Three regularization models of the Navier-Stokes equations

We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as SGS models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-alpha model are compared to two previously employed regularizations, LANS-alpha and Leray-alpha (at Re ~ 3300, Taylor Re ~ 790) and to a DNS. We derive the Karman-Howarth equation for both the Clark-alpha and Leray-alpha models. We confirm one of two possible scalings resulting from this equation for Clark as well as its associated k^(-1) energy spectrum. At sub-filter scales, Clark-alpha possesses similar total dissipation and characteristic time to reach a statistical turbulent steady-state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark reproduces the energy spectrum and intermittency properties of the DNS. For the Leray model, increasing the filter width decreases the nonlinearity and the effective Re is substantially decreased. Even for the smallest value of alpha studied, Leray-alpha was inadequate as a SGS model. The LANS energy spectrum k^1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in resolution. However, that this same feature reduces its intermittency compared to Clark-alpha (which shares a similar Karman-Howarth equation). Clark is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than alpha, whereas high-order intermittency properties for larger values of alpha are best reproduced by LANS-alpha.Comment: 21 pages, 8 figure

Optimal model parameters for multi-objective large-eddy simulations

A methodology is proposed for the assessment of error dynamics in large-eddy simulations. It is demonstrated that the optimization of model parameters with respect to one flow property can be obtained at the expense of the accuracy with which other flow properties are predicted. Therefore, an approach is introduced which allows to assess the total errors based on various flow properties simultaneously. We show that parameter settings exist, for which all monitored errors are "near optimal," and refer to such regions as "multi-objective optimal parameter regions." We focus on multi-objective errors that are obtained from weighted spectra, emphasizing both large- as well small-scale errors. These multi-objective optimal parameter regions depend strongly on the simulation Reynolds number and the resolution. At too coarse resolutions, no multi-objective optimal regions might exist as not all error-components might simultaneously be sufficiently small. The identification of multi-objective optimal parameter regions can be adopted to effectively compare different subgrid models. A comparison between large-eddy simulations using the Lilly-Smagorinsky model, the dynamic Smagorinsky model and a new Re-consistent eddy-viscosity model is made, which illustrates this. Based on the new methodology for error assessment the latter model is found to be the most accurate and robust among the selected subgrid models, in combination with the finite volume discretization used in the present study

Non-local modulation of the energy cascade in broad-band forced turbulence

Classically, large-scale forced turbulence is characterized by a transfer of energy from large to small scales via nonlinear interactions. We have investigated the changes in this energy transfer process in broad-band forced turbulence where an additional perturbation of flow at smaller scales is introduced. The modulation of the energy dynamics via the introduction of forcing at smaller scales occurs not only in the forced region but also in a broad range of length-scales outside the forced bands due to non-local triad interactions. Broad-band forcing changes the energy distribution and energy transfer function in a characteristic manner leading to a significant modulation of the turbulence. We studied the changes in this transfer of energy when changing the strength and location of the small-scale forcing support. The energy content in the larger scales was observed to decrease, while the energy transport power for scales in between the large and small scale forcing regions was enhanced. This was investigated further in terms of the detailed transfer function between the triad contributions and observing the long-time statistics of the flow. The energy is transferred toward smaller scales not only by wavenumbers of similar size as in the case of large-scale forced turbulence, but by a much wider extent of scales that can be externally controlled.Comment: submitted to Phys. Rev. E, 15 pages, 18 figures, uses revtex4.cl

Response maxima in time-modulated turbulence: Direct Numerical Simulations

The response of turbulent flow to time-modulated forcing is studied by direct numerical simulations of the Navier-Stokes equations. The large-scale forcing is modulated via periodic energy input variations at frequency $\omega$. The response is maximal for frequencies in the range of the inverse of the large eddy turnover time, confirming the mean-field predictions of von der Heydt, Grossmann and Lohse (Phys. Rev. E 67, 046308 (2003)). In accordance with the theory the response maximum shows only a small dependence on the Reynolds number and is also quite insensitive to the particular flow-quantity that is monitored, e.g., kinetic energy, dissipation-rate, or Taylor-Reynolds number. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as $1/\omega$. For frequencies beyond the range of maximal response, a significant change in phase-shift relative to the time-modulated forcing is observed.Comment: submitted to Europhysics Letters (EPL), 8 pages, 8 Postscript figures, uses epl.cl

