Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity. (arXiv:2007.12624v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Duguid_C/0/1/0/all/0/1">Craig D. Duguid</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Barker_A/0/1/0/all/0/1">Adrian J. Barker</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Jones_C/0/1/0/all/0/1">Chris A. Jones</a>
Turbulent convection is thought to act as an effective viscosity ($nu_E$) in
damping tidal flows in stars and giant planets. However, the efficiency of this
mechanism has long been debated, particularly in the regime of fast tides, when
the tidal frequency ($omega$) exceeds the turnover frequency of the dominant
convective eddies ($omega_c$). We present the results of hydrodynamical
simulations to study the interaction between tidal flows and convection in a
small patch of a convection zone. These simulations build upon our prior work
by simulating more turbulent convection in larger horizontal boxes, and here we
explore a wider range of parameters. We obtain several new results: 1) $nu_E$
is frequency-dependent, scaling as $omega^{-0.5}$ when $omega/omega_c
lesssim 1$, and appears to attain its maximum constant value only for very
small frequencies ($omega/omega_c lesssim 10^{-2}$). This
frequency-reduction for low frequency tidal forcing has never been observed
previously. 2) The frequency-dependence of $nu_E$ appears to follow the same
scaling as the frequency spectrum of the energy (or Reynolds stress) for low
and intermediate frequencies. 3) For high frequencies ($omega/omega_cgtrsim
1-5$), $nu_Epropto omega^{-2}$. 4) The energetically-dominant convective
modes always appear to contribute the most to $nu_E$, rather than the resonant
eddies in a Kolmogorov cascade. These results have important implications for
tidal dissipation in convection zones of stars and planets, and indicate that
the classical tidal theory of the equilibrium tide in stars and giant planets
should be revisited. We briefly touch upon the implications for planetary
orbital decay around evolving stars.
Turbulent convection is thought to act as an effective viscosity ($nu_E$) in
damping tidal flows in stars and giant planets. However, the efficiency of this
mechanism has long been debated, particularly in the regime of fast tides, when
the tidal frequency ($omega$) exceeds the turnover frequency of the dominant
convective eddies ($omega_c$). We present the results of hydrodynamical
simulations to study the interaction between tidal flows and convection in a
small patch of a convection zone. These simulations build upon our prior work
by simulating more turbulent convection in larger horizontal boxes, and here we
explore a wider range of parameters. We obtain several new results: 1) $nu_E$
is frequency-dependent, scaling as $omega^{-0.5}$ when $omega/omega_c
lesssim 1$, and appears to attain its maximum constant value only for very
small frequencies ($omega/omega_c lesssim 10^{-2}$). This
frequency-reduction for low frequency tidal forcing has never been observed
previously. 2) The frequency-dependence of $nu_E$ appears to follow the same
scaling as the frequency spectrum of the energy (or Reynolds stress) for low
and intermediate frequencies. 3) For high frequencies ($omega/omega_cgtrsim
1-5$), $nu_Epropto omega^{-2}$. 4) The energetically-dominant convective
modes always appear to contribute the most to $nu_E$, rather than the resonant
eddies in a Kolmogorov cascade. These results have important implications for
tidal dissipation in convection zones of stars and planets, and indicate that
the classical tidal theory of the equilibrium tide in stars and giant planets
should be revisited. We briefly touch upon the implications for planetary
orbital decay around evolving stars.
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