Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTurbulent viscosity and effective magnetic Prandtl number from simulations of isotropically forced turbulence
84
0
0.0
(
0
)
Added by
Petri K\\\"apyl\\\"a
Publication date
2019
fields
Physics
and research's language is
English
Authors
Petri J. Kapyla
Ask ChatGPT about the research
No Arabic abstract
(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${rm Pm}_{rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity is computed using the test-field method. The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (${rm Re}$) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. The results for the turbulent transport coefficients appear to converge at sufficiently high values of ${rm Re}$ and the scale separation ratio. However, a weak decreasing trend is found even at the largest values of ${rm Re}$. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large ${rm Re}$ whereas for small ${rm Re}$, we find values between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity. The actual value of ${rm Pm}_{rm t}$ found from the simulations ($approx0.9ldots0.95$) at large ${rm Re}$ and scale separation ratio is higher than any of the analytic predictions.
rate research
Read More
In this paper, we investigate the upward overshooting by three-dimensional numerical simulations. We find that the above convectively stable zone can be partitioned into three layers: the thermal adjustment layer (mixing both entropy and material), the turbulent dissipation layer (mixing material but not entropy), and the thermal dissipation layer (mixing neither entropy nor material). The turbulent dissipation layer is separated from the thermal adjustment layer and the thermal dissipation layer by the first and second zero points of the vertical velocity correlation. The simulation results are in good agreement with the prediction of the one-dimensional turbulent Reynolds stress model. First, the layer structure is similar. Second, the upper boundary of the thermal adjustment layer is close to the peak of the magnitude of the temperature perturbation. Third, the Peclet number at the upper boundary of the turbulent dissipation layer is close to 1. In addition, we have studied the scalings of the overshooting distance on the relative stability parameter $S$, the Prandtl number $rm Pr$, and the Peclet number $rm Pe$. The scaling on $S$ is not unique. The trend is that the overshooting distance decreases with $S$. Fitting on $rm Pr$ shows that the overshooting distance increases with $rm Pr$. Fitting on $rm Pe$ shows that the overshooting distance decreases with $rm Pe$. Finally, we calculate the ratio of the thickness of the turbulent dissipation layer to that of the thermal adjustment layer. The ratio remains almost constant, with an approximate value of 2.4.
(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to stronger downflows at lower Prandtl numbers, and to a strong dependence of overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number. At the highest Reynolds numbers the velocity power spectra are compatible with the Bolgiano-Obukhov $k^{-11/5}$ scaling. The horizontally averaged convected energy flux ($overline{F}_{rm conv}$) is independent of the Prandtl number within the CZ. However, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Benard convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions: The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical simulations.
The role of turbulence in current generation and self-excitation of magnetic fields has been studied in the geometry of a mechanically driven, spherical dynamo experiment, using a three dimensional numerical computation. A simple impeller model drives a flow which can generate a growing magnetic field, depending upon the magnetic Reynolds number, Rm, and the fluid Reynolds number. When the flow is laminar, the dynamo transition is governed by a simple threshold in Rm, above which a growing magnetic eigenmode is observed. The eigenmode is primarily a dipole field tranverse to axis of symmetry of the flow. In saturation the Lorentz force slows the flow such that the magnetic eigenmode becomes marginally stable. For turbulent flow, the dynamo eigenmode is suppressed. The mechanism of suppression is due to a combination of a time varying large-scale field and the presence of fluctuation driven currents which effectively enhance the magnetic diffusivity. For higher Rm a dynamo reappears, however the structure of the magnetic field is often different from the laminar dynamo; it is dominated by a dipolar magnetic field which is aligned with the axis of symmetry of the mean-flow, apparently generated by fluctuation-driven currents. The fluctuation-driven currents have been studied by applying a weak magnetic field to laminar and turbulent flows. The magnetic fields generated by the fluctuations are significant: a dipole moment aligned with the symmetry axis of the mean-flow is generated similar to those observed in the experiment, and both toroidal and poloidal flux expulsion are observed.
In this study, the stability dependence of turbulent Prandtl number ($Pr_t$) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $Pr_t$ and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.
Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a `secular shear instability in the low Peclet number regime with large Richardson numbers.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
