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Full-Text Articles in Physical Sciences and Mathematics
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability. © 2009 Springer …
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …
Boundary Layers In Channel Flow With Injection And Suction, R. Temam, X. Wang
Boundary Layers In Channel Flow With Injection And Suction, R. Temam, X. Wang
Mathematics and Statistics Faculty Research & Creative Works
We present a rigorous result regarding the boundary layer associated with the incompressible Newtonian channel flow with injection and suction. © 2000 Elsevier Science Ltd. All rights reserved.
Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang
Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang
Mathematics and Statistics Faculty Research & Creative Works
The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.
Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang
Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. for boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form ca Re3/2 where c is a universal constant, a denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed "outer" velocity scale. for fixed pressure …
Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang
Time Averaged Energy Dissipation Rate For Shear Driven Flows In ℝⁿ, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We drive an upper bound of the time averaged energy dissipation rate for boundary driven flows directly from the Navier-Stokes equations in ℝn. the upper bound is independent of the kinematic viscosity in accordance with Kolomogorov's scaling result. Copyright © 1997 Elsevier Science B.V. All rights reserved.
Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang
Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang
Mathematics and Statistics Faculty Research & Creative Works
In this article, we derive explicit asymptotic formulas for the solutions of Oseen's equations in space dimension two in a channel at large Reynolds number (small viscosity ε). These formulas exhibit typical boundary layers behaviors. Suitable correctors are defined to resolve the boundary obstacle and obtain convergence results valid up to the boundary. We study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infinity in which case the boundary layer tends to pervade the whole domain.