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Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star-planet and planet-moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave.Results. The vortex we consider is found to be centrifugally stable in the range −Ω p ≤ Ω 0 ≤ 3.62Ω p and unstable outside this range, where Ω 0 is the local rotation rate of the vortex at its center and Ω p is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0, 1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m > 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical ...
Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star-planet and planet-moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave.Results. The vortex we consider is found to be centrifugally stable in the range −Ω p ≤ Ω 0 ≤ 3.62Ω p and unstable outside this range, where Ω 0 is the local rotation rate of the vortex at its center and Ω p is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0, 1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m > 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical ...
The elliptical instability is an instability of elliptical streamlines, which can be excited by large-scale tidal flows in rotating fluid bodies, and excites inertial waves if the dimensionless tidal amplitude (ε) is sufficiently large. It operates in convection zones but its interactions with turbulent convection has not been studied in this context. We perform an extensive suite of Cartesian hydrodynamical simulations in wide boxes to explore the interactions of the elliptical instability and Rayleigh-Bénard convection. We find that geostrophic vortices generated by the elliptical instability dominate the flow, with energies far exceeding those of the inertial waves. Furthermore, we find that the elliptical instability can operate with convection, but it is suppressed for sufficiently strong convection, primarily by convectively-driven large-scale vortices. We examine the flow in Fourier space, allowing us to determine the energetically dominant frequencies and wave numbers. We find that power primarily concentrates in geostrophic vortices, in wave numbers that are convectively unstable, and along the inertial wave dispersion relation, even in non-elliptically deformed convective flows. Examining linear growth rates on a convective background, we find that convective large-scale vortices suppress the elliptical instability in the same way as the geostrophic vortices created by the elliptical instability itself. Finally, convective motions act as an effective viscosity on large-scale tidal flows, providing a sustained energy transfer (scaling as ε2). Furthermore, we find that the energy transfer resulting from bursts of elliptical instability, when it operates, is consistent with the ε3 scaling found in prior work.
Numerical solutions of the precession-driven flows inside a sphere are presented by means of a previously proposed spectral method based on helical wave decomposition, and flow properties are investigated in helical wave spectral space. Four different flow states can be generated under precession, including the steady, periodic, quasi-periodic, and turbulent ones. Flow fields are decomposed into two components of opposite polarity by the sign of the helicity of each helical wave. It is found that the flows in the steady and periodic states are polarity-symmetric, while the quasi-periodic and turbulent states are polarity-asymmetric, regarding the kinetic energy distribution for each polarity. The two components of opposite polarity for the quasi-periodic case have exactly the same frequency spectra with respect to the kinetic energy, differing from the turbulent case. At high Reynolds numbers, the helical wave energy spectra show a scaling of λ − 7 / 3, which is different from the scaling of k − 2 for the homogeneous turbulence under precession. The helical wave spectral dynamic equation is derived for the investigation of the mechanism of the turbulent flows. The energy to sustain the precession-driven flows comes from the boundary motion, which is equivalent to a body force being enforced on all scales in spectral space. The energy is concentrated on the largest scales and transferred to smaller scales through the nonlinear interaction. In contrast, the Coriolis force gives rise to an inverse cascade that transfers energy from small to large scales.
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