The radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical mean-field models have been successful in explaining this property of the solar NSSL, while global direct convection models have been unsuccessful. We investigate reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under NSSL conditions. Simulations have minimal ingredients. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. Parameters of the simulations are chosen such they match the weakly rotationally constrained NSSL. The simulations probe locally Cartesian patches of the star at a given depth and latitude. The depth of the patch is varied by changing the rotation rate such that the resulting Coriolis numbers<1. We measure the turbulent transport coefficient relevant for the non-diffusive and diffusive parts of the Reynolds stress and compare them with predictions of current mean-field theories. A negative radial gradient of mean flow similar to the solar NSSL is generated only at the equator where meridional flows are absent. At other latitudes the meridional flow is comparable to the mean flow corresponding to differential rotation. We also find that meridional components of the Reynolds stress cannot be ignored. Additionally, we find that the turbulent viscosity is quenched by rotation by about 50\% from the surface to the bottom of the NSSL. Our local simulations do not validate the explanation for the generation of the NSSL from mean-field theory where meridional stresses are neglected. However, the rotational dependence of turbulent viscosity in our simulations is in good agreement with theoretical prediction. Our results are in qualitative agreement with global convection simulations in that a NSSL obtained near the equator.
We show for the first time that sustained turbulence is possible at low magnetic Prandtl number for Keplerian flows with no mean magnetic flux. Our results indicate that increasing the vertical domain size is equivalent to increasing the dynamical range between the energy injection scale and the dissipative scale. This has important implications for a large variety of differentially rotating systems with low magnetic Prandtl number such as protostellar disks and laboratory experiments.
A subcritical transition to turbulence in magnetized Keplerian shear flows is investigated using a statistical approach. Three-dimensional numerical simulations of the shearing box equations with zero net magnetic flux are employed to determine the transition from decaying to sustained turbulence as a function of the magnetic Reynolds number Rm. The results reveal no clear transition to sustained turbulence as the average lifetime of the transients grows as an exponential function of Rm, in accordance with a type-II supertransient law.
According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the angular velocity is decreasing outward. Using a short-wavelength approximation we demonstrate that even flows with very steep positive shear can be destabilized by azimuthal magnetic fields which are current-free within the fluid. We illustrate the transition of this instability to a rotationally enhanced kink-type instability in case of a homogeneous current in …
Leveling of MHD turbulence imbalance in shear flows
Abastumani Astrophysical Observatory（阿巴斯图马尼天体物理观测站）；Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University（第比利斯国立大学精确与自然科学学院物理系）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；M. Nodia Institute of Geophysics（M.诺迪亚地球物理研究所）
Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive str…
Using different analytical methods (the quasi-linear approach, the path-integral technique and tau-relaxation approximation) we develop a comprehensive mean-field theory for a pumping effect of the mean magnetic field in homogeneous non-rotating helical turbulence with imposed large-scale shear. The effective pumping velocity is proportional to the product of alpha effect and large-scale vorticity associated with the shear, and causes a separation of the toroidal and poloidal components of the mean magnetic field along the direction of the mean vorticity. We also perform direct numerical simul…
The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to $k^{-2}$, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While the spectr…
We study incompressible imbalanced magnetohydrodynamic turbulence in the presence of background velocity shears. Using scaling arguments, we show that the turbulent cascade is significantly accelerated when the background velocity shear is stronger than the velocity shears in the subdominant Alfv% én waves at the injection scale. The spectral transport is then controlled by the background shear rather than the turbulent shears and the Tchen spectrum with spectral index $-1$ is formed. This spectrum extends from the injection scale to the scale of the spectral break where the subdominant wave s…
We discuss a mean-field theory of generation of large-scale vorticity in a rotating density stratified developed turbulence with inhomogeneous kinetic helicity. We show that the large-scale nonuniform flow is produced due to ether a combined action of a density stratified rotating turbulence and uniform kinetic helicity or a combined effect of a rotating incompressible turbulence and inhomogeneous kinetic helicity. These effects result in the formation of a large-scale shear, and in turn its interaction with the small-scale turbulence causes an excitation of the large-scale instability (known …
The turbulent diffusivity tensor is determined for linear shear flow turbulence using numerical simulations. For moderately strong shear, the diagonal components are found to increase quadratically with Peclet and Reynolds numbers below about 10 and then become constant. The diffusivity tensor is found to have components proportional to the symmetric and antisymmetric parts of the velocity gradient matrix, as well as products of these. All components decrease with the wave number of the mean field in a Lorentzian fashion. The components of the diffusivity tensor are found not to depend signifi…
This article presents a calculation of the mean electromotive force arising from general small-scale magnetohydrodynamical turbulence, within the framework of the second-order correlation approximation. With the goal of improving understanding of the accretion disk dynamo, effects arising through small-scale magnetic fluctuations, velocity gradients, density and turbulence stratification, and rotation, are included. The primary result, which supplements numerical findings, is that an off-diagonal turbulent resistivity due to magnetic fluctuations can produce large-scale dynamo action -- the ma…
From numerical simulations, we show that non-rotating magnetohydrodynamic shear flows are unstable to finite amplitude velocity perturbations and become turbulent, leading to the growth and sustenance of magnetic energy, including large scale fields. This supports the concept that sustained magnetic energy from turbulence is independent of the driving mechanism for large enough magnetic Reynolds numbers.
