Shear Turbulence. Fabian Waleffe. Depts. of Mathematics and Engineering Physics. Wisconsin
|
|
|
- Brandon York
- 5 years ago
- Views:
Transcription
1 Shear Turbulence Fabian Waleffe Depts. of Mathematics and Engineering Physics, Madison University of Wisconsin
2 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers
3 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers... by late stage researchers?!
4 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers Instability?... by late stage researchers?!
5 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers Instability?... by late stage researchers?! Subcritical instability?
6 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers Instability?... by late stage researchers?! Subcritical instability? Transition to turbulence?
7 Mini-Symposium on Subcritical Flow Instability for training of early stage researchers Instability?... by late stage researchers?! Subcritical instability? Transition to turbulence? What is turbulence?
8 Incompressible flow: Navier-Stokes equations 3D velocity field u(x, t): u = 0 t u + (uu) + p = 1 R 2 u R: Reynolds number
9 Simple geometries, simple flow? Pipe, Channel u = (1 y 2 ) ˆx R 2, 000 Plane Couette u = y ˆx R 350
10 Channel flow for R 2, not simple! Front Top Side Green, M. A., Rowley, C. W. & Haller, G. Detection of Lagrangian coherent structures in three-dimensional turbulence, J. Fluid Mech., 572, 2007,
11 Instability?
12 Instability? NSE: du dt = f (u; R)
13 Instability? NSE: du = f (u; R) dt Equilibrium u 0 : 0 = f (u 0 ; R)
14 Instability? du NSE: = f (u; R) dt Equilibrium u 0 : 0 = f (u 0 ; R) ( ) d(u u Linear stability: 0 ) f = (u u dt u 0 ) 0
15 Instability? du NSE: = f (u; R) dt Equilibrium u 0 : 0 = f (u 0 ; R) ( ) d(u u Linear stability: 0 ) f = (u u dt u 0 ) u u 0 = ve λt, 0 ( ) f u 0 v = λv, Instability if R(λ) > 0, typically for R > R c
16 Linear instability stable R c unstable R
17 Nonlinear bifurcation u u 0 stable R c unstable R
18 Bifurcations R c R Supercritical, NL stabilizes da dt = (R R c)a A 3
19 Bifurcations R c R Supercritical, NL stabilizes da dt = (R R c)a A 3 R c R Subcritical, NL de -stabilizes, da dt = (R R c)a+a 3
20 Bifurcations R c R Supercritical, NL stabilizes da dt = (R R c)a A 3 R c R Subcritical, NL de -stabilizes, da dt = (R R c)a+a 3 R c R Higher order NL stabilization? da dt = (R R c)a+a 3 A 5
21 Supercritical or subcritical?
22 Supercritical or subcritical? Nonlinearity decides: da dt = (R R c)a ± A 3
23 Supercritical or subcritical? Nonlinearity decides: NSE: du dt da dt = (R R c)a ± A 3 dv = f (u; R) dt = L(v; u 0, R) + N(v, v)
24 Supercritical or subcritical? Nonlinearity decides: NSE: du dt da dt = (R R c)a ± A 3 dv = f (u; R) dt = L(v; u 0, R) + N(v, v) v, N(v, v) = 0 d v, v dt = v, L(v) = v, L T (v)
25 Supercritical or subcritical? Nonlinearity decides: NSE: du dt da dt = (R R c)a ± A 3 dv = f (u; R) dt = L(v; u 0, R) + N(v, v) v, N(v, v) = 0 d v, v dt = v, L(v) = v, L T (v) sufficient for supercritical: L = L T
26 Supercritical or subcritical? Nonlinearity decides: NSE: du dt da dt = (R R c)a ± A 3 dv = f (u; R) dt = L(v; u 0, R) + N(v, v) v, N(v, v) = 0 d v, v dt = v, L(v) = v, L T (v) sufficient for supercritical: L = L T necessary for subcritical: L L T
