The nonlinear theory of gravitational instability

Computer Science – Sound

Scientific paper

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Gravitational Collapse, Nonlinear Equations, Stellar Gravitation, Burger Equation, Galactic Evolution

Scientific paper

Attention is given to the evolution of the velocity field of a gravitationally unstable medium whose particles possess proper thermal motions. It is shown that together with an increase of perturbation amplitude there is a characteristic averaging due to forces of pressure. To describe the nonlinear stage of the instability, a modified Burgers equation with a 'viscosity' coefficient that depends on the sound velocity in the medium and on the instability increment is proposed. Linearization of the equation results in the correct form for the dispersion relationship of the linear theory.

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