We investigate a massive ( g cm−2 at 1 au) protoplanetary disc model by means of 3D radiation magnetohydrodynamic simulations. The vertical structure of the disc is determined self‐consistently by a balance between turbulent heating caused by the magnetorotational turbulence and radiative cooling. Concerning the vertical structure, two different regions can be distinguished: a gas‐pressure‐dominated, optically thick mid‐plane region where most of the dissipation takes place, and a magnetically dominated, optically thin corona which is dominated by strong shocks. At the location of the photosphere, the turbulence is supersonic (), which is consistent with previous results obtained from the fitting of spectra of young stellar objects. It is known that the turbulent saturation level in simulations of MRI‐induced turbulence does depend on numerical factors such as the numerical resolution and the box size. However, by performing a suite of runs at different resolutions (using up to grid cells) and with varying box sizes (with up to 16 pressure scaleheights in the vertical direction), we find that both the saturation levels and the heating rates show a clear trend to converge once a sufficient resolution in the vertical direction has been achieved.

The aim of this paper is to investigate the spatial structure of a protoplanetary disc whose dynamics is governed by magnetorotational turbulence. We perform a series of local three‐dimensional chemoradiative magnetohydrodynamic simulations located at different radii of a disc which is twice as massive as the standard minimum mass solar nebula of Hayashi. The ionization state of the disc is calculated by including collisional ionization, stellar X‐rays, cosmic rays and the decay of radionuclides as ionization sources, and by solving a simplified chemical network which includes the effect of the absorption of free charges by μm‐sized dust grains. In the region where the ionization is too low to ensure good coupling between matter and magnetic fields, a non‐turbulent central ‘dead zone’ forms, which ranges approximately from a distance of 2 to 4 au from the central star. The approach taken in this work allows for the first time to derive the global spatial structure of a protoplanetary disc from a set of physically realistic numerical simulations.

We present a derivation of the transverse force acting on a hydrodynamic vortex in the presence of an incoming sound wave from a global solution of the scattering problem, using the method of matched asymptotic expansions. The solution presented includes a detailed treatment of the interaction of the incident wave with the vortex core, and is free from the singularities in the momentum exchange between vortex and sound wave which have led to contradictory results for the value of the transverse force in the literature.Comment: 7 pages of RevTex4, 1 figur

High-resolution large-eddy simulations of turbulent mixing at the inner surface of a dense shell which undergoes forced compression by a spherically imploding shock wave are presented. Perturbations on the inner surface grow as a result of Richtmyer-Meshkov and Rayleigh-Taylor instabilities and effects related to geometric convergence and compressibility. Three different cases with different initial surface perturbations, one broadband and two narrowband, are considered. The perturbation power spectrum is related to the mode number via Pℓ ∝ ℓn, where the case with broadband perturbations has n = −2, and modes in the range ℓ = 6–200. The narrowband perturbations have n = 0 and modes in the range ℓ = 50–100 and ℓ = 100–200. The simulations are carried out in spherical coordinates using the PLUTO hydrodynamics code. Results on the mix layer width, molecular mix, and turbulent kinetic energy distribution are presented, demonstrating clearly the impact of the amplitude and spectral form of the initial perturbation on the evolution of integral properties. A recently developed model predicting the growth of single mode perturbations in spherical implosions including shock waves is extended to predict mix layer amplitudes for broadband and narrowband cases, along with a model proposed by Mikaelian [“Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells,” Phys. Rev. A 42, 3400–3420 (1990)]. The resultant layer amplitude predictions from the new model are in good agreement with the numerical results while the longest wavelengths are not yet saturated, while Mikaelian’s model agrees well where the initial modes are saturated.

In this paper, we investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. The analysis is performed by the use of analytical and numerical means. We provide a general dispersion relation together with the corresponding eigenfunctions describing the growth rates of small disturbances on a homogeneous background shear flow. The dispersion relation includes compressibility and radiative effects in the flux‐limited diffusion approximation. By introducing an effective speed of sound, all the effects of radiation transport can be subsumed into one single parameter. It can be shown that the growth rates of the vertical modes – which are the fastest growing ones – are reduced by radiative transport. For the case of non‐vertical modes, the growth rates may instead be enhanced. We quantify the effects of compressibility and radiative diffusion on the growth rates for the gas‐pressure dominated case. The analytical discussion is supplemented by numerical simulations, which are also used for a first investigation of the non‐linear stage of the MRI in gas‐pressure dominated accretion discs with radiation transport included.