Libration driven elliptical instability Phys. Fluids 24, 061703 (2012) On integral length scales in anisotropic turbulence Phys. Fluids 24, 061702 (2012) An experimental study of small Atwood number Rayleigh-Taylor instability using the magnetic levitation of paramagnetic fluids Phys. Fluids 24, 052106 (2012) Direct measurement of the spectral transfer function of a laser based anemometer Rev. Sci. Instrum. 83, 033111 (2012) Additional information on Phys. Fluids A One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input apriori. The model is based on an algebraic identity between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

Explicit or implicit filtered representations of chaotic fields like spectral cut-offs or numerical discretizations are commonly used in the study of turbulence and particularly in the so-called large-eddy simulations. Peculiar to these representations is that they are produced by different filtering operators at different levels of resolution, and they can be hierarchically organized in terms of a characteristic parameter like a grid length or a spectral truncation mode. Unfortunately, in the case of a general implicit or explicit filtering operator the Reynolds rules of the mean are no longer valid, and the classical analysis of the turbulence in terms of mean values and fluctuations is not so simple.In this paper a new operatorial approach to the study of turbulence based on the general algebraic properties of the filtered representations of a turbulence field at different levels is presented. The main results of this analysis are the averaging invariance of the filtered Navier—Stokes equations in terms of the generalized central moments, and an algebraic identity that relates the turbulent stresses at different levels. The statistical approach uses the idea of a decomposition in mean values and fluctuations, and the original turbulent field is seen as the sum of different contributions. On the other hand this operatorial approach is based on the comparison of different representations of the turbulent field at different levels, and, in the opinion of the author, it is particularly fitted to study the similarity between the turbulence at different filtering levels. The best field of application of this approach is the numerical large-eddy simulation of turbulent flows where the large scale of the turbulent field is captured and the residual small scale is modelled. It is natural to define and to extract from the resolved field the resolved turbulence and to use the information that it contains to adapt the subgrid model to the real turbulent field. Following these ideas the application of this approach to the large-eddy simulation of the turbulent flow has been produced (Germano et al. 1991). It consists in a dynamic subgrid-scale eddy viscosity model that samples the resolved scale and uses this information to adjust locally the Smagorinsky constant to the local turbulence.

The problem of fully developed steady viscous incompressible flow in a helical pipe is studied. The predicted analytical expression in the literature for the flow rate is improved. The present result shows a reduction in the flow rate with increasing torsion, for a given curvature. Qualitatively this effect of torsion is seen to cause equivelocity contours in the normal section of the pipe, to undergo shear.

In this paper the Dean (1928) equations are extended to the case of a helical pipe flow, and it is shown that they depend not only on the Dean number K but also on a new parameter λ/[Rscr ] where λ is the ratio of the torsion τ to the curvature κ of the pipe axis and [Rscr ] the Reynolds number referred in the usual way to the pipe radius a and to the equivalent maximum speed in a straight pipe under the same axial pressure gradient. The fact that the torsion has no first-order effect on the flow is confirmed, but it is shown that this is peculiar to a circular cross-section. In the case of an elliptical cross-section there is a first-order effect of the torsion on the secondary flow, and in the limit λ/[Rscr ] → ∞ (twisted pipes, provided only with torsion), the first-order ‘displacement’ effect of the walls on the secondary flow, analysed in detail by Choi (1988), is recovered.Different systems of coordinates and different orders of approximations have recently been adopted in the study of the flow in a helical pipe. Thus comparisons between the equations and the results presented in different reports are in some cases difficult and uneasy. In this paper the extended Dean equations for a helical pipe flow recently derived by Kao (1987) are converted to a simpler form by introducing an appropriate modified stream function, and their equivalence with the present set of equations is recovered. Finally, the first-order equivalence of this set of equations with the equations obtained by Murata et al. (1981) is discussed.

Differential filters for the large eddy numerical simulation of turbulent flows are defined and their properties are discussed. Their main advantages are that the correlations can be expressed exactly in the so-called resolvable scale and the attenuation of the filtered function in the Fourier space can be carefully controlled

A redefinition of the Leonard term, the subgrid scale cross term, and the subgrid scale Reynolds stress is proposed, consistent with a general statement concerning turbulent stresses. The main advantage of the new redefined stresses consists of their term by term Galilean invariance.

Linear differential filters, i.e., filters in which the filtered function f̄ and the original function f are connected by a linear differential equation, are studied on a general basis concerning the elliptic operators of second order. In addition, a particular example of a parabolic filter depending on space and extended to past times is given, and its interest in the context of the large eddy simulation of turbulence is discussed.

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