The effect of disordered perturbations on the entropy of an unstable system

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Abstract

The contribution of disordered perturbations in density, velocity and pressure to the pair entropy of an unstable system, which sets the direction of its evolution, is estimated. Disordered perturbations arising in the incoming flow due to external influence are calculated by numerical integration of regular equations of multimoment hydrodynamics supplemented with stochastic components. The calculation of the distortion of the pair entropy of the system due to disordered perturbations is performed in the problem of flow around a stationary solid sphere. It is established that disordered perturbations of density, velocity and pressure do not have any noticeable effect on the parameters of the vortex street in the wake behind the sphere.

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About the authors

I. V. Lebed

Institute of Applied Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: lebed-ivl@yandex.ru
Russian Federation, Moscow

References

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2. Fig. 1. Time behavior of the paired entropy calculated within the hemispherical concentric layer H0 minus the spatial half-segment; r2 = 2.12, r3= 1.0, Re=400, t*= 6.99.

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3. Рис. 2. Hemispherical concentric layer H0: 1 ≤ ^r ≤ ^r2, p/2 ≤ q ≤ 0, 2p ≤ j ≤ 0; hemispherical concentric layer H1: 1 ≤ ^r ≤ ^r1, p/2 ≤ q ≤ 0, 2p ≤ j ≤ 0; hemispherical concentric layer H2: ^r1 ≤ ^r ≤ ^r2, p / 2 ≤ q ≤ 0, 2p ≤ j ≤ 0; cos a = 0.886.

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4. Рис. 3. Введение во временную производственную систему, при Re = 400. Функция =^СП(0(0,2))(т)/=т, рассчитанная по решению Соль 0 в пределах полусферического концентрического слоя н0 за вычетом пространственного полусегмента, представлена кривой 1; ^Р2 = 2.12, ^Р3 = 1.0. Сумма двух функций, ^СП(0(1,2))(т) и ^ИП(1(2,2))(т), представлена кривой 2. Составляющая ^СП(0(1,2))(т) рассчитана по решению Sol0 в пределах полусферического концентрического слоя Н1 ^Р1 = 1.571; составляющая ^ИП(1(2,2))(т) рассчитана по решению Sol1 в пределах области существования решения, расположенной на внешней границе полусферического концентрического слоя Н1. Время перемещения ^t1 = 6,9857, t = (Rea/(2 U0))^t.

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5. Fig. 4. Time behavior of the inverse pair entropy calculated by Sol0, Re = 400. The function ^S~p*(0(1,)2)(t*), calculated within the hemispherical concentric layer H1, is represented by curve 1; ^r1 =1.571. The function ^S~p*(0(0,)2)(t*), calculated within the hemispherical concentric layer H0 minus the spatial half-segment, is represented by curve 2; ^r2 = 2.12, ^r3 = 1.0. The function ^S~ p*(0(1–,2)2)( t*), calculated within a hemispherical concentric layer with a moving outer boundary ^r1(t), represented by curve 3. Rebuilding time ^t1 = 6.9857, separation time ^t1 = T = 6.99, t * = = (Re a/(2U0))^t *.

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