27 Linear stability: L L T... Back to shear flows
28 Back to shear flows Linear stability: L L T... Hard! Confusing!
29 Back to shear flows Linear stability: L L T... Hard! Confusing! Need inflection point for inviscid ( R = ) instability (Rayleigh 1880)
30 Back to shear flows Linear stability: L L T... Hard! Confusing! Need inflection point for inviscid ( R = ) instability (Rayleigh 1880) Viscosity can lead to instability! (Prandtl, Heisenberg, Tollmien, Lin)
31 Back to shear flows Linear stability: L L T... Hard! Confusing! Need inflection point for inviscid ( R = ) instability (Rayleigh 1880) Viscosity can lead to instability! (Prandtl, Heisenberg, Tollmien, Lin)... but only in BL and Channel, not pipe and plane Couette... and weak instability seems unrelated to natural transition
32 Back to shear flows Linear stability: L L T... Hard! Confusing! Need inflection point for inviscid ( R = ) instability (Rayleigh 1880) Viscosity can lead to instability! (Prandtl, Heisenberg, Tollmien, Lin)... but only in BL and Channel, not pipe and plane Couette... and weak instability seems unrelated to natural transition Who said: Subtle is the Lord, but malicious s/he is not.?!
33 Shear turbulence turbulence?! u u 0 stable stable?! R c R
34 Shear turbulence turbulence?! u u 0 transition?! stable stable?! R c R
35 Streaks in turbulent shear flows... R 10 9? (OK, some convection too... )
36 Streaks in turbulent channel flow... Skin friction (Kim, Moin, Moser JFM 2007)
37 Characteristic near-wall coherent structure Derek Stretch, CTR Stanford, 1990 Streaks + staggered quasi-streamwise vortices: why?
38 Self-Sustaining Process (SSP) advection of mean shear Streaks O(1) instability of U(y,z) Streamwise Rolls O(1/R) nonlinear self interaction Streak wave mode (3D) O(1/R) WKH 1993, HKW 1995, W 1995, 1997
39 SSP theory SSP method (1) Add F forcing of streamwise rolls to NSE R2 O( 1 R ) rolls, O(1) streaks ( Full NSE, Newton s method) PRL 1998, JFM 2001, PoF 2003
40 SSP theory SSP method (1) Add F forcing of streamwise rolls to NSE R2 O( 1 R ) rolls, O(1) streaks (2) Find F c subcritical bifurcation point (streak instability) ( Full NSE, Newton s method) PRL 1998, JFM 2001, PoF 2003
41 SSP theory SSP method (1) Add F forcing of streamwise rolls to NSE R2 O( 1 R ) rolls, O(1) streaks (2) Find F c subcritical bifurcation point (streak instability) (3) Continue to F = 0. Ta da! ( Full NSE, Newton s method) PRL 1998, JFM 2001, PoF 2003
42 SSP theory SSP method (1) Add F forcing of streamwise rolls to NSE R2 O( 1 R ) rolls, O(1) streaks (2) Find F c subcritical bifurcation point (streak instability) (3) Continue to F = 0. Ta da! (4) (optional) Recall: Subtle is the Lord, but malicious s/he is not. ( Full NSE, Newton s method) PRL 1998, JFM 2001, PoF 2003
43 Laminar Couette flow: u=0 & u= Wx Fr
44 SSP: Streamwise Rolls create Streaks Wx Fr
45 SSP: Rolls create Streaks Wx Fr
46 SSP: Rolls create Streaks Wx Fr
47 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
48 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
49 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
50 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
51 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
52 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
53 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
54 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
55 SSP in action: Subcritical Bifurcation from Streaks Wx Fr
56 SSP: Self-Sustained! 3D Lower branch Wx Fr
57 SSP: Self-Sustained! 3D Lower branch Wx Fr
58 SSP: Bifurcation from Streaks Wx Fr
59 SSP: Bifurcation from Streaks Wx Fr
60 SSP: Self-Sustained! 3D Upper branch Wx Fr
61 SSP: Self-Sustained! 3D Upper branch Wx Fr
62 Homotopy Free-Free Couette (FFC) Rigid-Free Poiseuille (RFP) µ = 0 1 BC : (1 µ) du dy + µu = 0 Flow : ( 1 U L (y) = y + µ 6 y 2 ) 2
