Efficiency of tidal dissipation in slowly rotating fully convective stars or planets. (arXiv:2007.13392v2 [astro-ph.SR] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Vidal_J/0/1/0/all/0/1">Jérémie Vidal</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Barker_A/0/1/0/all/0/1">Adrian J. Barker</a>
Turbulent convection is thought to act as an effective viscosity in damping
equilibrium tidal flows, driving spin and orbital evolution in close convective
binary systems. Compared to mixing-length predictions, this viscosity ought to
be reduced when the tidal frequency $|omega_t|$ exceeds the turnover frequency
$omega_{cnu}$ of the dominant convective eddies, but the efficiency of this
reduction has been disputed. We reexamine this long-standing controversy using
direct numerical simulations of an idealized global model. We simulate thermal
convection in a full sphere, and externally forced by the equilibrium tidal
flow, to measure the effective viscosity $nu_E$ acting on the tidal flow when
$|omega_t|/omega_{cnu} gtrsim 1$. We demonstrate that the frequency
reduction of $nu_E$ is correlated with the frequency spectrum of the
(unperturbed) convection. For intermediate frequencies below those in the
turbulent cascade ($|omega_t|/omega_{cnu} sim 1-5$), the frequency spectrum
displays an anomalous $1/omega^alpha$ power law that is responsible for the
frequency-reduction $nu_E propto 1/|omega_t|^{alpha}$, where $alpha < 1$
depends on the model parameters. We then get $|nu_E| propto
1/|omega_t|^{delta}$ with $delta > 1$ for higher frequencies, and $delta=2$
is obtained for a Kolmogorov turbulent cascade. A generic $|nu_E| propto
1/|omega_t|^{2}$ suppression is next found for higher frequencies within the
dissipation range of the convection (but with negative values). Our results
indicate that a better knowledge of the frequency spectrum of convection is
necessary to accurately predict the efficiency of tidal dissipation in stars
and planets resulting from this mechanism.
Turbulent convection is thought to act as an effective viscosity in damping
equilibrium tidal flows, driving spin and orbital evolution in close convective
binary systems. Compared to mixing-length predictions, this viscosity ought to
be reduced when the tidal frequency $|omega_t|$ exceeds the turnover frequency
$omega_{cnu}$ of the dominant convective eddies, but the efficiency of this
reduction has been disputed. We reexamine this long-standing controversy using
direct numerical simulations of an idealized global model. We simulate thermal
convection in a full sphere, and externally forced by the equilibrium tidal
flow, to measure the effective viscosity $nu_E$ acting on the tidal flow when
$|omega_t|/omega_{cnu} gtrsim 1$. We demonstrate that the frequency
reduction of $nu_E$ is correlated with the frequency spectrum of the
(unperturbed) convection. For intermediate frequencies below those in the
turbulent cascade ($|omega_t|/omega_{cnu} sim 1-5$), the frequency spectrum
displays an anomalous $1/omega^alpha$ power law that is responsible for the
frequency-reduction $nu_E propto 1/|omega_t|^{alpha}$, where $alpha < 1$
depends on the model parameters. We then get $|nu_E| propto
1/|omega_t|^{delta}$ with $delta > 1$ for higher frequencies, and $delta=2$
is obtained for a Kolmogorov turbulent cascade. A generic $|nu_E| propto
1/|omega_t|^{2}$ suppression is next found for higher frequencies within the
dissipation range of the convection (but with negative values). Our results
indicate that a better knowledge of the frequency spectrum of convection is
necessary to accurately predict the efficiency of tidal dissipation in stars
and planets resulting from this mechanism.
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