TY - JOUR

T1 - Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy

AU - Antonov, N.V.

AU - Kostenko, M.M.

PY - 2014

Y1 - 2014

N2 - The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t−t′)k4−d−y, where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields (“operators” in the quantum-field terminology), can be systematically calculated as se

AB - The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t−t′)k4−d−y, where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields (“operators” in the quantum-field terminology), can be systematically calculated as se

KW - Renormalization group

KW - anomalous scaling

KW - passive scalar advection

U2 - 10.1103/PhysRevE.90.063016

DO - 10.1103/PhysRevE.90.063016

M3 - Article

VL - 90

SP - 063016_1-21

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 6

ER -