63 FFC RFP
64 FFC RFP
65 FFC RFP
66 FFC RFP
67 FFC RFP
68 Poiseuille traveling wave!
69 Poiseuille traveling wave!
70 Optimum Traveling Wave: 100 +! min R τ = 2h + = 44 for L + x = 274, L + z = 105 just right!
71 Out-of-the-blue-sky DRAG R Lower branch does NOT bifurcate from laminar flow! RRC (α, γ) = (1, 2), (1.14, 2.5), up to R asymptotics
72 Vortex visualization ω x 2Q= 2 p = Ω ij Ω ij S ij S ij
73 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
74 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
75 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
76 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
77 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
78 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
79 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
80 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
81 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
82 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
83 Upper and Lower branches 0.6 max(q), (α, γ) = (1.14, 2.5).
84 Structure of LBS, R advection of mean shear Streamwise Rolls O(1/R) Streaks O(1) exp ( i α x) mode O(1/R) instability of U(y,z) nonlinear self-interaction u ū ˆx = [u 0 ū, v 0, w 0 ](y, z) + e iαx u 1 (y, z) y max z rms R
85 Structure of LBS, R = advection of mean shear Streamwise Rolls O(1/R) Streaks O(1) exp ( i α x) mode O(1/R) instability of U(y,z) nonlinear self-interaction u = [u 0, v 0, w 0 ](y, z) + e iαx [u 1, v 1, w 1 ](y, z) y u 0 (y, z), v 0 (y, z) w 1 (y, z) z y z critical layer!
86 LB eigenvalues, (α, γ) = (1.14, 2.5), (1, 2), R = Only 1 unstable eig!
87 Stability of LBS real(λ) R
88 LB Transition (α, γ) = (1.14, 2.5), (1, 2), R = Dissipation Rate Dissipation Rate Energy Input Rate Energy Input Rate Dissipation Rate Dissipation Rate Energy Input Rate Energy Input Rate
89 Lower branch R = max(q), R = 1000, (α, γ) = (1.14, 2.5).
90 Two states of fluid flow? Turbulent Laminar
91 Separatrix, transition threshold Turbulent Laminar
92 Unstable Coherent States! Turbulent Laminar
93 PCF data (R = 400) 5 4 Dissipation Rate Energy Input Rate Periodic solutions in HKW (1.14, 1.67) by Viswanath, JFM 2007 & Gibson (TBA)
94 Visualizing State Space ( 10 5 dof s) 0.1 u NB u LM a a a RRC, R=400, Gibson, Halcrow, Cvitanovic, JFM to appear arxiv.org/
95 Visualizing State Space (PCF, R=400) u UB 0.1 u LB τ z u UB u LM a 3 0 τ xz u LB τ x u UB τ xz u UB 0 a a 1 RRC, R=400, Gibson, Halcrow, Cvitanovic, JFM to appear arxiv.org/
96 Conclusions Go nonlinear, young men and women!
97 Conclusions Go nonlinear, young men and women! Instabilities? bifurcations! coherent flows!
98 Conclusions Go nonlinear, young men and women! Instabilities? bifurcations! coherent flows! Laminar or turbulent? lots, and lots of coherent too!
99 Conclusions Go nonlinear, young men and women! Instabilities? bifurcations! coherent flows! Laminar or turbulent? lots, and lots of coherent too! Go coherent, young men and women!
100 Conclusions Go nonlinear, young men and women! Instabilities? bifurcations! coherent flows! Laminar or turbulent? lots, and lots of coherent too! Go coherent, young men and women! Bypass transition = instability of streaks? NO! instability of Lower Branch States!
101 Conclusions Go nonlinear, young men and women! Instabilities? bifurcations! coherent flows! Laminar or turbulent? lots, and lots of coherent too! Go coherent, young men and women! Bypass transition = instability of streaks? NO! instability of Lower Branch States! Lower Branch = Gate to Turbulence!
