1,810 research outputs found
Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation
Any nonspherical distribution of density inside planets and stars gives rise
to a non-spherical external gravity and change of shape. If part or all of the
observed zonal flows at the cloud deck of Jupiter and Saturn represent deep
interior dynamics, then the density perturbations associated with the deep
zonal flows could generate gravitational signals detectable by the Juno mission
and the Cassini Grand Finale. Here we present a critical examination of the
applicability of the thermal wind equation to calculate the wind induced
gravity moments. Our analysis shows that wind induced gravity moments
calculated from TWE are in overall agreement with the full solution to the
Euler equation. However, the accuracy of individual high-degree moments
calculated from TWE depends crucially on retaining the nonsphericity of the
background density and gravity. Only when the background nonsphericity of the
planet is taken into account, does the TWE make accurate enough prediction
(with a few tens of percent errors) for individual high-degree gravity moments
associated with deep zonal flows. Since the TWE is derived from the curl of the
Euler equation and is a local relation, it necessarily says nothing about any
density perturbations that contribute irrotational terms to the Euler equation
and that have a non-local origin. However, the predicted corrections from these
density contributions to the low harmonic degree gravity moments are not
discernible from insignificant changes in interior models while the corrections
at high harmonic degree are very small, a few percent or less.Comment: 28 pages, 8 figures, 5 tables, accepted at JGR-Planet
Effects of Extreme Obliquity Variations on the Habitability of Exoplanets
We explore the impact of obliquity variations on planetary habitability in
hypothetical systems with high mutual inclination. We show that large
amplitude, high frequency obliquity oscillations on Earth-like exoplanets can
suppress the ice-albedo feedback, increasing the outer edge of the habitable
zone. We restrict our exploration to hypothetical systems consisting of a
solar-mass star, an Earth-mass planet at 1 AU, and 1 or 2 larger planets. We
verify that these systems are stable for years with N-body simulations,
and calculate the obliquity variations induced by the orbital evolution of the
Earth-mass planet and a torque from the host star. We run a simplified energy
balance model on the terrestrial planet to assess surface temperature and ice
coverage on the planet's surface, and we calculate differences in the outer
edge of the habitable zone for planets with rapid obliquity variations. For
each hypothetical system, we calculate the outer edge of habitability for two
conditions: 1) the full evolution of the planetary spin and orbit, and 2) the
eccentricity and obliquity fixed at their average values. We recover previous
results that higher values of fixed obliquity and eccentricity expand the
habitable zone, but also find that obliquity oscillations further expand
habitable orbits in all cases. Terrestrial planets near the outer edge of the
habitable zone may be more likely to support life in systems that induce rapid
obliquity oscillations as opposed to fixed-spin planets. Such planets may be
the easiest to directly characterize with space-borne telescopes.Comment: 46 pages, 12 Figures, 5 Table
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
Frequency spectrum of gravitational radiation from global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star
Recent time-dependent, ideal-magnetohydrodynamic (ideal-MHD) simulations of
polar magnetic burial in accreting neutron stars have demonstrated that stable,
magnetically confined mountains form at the magnetic poles, emitting
gravitational waves at (stellar spin frequency) and . Global
MHD oscillations of the mountain, whether natural or stochastically driven, act
to modulate the gravitational wave signal, creating broad sidebands (full-width
half-maximum ) in the frequency spectrum around and . The oscillations can enhance the signal-to-noise ratio achieved by a
long-baseline interferometer with coherent matched filtering by up to 15 per
cent, depending on where lies relative to the noise curve minimum.
Coherent, multi-detector searches for continuous waves from nonaxisymmetric
pulsars should be tailored accordingly.Comment: 4 figures, accepted for publication in Ap
Pressure torque of torsional Alfvén modes acting on an ellipsoidal mantle
We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfvén modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earth’s length-of-day
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