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The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in…

Astrophysics of Galaxies · Physics 2018-10-24 Liubin Pan , Paolo Padoan , Åke Nordlund

We explore the potential of a formulation of the Navier-Stokes equations incorporating a random description of the small-scale velocity component. This model, established from a version of the Reynolds transport theorem adapted to a…

Fluid Dynamics · Physics 2016-11-11 S. Kadri Harouna , E. Mémin

The development of advanced simulation tools is essential, both presently and in the future, for improving wind-energy design strategies, paving the way for a complete transition to sustainable solutions. The Reynolds-averaged Navier-Stokes…

Fluid Dynamics · Physics 2024-11-19 Ali Amarloo , Navid Zehtabiyan-Rezaie , Mahdi Abkar

The recent surge in machine learning augmented turbulence modelling is a promising approach for addressing the limitations of Reynolds-averaged Navier-Stokes (RANS) models. This work presents the development of the first open-source…

Fluid Dynamics · Physics 2021-10-01 Ryley McConkey , Eugene Yee , Fue-Sang Lien

There are two components in this work that allow solutions of the turbulent channel problem: one is the Galilean-transformed Navier-Stokes equation which gives a theoretical expression for the Reynolds stress; and the second the maximum…

Fluid Dynamics · Physics 2019-07-24 T. -W. Lee

We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly…

Numerical Analysis · Mathematics 2015-07-01 N. Aissiouene , M. -O. Bristeau , E. Godlewski , J. Sainte-Marie

We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed,…

Fluid Dynamics · Physics 2024-04-16 Atul Agrawal , Phaedon-Stelios Koutsourelakis

In this paper, the novel experimental data reported by Qin et al. [1] are used to assess the predictive capability of the Realizable k-epsilon (RKE) model and Reynolds stress transport (RST) model for buoyant jets and understand the reasons…

Fluid Dynamics · Physics 2023-01-18 Jiaxin Mao , Sunming Qin , Victor Petrov , Annalisa Manera

The high dimensionality and complex dynamics of turbulent flows in urban street canyons present significant challenges for wind and environmental engineering, particularly in addressing air quality, pollutant dispersion, and extreme wind…

Fluid Dynamics · Physics 2025-01-24 Tomek Jaroslawski , Aakash Patil , Beverley McKeon

A central obstacle to understanding the route to turbulence in wall-bounded flows is that the flows are composed of complex, highly fluctuating, and strongly nonlinear states. In the case of pipe flow, models have deepened our understanding…

Fluid Dynamics · Physics 2026-02-24 Santiago J. Benavides , Dwight Barkley

This study presents a novel approach for enhancing Reynolds-averaged Navier-Stokes (RANS) turbulence modeling through the application of a Relative Importance Term Analysis (RITA) methodology to develop a new zonally-augmented $k-\omega$…

Fluid Dynamics · Physics 2025-11-26 Tyler Buchanan , Monica Lăcătuş , Alastair West , Richard P. Dwight

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

We study the existence of weak solutions to the two-phase model of crowd motion. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two…

Analysis of PDEs · Mathematics 2018-03-02 Pierre Degond , Piotr Minakowski , Ewelina Zatorska

We study the Reynolds number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description…

Fluid Dynamics · Physics 2014-05-22 Rashad Moarref , Ati S. Sharma , Joel A. Tropp , Beverley J. McKeon

The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…

Numerical Analysis · Mathematics 2024-10-30 D. V. Lomasov , P. N. Vabishchevich

We introduce a field-wide benchmark challenge for machine learning in Reynolds-averaged Navier-Stokes (RANS) turbulence modelling. Though open-source datasets exist for training data-driven turbulence closure models, the field has been…

Fluid Dynamics · Physics 2026-04-01 Ryley McConkey , Tyler Buchanan , Tess Smidt , Abigail Bodner , Richard Dwight , Paola Cinnella

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

Analysis of PDEs · Mathematics 2007-05-23 W. J. Golz

We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…

Numerical Analysis · Mathematics 2025-10-07 Arbaz Khan , David Mora , Ricardo Ruíz-Baier , Jesus Vellojin

In this paper, we propose normalizing flows (NF) as a novel probability density function (PDF) turbulence model (NF-PDF model) for the Reynolds-averaged Navier-Stokes (RANS) equations. We propose to use normalizing flows in two different…

Fluid Dynamics · Physics 2021-01-12 Deniz A. Bezgin , Nikolaus A. Adams

A scale resolving hybrid RANS-LES technique is applied to an aircraft-nacelle configuration under transonic flow conditions using the unstructured, compressible TAU solver. Therefore, a wall modelled LES methodology is locally applied to…

Fluid Dynamics · Physics 2024-04-03 Marius Herr , Axel Probst , Rolf Radespiel
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