Straining of magnetic fields by large-scale shear flow, generally assumed to lead to intensification and generation of small scales, is re-examined in light of the persistent observation of large-scale magnetic fields in astrophysics. It is shown that, in magnetohydrodynamic turbulence, unstable shear flows have the unexpected effect of sequestering magnetic energy at large scales, due to counteracting straining motion of nonlinearly excited large-scale stable eigenmodes. This effect is quantified via dissipation rates, energy transfer rates, and visualizations of magnetic field evolution by a…
We find an instability resulting in generation of large-scale vorticity in a fast rotating small-scale turbulence or turbulent convection with inhomogeneous fluid density along the rotational axis in anelastic approximation. The large-scale instability causes excitation of two modes: (i) the mode with dominant vertical vorticity and with the mean velocity being independent of the vertical coordinate; (ii) the mode with dominant horizontal vorticity and with the mean momentum being independent of the vertical coordinate. The mode with the dominant vertical vorticity can be excited in a fast rot…
To understand the self-sustenance of subcritical turbulence in spectrally stable shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain and analyzed the dynamical processes in Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of perturbation harmonics due to the shear flow non-normality. This non-normality-induced, or nonmodal growth is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes …
Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers. Thus, the contribution of density stratification is less important than that of turbulent velocity. The alpha effect and other turbulent transport coefficients are determined by means of the test-field method. In…
It is proposed that critical balance - a scale-by-scale balance between the linear propagation and nonlinear interaction time scales - can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave systems. Magnetohydrodynamic (MHD), rotating and stratified turbulence are considered under this assumption and, in particular, a novel and experimentally testable energy cascade scenario and a set of scalings of the spectra are proposed for low-Rossby-number rotating turbulence. It is argued that in neutral fluids, the critically balanced anisotro…
We have advanced the energy and flux budget (EFB) turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGW) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGW, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level, propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate …
We have investigated how the degree of imbalance in solar wind turbulence is modified by large-scale velocity shears in the solar wind plasma. The balance between counterpropagating Alfvénic fluctuations, which interact nonlinearly to generate the turbulence, has been quantified by the cross helicity and Elsasser ratio. Velocity shears at a 30-min timescale were identified, with the shear amplitude defined in terms of the linear Kelvin-Helmholtz (KH) instability threshold. The shears were associated with 74 interplanetary coronal mass ejection (ICME) sheaths observed by the Wind spacecraft at …
Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady-state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate over time-scales longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy am…
A previously unknown instability creates space-filling lattices of 3D vortices in linearly-stable, rotating, stratified shear flows. The instability starts from an easily-excited critical layer. The layer intensifies by drawing energy from the background shear and rolls-up into vortices that excite new critical layers and vortices. The vortices self-similarly replicate to create lattices of turbulent vortices. The vortices persist for all time. This self-replication occurs in stratified Couette flows and in the dead zones of protoplanetary disks where it can de-stabilize Keplerian flows.
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by transient growth mechanism due to shear flow nonnormality. This mechanism appears to be essentially anisotropic in spectral (wavenumber) plane and operates mainly for spatial Fourier harmonic…
Turbulent transport driven by secular shear instabilities can lead to enhanced vertical mixing in hot Jupiter atmospheres, impacting their cloudiness, chemistry and overall vertical structure. We discuss the turbulent regime expected and evaluate theoretical uncertainties on the strength of the vertical mixing (i.e, $K_{\rm zz}$ values). We focus our work on three well-studied hot Jupiters with a hierarchy of atmospheric temperatures: HD189733b ($T_{\rm eq} \simeq 1200$K), HD209458b ($T_{\rm eq} \simeq 1450$K) and Kepler7b ($T_{\rm eq} \simeq 1630$K). $K_{\rm zz}$ uncertainties are large. They…
