On the mechanism of excitation of large-scale fluctuations

Sidorov S.V.

RF, Moscow, st. Red Mayak, 11, 3, 200

Of great interest are fluctuations whose wavelength is significantly longer than the characteristic microscopic scale (the intermolecular distance in liquids and the mean free path in gases), and whose decay time exceeds the time for establishing local equilibrium in small volumes with a large number of particles. The magnitude of such fluctuations is evidenced by estimates showing that the large-scale fluctuations observed in the layers are comparable in magnitude to the size of the layer itself. There is no final answer to the question about the appearance of such fluctuations [1].

The work numerically examines solutions to the Burgers equation


with a complex-valued function w(x,t) = u(x,t) + iv(x,t) and with a complex coefficient of dynamic viscosity, which determines the rheological properties of the medium.

The solution of equation (1) in the plane traveling wave approximation showed that, within the framework of the presented model, there are conditions that ensure the excitation of large-scale fluctuations by microscopic statistical fluctuations. These conditions are defined both for a highly rarefied gaseous medium and for a condensed medium. In this case, large-scale disturbances have a wave nature and are limited in time and space. The shape of the disturbances depends on the initial conditions, on the local viscosity coefficient and can take the form of a solitary wave, a switching wave, or a wave packet.

The results of the work make it possible to understand the mechanism of formation of developed turbulence in liquids and gases [2].


1. Zubarev D.N., Morozov V.G., Repke G. Statistical mechanics of nonequilibrium processes, in 2 volumes // M.: Fizmatlit, vol. 2, 2002, 296 p.

2. Rybakov Yu.P., Sidorov S.V. About one hydrodynamic model of turbulence\


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