TY - JOUR

T1 - Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4

AU - Антонов, Николай Викторович

AU - Гулицкий, Николай Михайлович

AU - Костенко, Мария Михайловна

AU - Lucivjansky, Tomas

PY - 2017/3/22

Y1 - 2017/3/22

N2 - The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d=4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d=3, at d=4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d=3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and epsilon=4-d. All calculations are performed in the leading one-loop approximation.

AB - The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d=4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d=3, at d=4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d=3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and epsilon=4-d. All calculations are performed in the leading one-loop approximation.

KW - Renormalization group

KW - Turbulence

KW - Passive advection

U2 - 10.1051/epjconf/201713710003

DO - 10.1051/epjconf/201713710003

M3 - Article

VL - 137

JO - EPJ Web of Conferences

JF - EPJ Web of Conferences

SN - 2100-014X

M1 - 10003

ER -