High-Energy Astrophysics American and Soviet Perspectives/Proceedings from the U.S.-U.S.S.R. Workshop on High-Energy Astrophysics (1991) / Chapter Skim
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TURBULIZATION OF SHEAR FLOWS IN ASTROPHYSICS
TURBULIZATION OF SHEAR FLOWS IN ASTROPHYSICS
Pages 55-64
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From page 55... ...
CHANISHVILT, AND J.G. LOMINADZE Abastumani Astrophysical Obsenatory INTRODUCTION According to a most widely spread representation (Shakura and Sunyaev 1973; Pringle 1981; Liang and Nolan 19843, the disk accretion phenomenon is based on the anomalous transport of the accreting matter angular momentum outward due to turbulent viscosity.
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From page 56... ...
To gain our aim, the Dow in the accretion disk can be modeled by a plane Couette flow, without regard for boundary conditions: it can be modelled by a plane shear Dow in infinite incompressible fluid. According to the present scenano, there is a critical perturbation level in the free shear flow.
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From page 57... ...
we especially emphasize the time dependence to stress that the spatial scale of Fourier modes varies in time along the X-axis. We must also stress that the Fourier expansion was done in terms of the variables x, and ye (see equation (93)
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From page 58... ...
processes come into play that can provide turbulization of the flow. LINEAR THEORY OF PERTURBATION Let us consider the linear theory of the temporal evolution of twodimensional perturbances irk a plane, free-shear flow of incompressible fluid.
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, the quantifies us end Al are components of the perturbation velocity in a Cartesian coordinate system. The coefficients of the initial linear equation system (1~-~3)
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. We have performed Founer analysis of perturbances for the variables x1 and ye and followed the time evolution of Founer harmonic amplitudes.
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Naturally, osmosis impedes perturbation grown. For every specific z, one can find Me minimum characteristic dimension of perturbations (maximal k-~/~)
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. When it becomes zero, knots reverses sign, as it follows from the linear theory, and the growth changes to weakening: the Fourier harmonic returns the energy back to the main flow.
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From page 63... ...
What can be observed at small initial perturbations? Because of the linear drift, the Fourier harmonics will be driven out of the "growth area," and because of the smallness of the amplitude, the decay processes will be weak and will not be able to resist the permanent linear theory drift.
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From page 64... ...
The local theory of turbulization of a plane Couette flow presented here can be applied not only to accretion disks, but to other shear flows in astrophysics, such as galactic disks, planetary rings, protostellar nebulae and possibly, to some rotating stars as well We think that beyond astrophysical applications, this theory is a ray of hope for explanations of turbulization of some "earthly" hydrodynamic flows which are steady to infinitesimal perturbations but are turbulized by finite ones. Of course, our theory is qualitative and needs more rigorous mathematical formulation in order to be quite reliable: a theory of weak and strong turbulence is to be developed.
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