, graupel, and lightning production. This study explores the transition from maritime to continental convection by comparing the trends in Tropical Rainfall Measuring Mission (TRMM) radar and microwave (37 and 85 GHz) observations over islands of increasing size to those simulated by a cloudresolving model. The observed storms were essentially maritime over islands of ,100 km 2 and continental over islands .10 000 km 2 , with a gradual transition in between. Equivalent radar and microwave quantities were simulated from cloud-resolving runs of the Weather Research andForecasting model viaofflineradiation codes. The model configuration wasidealized,with islands represented by regions of uniform surface heat flux without orography, using a range of initial sounding conditions without strong horizontal winds or aerosols. Simulated storm strength varied with initial sounding, as expected, but also increased sharply with island size in a manner similar to observations. Stronger simulated storms were associated with higher concentrations of large hydrometeors. Although biases varied with different ice microphysical schemes, the trend was similar for all three schemes tested and was also seen in 2D and 3D model configurations. The successful reproduction of the trend with such idealized forcing supports previous suggestions that mesoscale variation in surface heating—rather than any difference in humidity, aerosol, or other aspects of the atmospheric state—is the main reason that convection is more intense over continents and large islands than over oceans. Some dynamical storm aspects, notably the peak rainfall and minimum surface pressure low, were more sensitive to surface forcing than to the atmospheric sounding or ice scheme. Large hydrometeor concentrations and simulated microwave and radar signatures, however, were at least as sensitive to initial humidity levels as to surface forcing and were more sensitive to the ice scheme. IssueswithrunningtheTRMMsimulatoron2Dsimulationsarediscussed,buttheyappeartobelessserious than sensitivities to model microphysics, which were similar in 2D and 3D. This supportsthe furtheruse of 2D simulations to economically explore modeling uncertainties.

A Numerical Modeling Study of the Propagation of Idealized Sea-Breeze Density Currents*

AbstractSea breezes are often modeled as a wave response to transient heating in a stratified environment. They occur, however, as density currents with well-defined fronts, the understanding of which rests primarily on experiments and theory that do not include the stratification within and above the current and the steady heat input at the land surface. These gaps are investigated here via a sequence of idealized 2D density current simulations, progressing from the simplest classical case to more realistic surface heating and stratification.In the classical situation where the entire horizontal density contrast is imposed initially, the front quickly attains a constant speed determined by traditional formulas based on the density contrast across the front and the current depth, or by the amount of heat needed to produce it from an initially barotropic fluid. However, these diagnostic and prognostic tools fail completely if the current is driven by a gradual input of heat, analogous to a real sea-breeze ...

The Nature of p-Modes and Granulation in Procyon: New MOST* Photometry and New Yale Convection Models

We present new photometry of Procyon, obtained by MOST during a 38 day run in 2007, and frequency analyses of those data. The long time coverage and low point-to-point scatter of the light curve yield an average noise amplitude of about 1.5-2.0 ppm in the frequency range 500-1500 μHz. This is half the noise level obtained from each of the previous two Procyon campaigns by MOST in 2004 and 2005. The 2007 MOST amplitude spectrum shows some evidence for p-mode signal: excess power centered near 1000 μHz and an autocorrelation signal near 55 μHz (suggestive of a mode spacing around that frequency), both consistent with p-mode model predictions. However, we do not see regularly spaced frequencies aligned in common l-valued ridges in echelle diagrams of the most significant peaks in the spectrum unless we select modes from the spectrum using a priori assumptions. The most significant peaks in the spectrum are scattered by more than ±5 μHz about the predicted l-valued ridges, a value that is consistent with the scatter among individually identified frequencies obtained from ground-based radial velocity (RV) observations. We argue that the observed scatter is intrinsic to the star, due to short lifetimes of the modes and the dynamic structure of Procyons thin convection zone. We compare the MOST Procyon amplitude and power density spectra with preliminary results of three-dimensional numerical models of convection by the Yale group. These models show that, unlike in the Sun, Procyons granulation signal in luminosity has a peak coinciding with the expected frequency region for p-modes near 1000 μHz.

Dissipation Efficiency in Turbulent Convective Zones in Low Mass Stars

We extend the analysis of Penev et al. to calculate effective viscosities for the surface convective zones of three main-sequence stars of 0.775 M{sub sun}, 0.85 M{sub sun}, and the present day Sun. In addition, we also pay careful attention to all normalization factors and assumptions in order to derive actual numerical prescriptions for the effective viscosity as a function of the period and direction of the external shear. Our results are applicable for periods that are too long to correspond to eddies that fall within the inertial subrange of Kolmogorov scaling, but no larger than the convective turnover time, when the assumptions of the calculation break down. We find moderately anisotropic viscosity, scaling linearly with the period of the external perturbation, with its components having magnitudes between three and ten times smaller than the Zahns prescription.

Modeling the Impact of Convective Entrainment on the Tropical Tropopause

Abstract Simulations with the Weather Research and Forecasting (WRF) cloud-resolving model of deep moist convective events reveal net cooling near the tropopause (∼15–18 km above ground), caused by a combination of large-scale ascent and small-scale cooling by the irreversible mixing of turbulent eddies overshooting their level of neutral buoyancy. The turbulent cooling occurred at all CAPE values investigated (local peak values ranging from 1900 to 3500 J kg−1) and was robust to grid resolution, subgrid-scale turbulence parameterization, horizontal domain size, model dimension, and treatment of ice microphysics. The ratio of the maximum downward heat flux in the tropopause to the maximum tropospheric upward heat flux was close to 0.1. This value was independent of CAPE but was affected by changes in microphysics or subgrid-scale turbulence parameterization. The convective cooling peaked roughly 1 km above the cold point in the background input sounding and the mean cloud- and (turbulent kinetic energy) T...