Abstract
We study the interaction between tides and convection in astrophysical bodies by analysing the effect of a homogeneous oscillatory shear on a fluid flow. This model can be taken to represent the interaction between a large-scale periodic tidal deformation and a smaller scale convective motion. We first consider analytically the limit in which the shear is of low amplitude and the oscillation period is short compared to the time-scales of the unperturbed flow. In this limit there is a viscoelastic response and we obtain expressions for the effective elastic modulus and viscosity coefficient. The effective viscosity is inversely proportional to the square of the oscillation frequency, with a coefficient that can be positive, negative or zero depending on the properties of the unperturbed flow. We also carry out direct numerical simulations of Boussinesq convection in an oscillatory shearing box and measure the time-dependent Reynolds stress. The results indicate that the effective viscosity of turbulent convection falls rapidly as the oscillation frequency is increased, attaining small negative values in the cases we have examined, although significant uncertainties remain because of the turbulent noise. We discuss the implications of this analysis for astrophysical tides.
Highlights
Tidal interactions determine the orbital and spin evolution of astrophysical bodies when they orbit sufficiently close to one another
In this paper we have studied the interaction between tides and convection in astrophysical bodies by analysing the effect of a homogeneous oscillatory shear on a fluid flow
This model can be taken to represent the interaction between a large-scale periodic tidal deformation and a smaller-scale convective motion
Summary
Tidal interactions determine the orbital and spin evolution of astrophysical bodies when they orbit sufficiently close to one another. For a Kolmogorov spectrum, this argument gives a more powerful suppression, such that the effective viscosity is proportional to the square of the oscillation period for short periods While these authors relied on simple physical arguments and order-of-magnitude estimates, Goodman & Oh (1997), who provide a clear review of the controversy, introduced a more formal procedure for determining the effec-. In Penev, Barranco & Sasselov (2009) an oscillatory forcing was introduced directly into the convection simulation and the effective viscosity was estimated by measuring the work done by this force The results of these studies suggest that something closer to the prescription of Zahn (1966) may be appropriate, not for the reasons originally suggested, but possibly because the power spectrum of the convection is less steep than the Kolmogorov spectrum assumed by Goldreich & Nicholson (1977). Direct numerical simulations of convection in an oscillatory shearing box are reported and interpreted in Section 4, followed by a summary and discussion of the results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
