Book contents
- Frontmatter
- Contents
- Preface
- Names and addresses of participants
- Conference photograph
- Spiral waves in Saturn's rings
- Structure of the Uranian rings
- Planetary rings: theory
- Simulations of light scattering in planetary rings
- Accretion discs around young stellar objects and the proto-Sun
- The β Pictoris disc: a planetary rather than a protoplanetary one
- Optical polarimetry and thermal imaging of the disc around β Pictoris
- Observations of discs around protostars and young stars
- VLA observations of ammonia toward molecular outflow sources
- Derivation of the physical properties of molecular discs by an MEM method
- Masers associated with discs around young stars
- The nature of polarisation discs around young stars
- The correlation between the main parameters of the interstellar gas (including Salpeter's spectrum of masses) as a result of the development of turbulent Rossby waves
- Discs in cataclysmic variables and X-ray binaries
- A disc instability model for soft X-ray transients containing black holes
- X-ray variability from the accretion disc of NGC 5548
- Viscously heated coronae and winds around accretion discs
- Optical emission line profiles of symbiotic stars
- The effect of formation of Fell in winds confined to discs for luminous stars
- Observational evidence for accretion discs in active galactic nuclei
- The fuelling of active galactic nuclei by non-axisymmetric instabilities
- The circum-nuclear disc in the Galactic centre
- Non-axisymmetric instabilities in thin self-gravitating differentially rotating gaseous discs
- Non-linear evolution of non-axisymmetric perturbations in thin self-gravitating gaseous discs
- Eccentric gravitational instabilities in nearly Keplerian discs
- Gravity mode instabilities in accretion tori
- The stability of viscous supersonic shear flows – critical Reynolds numbers and their implications for accretion discs
- Asymptotic analysis of overstable convective modes of uniformly rotating stars
- Polytropic models in very rapid rotation
- Distribution and kinematics of gas in galaxy discs
- Are the smallest galaxies optically invisible?
- Can we understand the constancy of rotation curves?
- How well do we know the surface density of the Galactic disc?
- On the heating of the Galactic disc
- The bulge-disc interaction in galactic centres
- Dynamics of the large-scale disc in NGC 1068
- The flow of gas in barred galaxies
- The warped dust lane in A1029-459
- Structure and evolution of dissipative non-planar galactic discs
- Non-axisymmetric magnetic fields in turbulent gas discs
- Non-axisymmetric disturbances in galactic discs
- Spiral instabilities in N-body simulations
- Long-lived spiral waves in N-body simulations
- Overstable modes in stellar disc systems
- Galactic seismological approach to the spiral galaxy NGC 3198
- Characteristics of bars from 3-D simulations
- Spirals and bars in linear theory
- Stellar hydrodynamical solutions for Eddington discs
- Theory of gradient instabilities of the gaseous Galactic disc and rotating shallow water
- Stability criteria for gravitating discs
- Stability of two-component galactic discs
- The smoothed particle hydrodynamics of galactic discs
- Tidal triggering of active disc galaxies by rich clusters
- The formation of spiral arms in early stages of galaxy interaction
- Formation of leading spiral arms in retrograde galaxy encounters
- The influence of galaxy interactions on stellar bars
- Disc galaxies – work in progress in Gothenburg
- Motion of a satellite in a disc potential
- Observer's summary
- Common processes and problems in disc dynamics
- Citation index
- Index of authors
- Subject index
The stability of viscous supersonic shear flows – critical Reynolds numbers and their implications for accretion discs
Published online by Cambridge University Press: 06 July 2010
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Book contents
- Frontmatter
- Contents
- Preface
- Names and addresses of participants
- Conference photograph
- Spiral waves in Saturn's rings
- Structure of the Uranian rings
- Planetary rings: theory
- Simulations of light scattering in planetary rings
- Accretion discs around young stellar objects and the proto-Sun
- The β Pictoris disc: a planetary rather than a protoplanetary one
- Optical polarimetry and thermal imaging of the disc around β Pictoris
- Observations of discs around protostars and young stars
- VLA observations of ammonia toward molecular outflow sources
- Derivation of the physical properties of molecular discs by an MEM method
- Masers associated with discs around young stars
