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Register a new userDissipation Efficiency in Turbulent Convective Zones in Low Mass Stars
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We extend the analysis of Penev et al. (2007) to calculate effective viscosities for the surface convective zones of three main sequence stars of 0.775Msun, 0.85Msun 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 linear scaling of effective viscosity with period and magnitudes at least three times larger than the Zahn (1966, 1989) prescription.
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Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the long-term orbital and rotational evolution of the bodies involved. If the primary star rotates as a solid body, inertial waves have a Doppler-shifted frequency restricted to the range $[-2Omega, 2Omega]$ ($Omega$ being the angular velocity of the star), and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that modifies the frequency range and propagation domain of inertial waves and allows corotation resonances for non-axisymmetric oscillations. In this work, we perform numerical simulations of tidally excited inertial waves in a differentially rotating convective envelope with a conical (or latitudinal) rotation profile. The tidal forcing that we adopt contains spherical harmonics that correspond to the case of a circular and coplanar orbit. We study the viscous dissipation of the waves as a function of tidal frequency for various stellar masses and differential rotation parameters, as well as its dependence on the turbulent viscosity coefficient. We compare our results with previous studies assuming solid-body rotation and point out the potential key role of corotation resonances in the dynamical evolution of close-in star-planet or binary systems.
The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of anelastic convection with external forcing. We show that the effects of the turbulent flow are well represented by an effective viscosity coefficient, we provide the values of the effective viscosity as a function of the perturbation frequency and compare our results to the perturbative method for finding the effective viscosity of Penev et al. that can be applied to actual simulations of the surface convective zones of stars.
The development of 2D and 3D 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, parametrized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh 1997, applied to a numerical model of solar convection (Robinson et al. 2003) to calculate an effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of Kolmogorov turbulence (Zahn 1966, Goldreich & Keeley 1977). The results match quite closely a linear scaling with period, even though this same formalism applied to a Kolmogorov spectrum of eddies gives a scaling with power-law index of 5/3.
We examine the chemical and emission properties of mildly irradiated (G0=1) magnetised shocks in diffuse media (nH=10^2 to 10^4 /cm3) at low to moderate velocities (from 3 to 40 km/s). Results: The formation of some molecules relies on endoergic reactions. In J-shocks, their abundances are enhanced by several orders of magnitude for shock velocities as low as 7 km/s. Otherwise most chemical properties of J-type shocks vary over less than an order of magnitude between velocities from about 7 to about 30 km/s, where H2 dissociation sets in. C-type shocks display a more gradual molecular enhancement as the shock velocity increases. We quantify the energy flux budget (fluxes of kinetic, radiated and magnetic energies) with emphasis on the main cooling lines of the cold interstellar medium. Their sensitivity to shock velocity is such that it allows observations to constrain statistical distributions of shock velocities. We fit various probability distribution functions (PDFs) of shock velocities to spectroscopic observations of the galaxy-wide shock in Stephans Quintet (SQ) and of a Galactic line of sight sampling diffuse molecular gas in Chamaeleon. In both cases, low velocities bear the greatest statistical weight and the PDF is consistent with a bimodal distribution. In the very low velocity shocks (below 5 km/s), dissipation is due to ion-neutral friction which powers H2 low energy transitions and atomic lines. In moderate velocity shocks (20 km/s and above), the dissipation is due to viscous heating and accounts for most of the molecular emission. In our interpretation a significant fraction of the gas on the line of sight is shocked (from 4% to 66%). For example, C+ emission may trace shocks in UV irradiated gas where C+ is the dominant carbon species.
In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunneling occurs. We find that efficient wave transmission can be achieved by `resonant propagation or `resonant tunneling, even when stable layers are strongly stratified, and we call this phenomenon `enhanced wave transmission. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable layers are alternatingly embedded within clamping convective layers, or vise versa). For wave propagation, the occurrence of enhanced wave transmission requires that clamping layers have similar properties, the thickness of each clamping layer is close to a multiple of the half wavelength of the corresponding propagative wave, and the total thickness of embedded layers is close to a multiple of the half wavelength of the corresponding propagating wave (resonant propagation). For wave tunneling, we have considered two cases: tunneling of gravity waves and tunneling of inertial waves. In both cases, efficient tunneling requires that clamping layers have similar properties, the thickness of each embedded layer is much smaller than the corresponding e-folding decay distance, and the thickness of each clamping layer is close to a multiple-and-a-half of half wavelength (resonant tunneling).
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