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Register a new userCompressible helical turbulence: Fastened-structure geometry and statistics
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Jian-Zhou Zhu
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Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the Taylor-Proudman theorem and its analogues. A `chiral base flow/field, rooted in the generic intrinsic local structure, as well as an `equivalence principle is explained and used to bridge the single-structure mechanics and the helical statistics. The electric field fluctuations may similarly be depressed by the (self-)helicities of the two-fluid plasma model, with the geometry lying in the relation between the electric and density fields in a Maxwell equation.
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We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that helicity affects the inertial range scaling of the velocity and of the passive scalar when rotation is present, with a spectral law consistent with $sim k_{perp}^{-1.4}$ for the passive scalar variance spectrum. This scaling law is consistent with the phenomenological argument presented in cite{imazio2011} for rotating non-helical flows, wich states that if energy follows a $E(k)sim k^{-n}$ law, then the passive scalar variance follows a law $V(k) sim k^{-n_{theta}}$ with $n_{theta}=(5-n)/2$. With the second order scaling exponent obtained from this law, and using the Kraichnan model, we obtain anomalous scaling exponents for the passive scalar that are in good agreement with the numerical results. Intermittency of the passive scalar is found to be stronger than in the non-helical rotating case, a result that is also confirmed by stronger non-Gaussian tails in the probability density functions of field increments. Finally, Ficks law is used to compute the effective diffusion coefficients in the directions parallel and perpendicular to the rotation axis. Calculations indicate that horizontal diffusion decreases in the presence of helicity in rotating flows, while vertical diffusion increases. We use a mean field argument to explain this behavior in terms of the amplitude of velocity field fluctuations.
The conventional approach to the turbulent energy cascade, based on Richardson-Kolmogorov phenomenology, ignores the topology of emerging vortices, which is related to the helicity of the turbulent flow. It is generally believed that helicity can play a significant role in turbulent systems, e.g., supporting the generation of large-scale magnetic fields, but its impact on the energy cascade to small scales has never been observed. We suggest for the first time a generalized phenomenology for isotropic turbulence with an arbitrary spectral distribution of the helicity. We discuss various scenarios of direct turbulent cascades with new helicity effect, which can be interpreted as a hindering of the spectral energy transfer. Therefore the energy is accumulated and redistributed so that the efficiency of non-linear interactions will be sufficient to provide a constant energy flux. We confirm our phenomenology by high Reynolds number numerical simulations based on a shell model of helical turbulence. The energy in our model is injected at a certain large scale only, whereas the source of helicity is distributed over all scales. In particular, we found that the helical bottleneck effect can appear in the inertial interval of the energy spectrum.
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