- The nature of polarisation discs around young stars
- The correlation between the main parameters of the interstellar gas (including Salpeter's spectrum of masses) as a result of the development of turbulent Rossby waves
- Discs in cataclysmic variables and X-ray binaries
- A disc instability model for soft X-ray transients containing black holes
- X-ray variability from the accretion disc of NGC 5548
- Viscously heated coronae and winds around accretion discs
- Optical emission line profiles of symbiotic stars
- The effect of formation of Fell in winds confined to discs for luminous stars
- Observational evidence for accretion discs in active galactic nuclei
- The fuelling of active galactic nuclei by non-axisymmetric instabilities
- The circum-nuclear disc in the Galactic centre
- Non-axisymmetric instabilities in thin self-gravitating differentially rotating gaseous discs
- Non-linear evolution of non-axisymmetric perturbations in thin self-gravitating gaseous discs
- Eccentric gravitational instabilities in nearly Keplerian discs
- Gravity mode instabilities in accretion tori
- The stability of viscous supersonic shear flows – critical Reynolds numbers and their implications for accretion discs
- Asymptotic analysis of overstable convective modes of uniformly rotating stars
- Polytropic models in very rapid rotation
- Distribution and kinematics of gas in galaxy discs
- Are the smallest galaxies optically invisible?
- Can we understand the constancy of rotation curves?
- How well do we know the surface density of the Galactic disc?
- On the heating of the Galactic disc
- The bulge-disc interaction in galactic centres
- Dynamics of the large-scale disc in NGC 1068
- The flow of gas in barred galaxies
- The warped dust lane in A1029-459
- Structure and evolution of dissipative non-planar galactic discs
- Non-axisymmetric magnetic fields in turbulent gas discs
- Non-axisymmetric disturbances in galactic discs
- Spiral instabilities in N-body simulations
- Long-lived spiral waves in N-body simulations
- Overstable modes in stellar disc systems
- Galactic seismological approach to the spiral galaxy NGC 3198
- Characteristics of bars from 3-D simulations
- Spirals and bars in linear theory
- Stellar hydrodynamical solutions for Eddington discs
- Theory of gradient instabilities of the gaseous Galactic disc and rotating shallow water
- Stability criteria for gravitating discs
- Stability of two-component galactic discs
- The smoothed particle hydrodynamics of galactic discs
- Tidal triggering of active disc galaxies by rich clusters
- The formation of spiral arms in early stages of galaxy interaction
- Formation of leading spiral arms in retrograde galaxy encounters
- The influence of galaxy interactions on stellar bars
- Disc galaxies – work in progress in Gothenburg
- Motion of a satellite in a disc potential
- Observer's summary
- Common processes and problems in disc dynamics
- Citation index
- Index of authors
- Subject index
Summary
The model
We consider the linear stability of a plane shear layer, including the effects of compressibility and viscosity, as the simplest model for viscous supersonic shear flows occurring in accretion processes. Details of this investigation can be found in Glatzel (1989). Measuring lengths and velocities in units of half of the thickness of the shear layer and the flow velocity at its edge respectively, the flow may then be described by dimensionless numbers, the influence of compressibility is described by the Mach number, M, and viscosity by two Reynolds numbers, Reν and Reµ, corresponding to shear and volume viscosity respectively.
Instabilities and critical Reynolds numbers
We distinguish two types of modes, viscous modes and sonic modes, according to their physical origin: shear viscosity and compressibility. Shear-driven pairing of viscous modes, and distortion of the pattern speed of sonic modes, leads to mode crossings among the sonic, and between viscous and sonic modes, which unfold into bands of instability. The viscous-sonic resonances provide a new example of viscous instability; the role of viscosity is merely to provide an additional discrete spectrum, while shear is needed to produce mode crossings. The instability is ultimately caused by resonant exchange of energy between the crossing modes.
Critical Reynolds numbers for some resonances are plotted in Figure 1 as a function of the Mach number, M, for zero volume viscosity (Reµ = 3Reν).
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- Dynamics of Astrophysical Discs , pp. 123 - 124Publisher: Cambridge University PressPrint publication year: 1989