scholarly journals On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

scholarly journals Machine-aided turbulence theory

2018 ◽  
Vol 854 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
A Priori ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Future Evolution ◽  
Decaying Turbulence

The question of whether significant subvolumes of a turbulent flow can be identified by automatic means, independently of a priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined as influence on the future evolution of the flow, and the problem is cast as an unsupervised machine ‘game’ in which the rules are the Navier–Stokes equations. It is shown that significance is an intermittent quantity in this particular flow, and that, in accordance with previous intuition, its most significant features are vortices, while the least significant ones are dominated by strain. Subject to cost considerations, the method should be applicable to more general turbulent flows.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals On the self-sustained nature of large-scale motions in turbulent Couette flow

2015 ◽  
Vol 782 ◽  
pp. 515-540 ◽  
Author(s):  
Subhandu Rawat ◽  
Carlo Cossu ◽  
Yongyun Hwang ◽  
François Rincon
Keyword(s):  
Couette Flow ◽  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Buffer Layers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Solutions ◽  
Smagorinsky Constant

Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at $Re=2150$ self-sustain, even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant $C_{s}$ in large-eddy simulations (LES). These results are in agreement with earlier results on pressure-driven turbulent channel flows. We further investigate the nature of the large-scale coherent motions by computing upper- and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton–Krylov solver, and find that they are connected by a saddle–node bifurcation at large values of $C_{s}$. Upper-branch solutions for the filtered large-scale motions are computed for Reynolds numbers up to $Re=2187$ using specific paths in the $Re{-}C_{s}$ parameter plane and compared to large-scale coherent motions. Continuation to $C_{s}=0$ reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata–Clever–Busse–Waleffe branch of steady solutions of the Navier–Stokes equations. In contrast, we find it impossible to connect the latter to buffer-layer motions through a continuation to higher Reynolds numbers in minimal flow units.

On Direct Numerical Simulation of Turbulent Flows

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
High Performance Computing ◽  
Turbulent Flows ◽  
High Performance ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Navier Stokes Equations ◽  
Performance Computing

The direct numerical simulation of turbulence (DNS) has become a method of outmost importance for the investigation of turbulence physics, and its relevance is constantly growing due to the increasing popularity of high-performance-computing techniques. In the present work, the DNS approach is discussed mainly with regard to turbulent shear flows of incompressible fluids with constant properties. A body of literature is reviewed, dealing with the numerical integration of the Navier-Stokes equations, results obtained from the simulations, and appropriate use of the numerical databases for a better understanding of turbulence physics. Overall, it appears that high-performance computing is the only way to advance in turbulence research through the front of the direct numerical simulation.

scholarly journals MHD convection ow in a constricted channel

2018 ◽  
Vol 26 (2) ◽  
pp. 267-283
Author(s):  
M. Tezer-Sezgin ◽  
Merve Gürbüz
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Hartmann Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Particular Solution ◽  
Laminar Convection ◽  
Long Channel ◽  
Velocity Pressure

Abstract We consider the steady, laminar, convection ow in a long channel of 2D rectangular constricted cross-section under the inuence of an applied magnetic field. The Navier-Stokes equations including Lorentz and buoyancy forces are coupled with the temperature equation and are solved by using linear radial basis function (RBF) approximations in terms of the velocity, pressure and the temperature of the fluid. RBFs are used in the approximation of the particular solution which becomes also the approximate solution of the problem. Results are obtained for several values of Grashof number (Gr), Hartmann number (M) and the constriction ratios (CR) to see the effects on the ow and isotherms for fixed values of Reynolds number and Prandtl number. As M increases, the ow is flattened. An increase in Gr increases the magnitude of the ow in the channel. Isolines undergo an inversion at the center of the channel indicating convection dominance due to the strong buoyancy force, but this inversion is retarded with the increase in the strength of the applied magnetic field. When both Hartmann number and constriction ratio are increased, ow is divided into more loops symmetrically with respect to the axes.

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