Transition Threshold for the 3D Couette Flow in a Finite Channel PDF Download
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Author: Qi Chen
Publisher: American Mathematical Society
ISBN: 1470468956
Category : Mathematics
Languages : en
Pages : 190
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Book Description
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Author: Qi Chen
Publisher: American Mathematical Society
ISBN: 1470468956
Category : Mathematics
Languages : en
Pages : 190
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Book Description
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Author: Jacob Bedrossian
Publisher:
ISBN: 9781470462512
Category : Damping (Mechanics)
Languages : en
Pages : 170
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Book Description
"We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. We prove that for sufficiently regular initial data of size [epsilon] [less than or equal to] c0Re-1 for some universal c0 > 0, the solution is global, remains within O(c0) of the Couette flow in L2, and returns to the Couette flow as t [right arrow] [infinity]. For times t >/-Re1/3, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwise-independent solutions referred to as streaks. Our analysis contains perturbations that experience a transient growth of kinetic energy from O(Re-1) to O(c0) due to the algebraic linear instability known as the lift-up effect. Furthermore, solutions can exhibit a direct cascade of energy to small scales. The behavior is very different from the 2D Couette flow, in which stability is independent of Re, enstrophy experiences a direct cascade, and inviscid damping is dominant (resulting in a kind of inverse energy cascade). In 3D, inviscid damping will play a role on one component of the velocity, but the primary stability mechanism is the mixing-enhanced dissipation. Central to the proof is a detailed analysis of the interplay between the stabilizing effects of the mixing and enhanced dissipation and the destabilizing effects of the lift-up effect, vortex stretching, and weakly nonlinear instabilities connected to the non-normal nature of the linearization"--
Author: Brandon Doherty
Publisher: American Mathematical Society
ISBN: 1470468948
Category : Mathematics
Languages : en
Pages : 122
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Author: David Burns
Publisher: American Mathematical Society
ISBN: 1470469669
Category : Mathematics
Languages : en
Pages : 168
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Author: M. Gekhtman
Publisher: American Mathematical Society
ISBN: 1470469707
Category : Mathematics
Languages : en
Pages : 116
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Author: Masao Oi
Publisher: American Mathematical Society
ISBN: 1470469561
Category : Mathematics
Languages : en
Pages : 174
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Author: David Ayala
Publisher: American Mathematical Society
ISBN: 1470469626
Category : Mathematics
Languages : en
Pages : 272
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Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470472252
Category : Mathematics
Languages : en
Pages : 148
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Author: Jacob Bedrossian
Publisher: American Mathematical Soc.
ISBN: 1470442175
Category : Mathematics
Languages : en
Pages : 154
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Book Description
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
Author: Oscar Gonzalez
Publisher: American Mathematical Society
ISBN: 147046991X
Category : Mathematics
Languages : en
Pages : 228
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Book Description
The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear algebra and ordinary differential equations. The subjects explored in the book are dimensional analysis and scaling, dynamical systems, perturbation methods, and calculus of variations. These are immense subjects of wide applicability and a fertile ground for critical thinking and quantitative reasoning, in which every student of mathematics should have some experience. Students who use this book will enhance their understanding of mathematics, acquire tools to explore meaningful scientific problems, and increase their preparedness for future research and advanced studies. The highlights of the book are case studies and mini-projects, which illustrate the mathematics in action. The book also contains a wealth of examples, figures, and regular exercises to support teaching and learning. The book includes opportunities for computer-aided explorations, and each chapter contains a bibliography with references covering further details of the material.
