Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability

Belyaev, Mikhail

doi:10.3847/1538-4357/835/2/238

Cited by 12 publications

(11 citation statements)

References 56 publications

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“…On the other hand, shear-acoustic instabilities can be viewed as the destabilization of an incompressible mode by direct emission of acoustic radiation (Belyaev 2017). This does not involve coupling between the two edges of the shear layer, and the excitation region of an unstable shearacoustic mode exists over only a small radial extent, near the corotation radius in the BL.…”

Section: Discussionmentioning

confidence: 99%

“…Another interesting question concerns the dominance of the m = 14 mode in the simulation. Although a spectrum of shear-acoustic modes is expected to be excited in the BL, Belyaev (2017) showed that a sound wave which reflects off the inner Lindblad radius in the disk and returns in phase with the outgoing mode in the BL can be pumped to higher amplitudes in the disk with same forcing amplitude in the BL. The criterion for this to occur is…”

Section: Verificationmentioning

confidence: 99%

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Inefficient angular momentum transport in accretion disc boundary layers: angular momentum belt in the boundary layer

Belyaev

Quataert

2018

Monthly Notices of the Royal Astronomical Society

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We present unstratified 3D MHD simulations of an accretion disk with a boundary layer (BL) that have a duration ∼ 1000 orbital periods at the inner radius of the accretion disk. We find the surprising result that angular momentum piles up in the boundary layer, which results in a rapidly rotating belt of accreted material at the surface of the star. The angular momentum stored in this belt increases monotonically in time, which implies that angular momentum transport mechanisms in the BL are inefficient and do not couple the accretion disk to the star. This is in spite of the fact that magnetic fields are advected into the BL from the disk and supersonic shear instabilities in the BL excite acoustic waves. In our simulations, these waves only carry a small fraction (∼ 10%) of the angular momentum required for steady state accretion. Using analytical theory and 2D viscous simulations in the R − φ plane, we derive an analytical criterion for belt formation to occur in the BL in terms of the ratio of the viscosity in the accretion disk to the viscosity in the BL. Our MHD simulations have a dimensionless viscosity (α) in the BL that is at least a factor of ∼ 100 smaller than that in the disk. We discuss the implications of these results for BL dynamics and emission.

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Section: Discussionmentioning

confidence: 99%

Section: Verificationmentioning

confidence: 99%

Inefficient angular momentum transport in accretion disc boundary layers: angular momentum belt in the boundary layer

Belyaev

Quataert

2018

Monthly Notices of the Royal Astronomical Society

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“…The present study is limited by the isothermal equation of state employed, although (Hertfelder & Kley 2015) found that global acoustic-wave-mediated mass and angular momentum transport persists when more realistic equations of state are employed. However, our isothermal equation of state precluded excitation of modes through coupling with inertial modes in the star or planet (Belyaev 2017). Additionally, the entropy profile of the disk plays a key role in the development of vortices through the Rossby wave instability (Lovelace et al 1999), which may lead to significant differences in transport due to vortex-driven modes.…”

Section: Comparison With Previous Studiesmentioning

confidence: 99%

On the Terminal Spins of Accreting Stars and Planets: Boundary Layers

Dittmann

2021

Preprint

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The origin of the spins of giant planets is an open question in astrophysics. As planets and stars accrete from discs, if the specific angular momentum accreted corresponds to that of a Keplerian orbit at the surface of the object, it is possible for planets and stars to be spun up to near-breakup speeds. However, accretion cannot proceed onto planets and stars in the same way that accretion proceeds through the disk. For example, the magneto-rotational instability cannot operate in the region between the nearly-Keplerian disk and more slowlyrotating surface because of the sign of the angular velocity gradient. Through this boundary layer where the angular velocity sharply changes, mass and angular momentum transport is thought to be driven by acoustic waves generated by global supersonic shear instabilities and vortices. We present the first study of this mechanism for angular momentum transport around rotating stars and planets using 2D vertically-integrated moving-mesh simulations of ideal hydrodynamics. We find that above rotation rates of ∼ 0.4 − 0.6 times the Keplerian rate at the surface, depending on the gas sound speed, the rate at which angular momentum is transported inwards through the boundary layer by waves decreases by ∼ 1 − 3 orders of magnitude. We also find that the accretion rate through the boundary layer decreases commensurately and becomes less variable for faster-rotating objects. Our results provide a purely hydrodynamic mechanism for limiting the spins of accreting planets and stars to factors of a few less than the breakup speed.

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“…Following the definition in (22), applying the standard differentiation and integration properties of the Laplace transform to (21) and taking into account (23) and (25), we find…”

Section: Explicit Expression For the Membrane Displacement By Means O...mentioning

confidence: 99%

Radiation-induced instability of a finite-chord Nemtsov membrane

Labarbe,

Kirillov

2021

Preprint

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We consider a problem of stability of a membrane of an infinite span and a finite chord length that is submerged in a uniform flow of finite depth with free surface. In the shallow water approximation, Nemtsov (1985) has shown that an infinite-chord membrane is susceptible to flutter instability due to excitation of long gravity waves on the free surface if the velocity of the flow exceeds the phase velocity of the waves and placed this phenomenon into the general physical context of the anomalous Doppler effect. In the present work we derive a full nonlinear eigenvalue problem for an integro-differential equation in the case of the finite-chord Nemtsov membrane in the finite-depth flow. In the shallow-and deep water limits we develop a perturbation theory in the small added mass ratio parameter acting as an effective dissipation parameter in the system, to find explicit analytical expressions for the frequencies and the growth rates of the membrane modes coupled to the surface waves. This result reveals a new intricate pattern of instability pockets in the parameter space and allows for its analytical description. The case of an arbitrary depth flow with free surface requires numerical solution of a new non-polynomial nonlinear eigenvalue problem. We propose an original approach combining methods of complex analysis and residue calculus, Galerkin discretization, Newton method and parallelization techniques implemented in MATLAB to produce high-accuracy stability diagrams within an unprecedentedly wide range of system's parameters. We believe that the Nemtsov membrane appears to play the same paradigmatic role for understanding radiation-induced instabilities as the famous Lamb oscillator coupled to a string has played for understanding radiation damping.

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Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability

Cited by 12 publications

References 56 publications

Inefficient angular momentum transport in accretion disc boundary layers: angular momentum belt in the boundary layer

Inefficient angular momentum transport in accretion disc boundary layers: angular momentum belt in the boundary layer

On the Terminal Spins of Accreting Stars and Planets: Boundary Layers

Radiation-induced instability of a finite-chord Nemtsov membrane

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