Two-parameter expansion in the renormalization-group analysis of turbulence

Bose condensation: The viscosity critical dimension and developed turbulence

“…in place of velocity correlation function (5), as was done before in [6], [7] and as is standard in the developed turbulence theory (see [4]). For g 4 = ν −2 and − δ = 2, this representation coincides with (5).…”

“…Our approach is based on the double expansion in the parameters = 4 − d (d is the space dimension) and δ, which is the measure of the deviation of the turbulence energy pumping exponent from its logarithmic value. We note that this method was developed in [6], [7] and was used in [8] to take the influence of hydrodynamic modes in model A of critical dynamics into account.…”

Бозе-Конденсация: Критическая Размерность Вязкости, Развитая Турбулентность

“…как это было выполнено ранее в работах [6], [7] и принято в теории развитой турбу-лентности (см. [4]).…”

“…Применяемый подход основан на двойном разложении по параметрам ϵ = 4 − d (d -размерность пространства) и δ -отклонению степени накачки турбулентной энергии от логарифмического значения. Отметим, что данный подход был развит в работах [6], [7] и использован в [8] для учета влияния гидродинамических мод в модели A критической динамики.…”

Renormalization-group analysis on the stability of large-scale electrostatic fluctuations of two-dimensional plasmas

“…͑1͒ suggests, since small-scale drift-wave turbulence ͑indexed as k͒ may drive the largescale fluctuations anisotropically, we model it as a random anisotropic external forcing peaked at high k. Twodimensional turbulence poses yet higher level of complexity than the three-dimensional problem, though, in that additional divergent diagram arises which demands a noise renormalization and, thus, new smallness parameter ␦ϭ2Ϫd as explained by Honkonen and Nalimov. 6 In Sec. II, we formulate the action integral of the forced HME that includes both the nonlocal and the local noises in order to properly treat the renormalizations.…”