On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

Herreman, Wietze; Bars, Michaël Le; Gal, Patrice Le

doi:10.1063/1.3119102

Cited by 27 publications

(58 citation statements)

References 25 publications

(76 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One should also notice that our present study focus on hydrodynamical aspects of the tidal instability only, neglecting Lorentz forces related to planetary or stellar magnetic fields. This simplification is fully justified in the case of Io (see Herreman et al, 2009), but magnetic effects may be predominant in other situations. Anyway, the key point demonstrated here is that even if the tidal deformation is very small, its subsequent instability may have a velocity amplitude of first order over the whole domain and takes various and complex forms.…”

Section: Resultsmentioning

confidence: 99%

“…Its presence in planetary and stellar systems, elliptically deformed by gravitational tides, has been suggested for several years. It could for instance be responsible for the surprising existence of a mag-netic field in Io (Kerswell and Malkus, 1998;Lacaze et al, 2006;Herreman et al, 2009) and for fluctuations in the Earth's magnetic field on a typical timescale of 10,000 years (Aldridge et al, 1997). It may also have a significant influence on the evolution of binary stars (e.g.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Tidal instability in stellar and planetary binary systems

Bars

Lacaze

Dizès

et al. 2010

Physics of the Earth and Planetary Interiors

Self Cite

View full text Add to dashboard Cite

a b s t r a c tIn this paper, we combine theoretical and experimental approaches to study the tidal instability in planetary liquid cores and stars. We demonstrate that numerous complex modes can be excited depending on the relative values of the orbital angular velocity˝o rbit and of the spinning angular velocity˝s pin , except in a stable range characterized by˝s pin /˝o rbit ∈ [−1;1/3]. Even if the tidal deformation is small, its subsequent instability -coming from a resonance process -may induce motions with large amplitude, which play a fundamental role at the planetary scale. This general conclusion is illustrated in the case of Jupiter's moon Io by a coupled model of synchronization, demonstrating the importance of energy dissipation by elliptical instability.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tidal instability in stellar and planetary binary systems

Bars

Lacaze

Dizès

et al. 2010

Physics of the Earth and Planetary Interiors

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the following, we derive the coupled (WKB) stability equations for arbitrary, spatially varying Boussinesq and magnetic background states. We emphasise that their derivation is intrinsically different from the one of Kelvin wave stability equations (Craik & Criminale 1986;Craik 1989), also accounting for magnetic fields (Craik 1988;Fabijonas 2002;Lebovitz & Zweibel 2004;Herreman et al 2009;Mizerski & Bajer 2011;Cébron et al 2012b;Mizerski & Lyra 2012;Bajer & Mizerski 2013) and buoyancy effects (Cébron et al 2012b). Indeed, the Kelvin wave method cannot investigate the stability of arbitrary background states, contrary to the WKB method.…”

Section: Appendix A: Local (Wkb) Stability Equationsmentioning

confidence: 97%

Fossil field decay due to nonlinear tides in massive binaries

Vidal

Cébron

ud‐Doula

et al. 2019

A&A

View full text Add to dashboard Cite

Context. Surface magnetic fields have been detected in 5 to 10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars) collaboration. Aims. Different physical conditions in the molecular clouds giving birth to isolated stars and binaries are commonly invoked. In addition, we propose that the observed lower magnetic incidence in close binaries may be due to nonlinear tides. Indeed, close binaries are probably prone to tidal instability, a fluid instability growing upon the equilibrium tidal flow via nonlinear effects. Yet, stratified effects have hitherto been largely overlooked. Methods. We theoretically and numerically investigate tidal instability in rapidly rotating, stably stratified fluids permeated by magnetic fields. We use the short-wavelength stability method to propose a comprehensive (local) theory of tidal instability at the linear onset, discussing damping effects. Then, we propose a mixing-length theory for the mixing generated by tidal instability in the nonlinear regime. We successfully assess our theoretical predictions against proofof-concept, direct numerical simulations. Finally, we compare our predictions with the observations of short-period, double-lined spectroscopic binary systems. Results. Using new analytical results, cross-validated by a direct integration of the stability equations, we show that tidal instability can be generated by nonlinear couplings of inertia-gravity waves with the equilibrium tidal flow in short-period massive binaries, even against the Joule diffusion. In the nonlinear regime, a fossil magnetic field can be dissipated by the turbulent magnetic diffusion induced by the saturated tidal flows. Conclusions. We predict that the turbulent Joule diffusion of fossil fields would occur in a few million years for several short-period massive binaries. Therefore, turbulent tidal flows could explain the observed dearth of some short-period magnetic binaries.

show abstract

“…However this instability is also studied in geophysical and astrophysical tidally deformed bodies: for example, its presence has been suggested (i) in binary stars (Rieutord 2003; Le Bars et al 2010) and accretion discs (Goodman 1993; Ryu & Goodman 1994), where they could participate in the energy and angular momentum exchanges between neighbouring systems (Lubow et al 1993), and (ii) in planetary cores (e.g. Aldridge et al 1997; Cébron et al 2010), where they could play an important role in the induction of a magnetic field (Kerswell & Malkus 1998; Lacaze et al 2006; Herreman et al 2009) and even in planetary dynamos (Malkus 1993).…”

Section: Introductionmentioning

confidence: 99%

Tidal instability in a rotating and differentially heated ellipsoidal shell

Cébron¹,

Maubert²,

Bars³

2010

Geophysical Journal International

Self Cite

View full text Add to dashboard Cite

International audienceThe stability of a rotating flow in a triaxial ellipsoidal shell with an imposed temperature difference between inner and outer boundaries is studied numerically. We demonstrate that (i) a stable temperature field encourages the tidal instability, (ii) the tidal instability can grow on a convective flow, which confirms its relevance to geo- and astrophysical contexts and (iii) its growth rate decreases when the intensity of convection increases. Simple scaling laws characterizing the evolution of the heat flux based on a competition between viscous and thermal boundary layers are derived analytically and verified numerically. Our results confirm that thermal and tidal effects have to be simultaneously taken into account when studying geophysical and astrophysical flows

show abstract

On the effects of an imposed magnetic field on the elliptical instability in rotating spheroids

Cited by 27 publications

References 25 publications

Tidal instability in stellar and planetary binary systems

Tidal instability in stellar and planetary binary systems

Fossil field decay due to nonlinear tides in massive binaries

Tidal instability in a rotating and differentially heated ellipsoidal shell

Contact Info

Product

Resources

About