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Regular version of the site
Of all publications in the section: 6
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Article
Belan S., Lebedev V., Chernykh A. Journal of Fluid Mechanics. 2018. Vol. 855. P. 910-921.

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As has been established experimentally, elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically the statistics of the polymer conformation, which is highly non-uniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of the mean flow to the magnitude of the flow fluctuations. This ratio is determined by the polymer concentration, the radius of gyration of polymers and their length in the fully extended state. The results of our asymptotic analysis reproduce the qualitative features of elastic turbulence at finite Weissenberg numbers.

Added: Feb 5, 2020
Article
Пелиновский Е. Н., Kharif C. Journal of Fluid Mechanics. 2008. № 594. С. 209-247.
Added: Jun 5, 2011
Article
Pelinovsky E., Didenkulova I., Rybkin A. Journal of Fluid Mechanics. 2014. Vol. 748. P. 416-432.

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on a plane beach. As a result, the nonlinear shallow water equations are reduced to a single one-dimensional linear wave equation for an auxiliary function and all physical variables can be expressed in terms of this function by purely algebraic formulas. In the special case of a U-shaped channel this equation coincides with a spherically symmetric wave equation in space, whose dimension is defined by the channel cross-section and can be fractional. As an example, the run-up of a sinusoidal wave on a beach is considered for channels of several different cross-sections and the influence of the cross-section on wave run-up characteristics is studied

Added: Nov 19, 2014
Article
Kolokolov I., Lebedev V., Chertkov M. et al. Journal of Fluid Mechanics. 2005. P. 251-260.
We consider the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, to explain how the polymer statistics changes with Weissenberg number, Wi, the product of the polymer relaxation time and the Lyapunov exponent of the flow, ¯ λ. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction, having algebraic tails. The PDF of the tumbling time (separating two subsequent flips), τ , has a maximum estimated as ¯λ−1. This PDF shows an exponential tail for large τ and a small-τ tail determined by the simultaneous statistics of the velocity PDF. Four regimes of Wi are identified for the extension statistics: one below the coil–stretched transition and three above the coil–stretched transition. Emphasis is given to explaining these regimes in terms of the polymer dynamics.
Added: Feb 12, 2017
Article
Parfenyev V., Belan S., Lebedev V. Journal of Fluid Mechanics. 2019. Vol. 862. P. 1084-1104.

Stochastic roughness is a widespread feature of natural surfaces and is an inherent byproduct of most fabrication techniques. In view of the rapid development of microfluidics, the important question is how this inevitable problem affects the low-Reynolds-number flows that are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially ‘tuned’ random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.

Added: Jan 22, 2019
Article
I.V.Kolokolov, V.V.Lebedev. Journal of Fluid Mechanics. 2016. Vol. 809. No. paper R2. P. 1-11.

We analyze velocity fluctuations inside  coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \citep{16KL}, the universal velocity profile, established in \citep{14LBFKL}, corresponds to the passive regime of the flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present the results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the structure function.

Added: Oct 23, 2016