arXiv subjects

Mark Warnecke

Publications and source records attributed to Mark Warnecke.

3 recordsLinked to original sources

arXiv2026

Multipoint Statistical Turbulent Dynamics from Hopf Equation Closures

Obtaining accurate multipoint statistics of turbulence is computationally very expensive and therefore these statistics have remained largely unexplored from a theoretical standpoint. In this paper, (i) a first-principles-based closure of the $n$th-order structure function governing equation proposed by Sreenivasan & Yakhot (2021) is generalized to a closure of the velocity increment Hopf equation itself. Then (ii) the closure is further generalized to the $N$-point Hopf equation. Finally, (iii) an example of the method is provided to analytically determine the $3$-point structure function transition between the known $2$-point structure function and the $3$-point fusion rules from the closed $(N=3)$-point velocity increment Hopf equation. The analytical solution takes the form of a Batchelor interpolation and shows promising agreement with preliminary DNS data for the cases examined. Since the $N$-point velocity increment Hopf equation is closed, its solution can be numerically approximated. It is expected that similar methods, applied here to obtain the $2$-point structure function and $3$-point structure function transition, can be used to obtain further analytical predictions of various multipoint quantities to deepen our understanding of turbulence.

physics.flu-dyn↗

arXiv2025

An ensemble of Gaussian fields with multifractal statistics for turbulence

Obtaining accurate field statistics continues to be one of the major challenges in turbulence theory and modeling. From the various existing modeling approaches, multifractal models have been successful in capturing intermittency in velocity gradient and increment distributions. On the other hand, superstatistical models from nonequilibrium statistical mechanics have shown the capacity to model PDFs of various statistical turbulent quantities as ensembles of simpler stochastic processes. Here, we present an approach that generates field statistics in the form of a characteristic functional by promoting a model for multifractal increment statistics to an ensemble of Gaussian fields. By carefully designing the correlation function and the corresponding weight of each subensemble, we are able to define a functional that exhibits multifractal two-point inertial-range and dissipation-range statistics, and that blends into realistic large-scale behavior. Additionally, the method is capable of producing multifractal statistics with any of the widely used singularity spectra. We characterize the fidelity of our approach through comparisons to literature results from direct numerical simulations. Overall, our framework thereby bridges between three different perspectives to turbulence: superstatistics, multifractals, and functional approaches to turbulence.

physics.flu-dyn↗

arXiv2025

Turbulence-Resolving Integral Simulations for Wall-Bounded Flows

The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for Turbulence-Resolving Integral Simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier-Stokes with relatively simple closure approximations. Evidence from Direct Numerical Simulations (DNS) suggests that TRIS can theoretically resolve 35-40% of the turbulent skin friction enhancement for friction Reynolds numbers between 180 and 5200, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in ~1 minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of 395 and 590 show that TRIS generates a relatively accurate representation of the flow, while highlight discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modeling, motivating extension to more general flow configurations such as boundary layers on immersed objects.

physics.flu-dyn↗