Advection of a passive scalar field by turbulent compressible fluid: renormalization group analysis near d = 4
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 th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2017-01-01
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| Series: | EPJ Web of Conferences |
| Online Access: | https://doi.org/10.1051/epjconf/201713710003 |
| Summary: | 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 ε = 4 − d. All calculations are performed in the leading one-loop approximation. |
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| ISSN: | 2100-014X |