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The renormalization group approach and the operator product expansiontechnique are applied to the model of a tracer field advected by theNavier-Stokes velocity ensemble for a compressible fluid. The model isconsidered in the vicinity of the specific space dimension $d=4$. Theproperties of the equal-time structure functions are investigated. Themultifractal behaviour of various correlation functions is established. Allcalculations are performed in the leading one-loop approximation.

Stochastic Navier-Stokes equation and advection of a tracer field: One-loop renormalization near $d=4$