Leray and LANS-α\alpha modeling of turbulent mixing

Mathematical regularisation of the nonlinear terms in the Navier-Stokes equations provides a systematic approach to deriving subgrid closures for numerical simulations of turbulent flow. By construction, these subgrid closures imply existence and uniqueness of strong solutions to the corresponding modelled system of equations. We will consider the large eddy interpretation of two such mathematical regularisation principles, i.e., Leray and LANS$-\alpha$ regularisation. The Leray principle introduces a {\bfi smoothed transport velocity} as part of the regularised convective nonlinearity. The LANS$-\alpha$ principle extends the Leray formulation in a natural way in which a {\bfi filtered Kelvin circulation theorem}, incorporating the smoothed transport velocity, is explicitly satisfied. These regularisation principles give rise to implied subgrid closures which will be applied in large eddy simulation of turbulent mixing. Comparison with filtered direct numerical simulation data, and with predictions obtained from popular dynamic eddy-viscosity modelling, shows that these mathematical regularisation models are considerably more accurate, at a lower computational cost.Comment: 42 pages, 12 figure

Flow and bubble statistics of turbulent bubble-laden downflow channel

Direct numerical simulations of fully developed turbulent channel downflow at bulk Re equal to 6300, loaded with monodisperse bubbles at gas volume fractions α=0.5% , α=2.5% and α=10 have been carried out. Bubble deformability, surface tension, as well as discontinuity in the material properties across the bubble interfaces are explicitly accounted for. A full-scale channel of size 4πH × 2H × 4πH/3 in terms of the channel half-width H containing a number of bubbles up to O(103) is considered. The statistical structure of the bubbles, the probability density function describing the bubble velocity and the liquid kinetic energy spectra have been determined. A close range preferential clustering of the bubbles was found with a maximum density independent of the gas volume fraction at a separation distance of about 2.2R, with R the bubble radius. Preferential horizontal alignment and a general tendency to repulsion is shown for separation distances smaller than 3R. At larger separation distances a close to random distribution is observed for α=2.5% and α=10%, while tendency to vertical alignment is observed for α=0.5% . The pdf of the bubble velocity fluctuations was found to be well approximated by a Gaussian distribution. The liquid kinetic energy spectra in the channel core do not show a marked -3  scaling, which was previously reported for homogeneous isotropic turbulence and pseudo-turbulence

Distributed utterances

I propose an apparatus for handling intrasentential change in context. The standard approach has problems with sentences with multiple occurrences of the same demonstrative or indexical. My proposal involves the idea that contexts can be complex. Complex contexts are built out of (“simple”) Kaplanian contexts by ordered n-tupling. With these we can revise the clauses of Kaplan’s Logic of Demonstratives so that each part of a sentence is taken in a different component of a complex context. I consider other applications of the framework: to agentially distributed utterances (ones made partly by one speaker and partly by another); to an account of scare-quoting; and to an account of a binding-like phenomenon that avoids what Kit Fine calls “the antinomy of the variable.

Simple Front End Electronics for Multigap Resistive Plate Chambers

A simple circuit for the presentation of the signals from Multi-gap Resistive Plate Chambers (MRPCs) to standard existing digitization electronics is described. The circuit is based on "off-the-shelf" discrete components. An optimization of the values of specific components is required to match the aspects of the MRPCs for the given application. This simple circuit is an attractive option for the initial signal processing for MRPC prototyping and bench- or beam-testing efforts, as well as for final implementations of small-area Time-of-Flight systems with existing data acquisition systems.Comment: submitted to Nucl. Inst. and Methods, Section