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Register a new userInternal energy dissipation in Enceladuss ocean from tides and libration and the role of inertial waves
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Enceladus is characterised by a south polar hot spot associated with a large outflow of heat, the source of which remains unclear. We compute the viscous dissipation resulting from tidal and libration forcing in the moons subsurface ocean using the linearised Navier-Stokes equation in a 3-dimensional spherical model. We conclude that libration is the dominant cause of dissipation at the linear order, providing up to about 0.001 GW of heat to the ocean, which remains insufficient to explain the (about) 10 GW observed by Cassini. We also illustrate how resonances with inertial modes can significantly augment the dissipation. Our work is an extension to Rovira-Navarro et al. [2019] to include the effects of libration. The model developed here is readily applicable to the study of other moons and planets.
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Seismology was developed on Earth and shaped our model of the Earths interior over the 20th century. With the exception of the Philae lander, all in situ extraterrestrial seismological effort to date was limited to other terrestrial planets. All have in common a rigid crust above a solid mantle. The coming years may see the installation of seismometers on Europa, Titan and Enceladus, so it is necessary to adapt seismological concepts to the setting of worlds with global oceans covered in ice. Here we use waveform analyses to identify and classify wave types, developing a lexicon for icy ocean world seismology intended to be useful to both seismologists and planetary scientists. We use results from spectral-element simulations of broadband seismic wavefields to adapt seismological concepts to icy ocean worlds. We present a concise naming scheme for seismic waves and an overview of the features of the seismic wavefield on Europa, Titan, Ganymede and Enceladus. In close connection with geophysical interior models, we analyze simulated seismic measurements of Europa and Titan that might be used to constrain geochemical parameters governing the habitability of a sub-ice ocean.
We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band ($0.1-100,{rm mHz}$). We show that for stars not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.
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.
We have advanced the energy and flux budget (EFB) turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGW) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGW, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level, propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turns, results in strong damping of IGW. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGW. The anisotropy of the turbulence produced by less intensive IGW is stronger than that caused by more intensive waves. The low amplitude IGW produce turbulence consisting up to 90 % of turbulent potential energy. This resembles the properties of the observed high altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.
Melting beneath mid-ocean ridges occurs over a region that is much broader than the zone of magmatic emplacement to form the oceanic crust. Magma is focused into this zone by lateral transport. This focusing has typically been explained by dynamic pressure gradients associated with corner flow, or by a sub-lithospheric channel sloping upward toward the ridge axis. Here we discuss a novel mechanism for magmatic focusing: lateral transport driven by gradients in compaction pressure within the asthenosphere. These gradients arise from the co-variation of melting rate and compaction viscosity. The compaction viscosity, in previous models, was given as a function of melt fraction and temperature. In contrast, we show that the viscosity variations relevant to melt focusing arise from grain-size variability and non-Newtonian creep. The asthenospheric distribution of melt fraction predicted by our models provides an improved ex- planation of the electrical resistivity structure beneath one location on the East Pacific Rise. More generally, although grain size and non-Newtonian viscosity are properties of the solid phase, we find that in the context of mid-ocean ridges, their effect on melt transport is more profound than their effect on the mantle corner-flow.
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