102 Upper and Lower branches no-slip Couette 5 4 Dissipation Rate Energy Input Rate Steady State & turbulent (by Jue Wang & John Gibson) in RRC, R = 400, (α, γ)=(0.95,1.67)
103 Upper branches Turbulence (no-slip Couette) y 0 y U RMS solid: Turbulent (avg t=2000), dash: fixed point Mean and RMS velocity profiles
What is Turbulence? Fabian Waleffe. Depts of Mathematics and Engineering Physics University of Wisconsin, Madison
What is Turbulence? Fabian Waleffe Depts of Mathematics and Engineering Physics University of Wisconsin, Madison it s all around,... and inside us! Leonardo da Vinci (c. 1500) River flow, pipe flow, flow
Stability of Shear Flow
Stability of Shear Flow notes by Zhan Wang and Sam Potter Revised by FW WHOI GFD Lecture 3 June, 011 A look at energy stability, valid for all amplitudes, and linear stability for shear flows. 1 Nonlinear
EXACT COHERENT STRUCTURES IN TURBULENT SHEAR FLOWS
EXACT COHERENT STRUCTURES IN TURBULENT SHEAR FLOWS Fabian Waleffe Departments of Mathematics and Engineering Physics University of Wisconsin, Madison, WI 53706, USA waleffe@math.wisc.edu Abstract Exact
Exact coherent structures and their instabilities: toward a dynamical-system theory of shear turbulence 1
Exact coherent structures and their instabilities: toward a dynamical-system theory of shear turbulence 1 Fabian Waleffe Departments of Mathematics and Engineering Physics University of Wisconsin-Madison,
Transition to turbulence in plane Poiseuille flow
Proceedings of the 55th Israel Annual Conference on Aerospace Sciences, Tel-Aviv & Haifa, Israel, February 25-26, 2015 ThL2T5.1 Transition to turbulence in plane Poiseuille flow F. Roizner, M. Karp and
Turbulent boundary layer
Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic
V (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
General introduction to Hydrodynamic Instabilities
KTH ROYAL INSTITUTE OF TECHNOLOGY General introduction to Hydrodynamic Instabilities L. Brandt & J.-Ch. Loiseau KTH Mechanics, November 2015 Luca Brandt Professor at KTH Mechanics Email: luca@mech.kth.se
OPTIMIZATION OF HEAT TRANSFER ENHANCEMENT IN PLANE COUETTE FLOW
OPTIMIZATION OF HEAT TRANSFER ENHANCEMENT IN PLANE COUETTE FLOW Shingo Motoki, Genta Kawahara and Masaki Shimizu Graduate School of Engineering Science Osaka University 1-3 Machikaneyama, Toyonaka, Osaka
Stability of Shear Flow: part 2
Stability of Shear Flow: part 2 Fabian Waleffe notes by Matthew Chantry and Lindsey Ritchie Revised by FW WHOI GFD Lecture 4 June 23, 2011 We derive necessary conditions for linear instability of shear
Flow Transition in Plane Couette Flow
Flow Transition in Plane Couette Flow Hua-Shu Dou 1,, Boo Cheong Khoo, and Khoon Seng Yeo 1 Temasek Laboratories, National University of Singapore, Singapore 11960 Fluid Mechanics Division, Department
Visualizing the geometry of state space in plane Couette flow
Accepted for publication in J. Fluid Mech. 1 Visualizing the geometry of state space in plane Couette flow By J. F. G I B S O N, J. H A L C R O W A N D P. C V I T A N O V I Ć School of Physics, Georgia
Feedback on vertical velocity. Rotation, convection, self-sustaining process.
Feedback on vertical velocity. Rotation, convection, self-sustaining process. Fabian Waleffe//notes by Andrew Crosby, Keiji Kimura, Adele Morrison Revised by FW WHOI GFD Lecture 5 June 24, 2011 We have
Energy Transfer Analysis of Turbulent Plane Couette Flow
Energy Transfer Analysis of Turbulent Plane Couette Flow Satish C. Reddy! and Petros J. Ioannou2 1 Department of Mathematics, Oregon State University, Corvallis, OR 97331 USA, reddy@math.orst.edu 2 Department
Equilibrium and traveling-wave solutions of plane Couette flow
To be submitted to J. Fluid Mech. 1 Equilibrium and traveling-wave solutions of plane Couette flow By J. H A L C R O W, J. F. G I B S O N A N D P. C V I T A N O V I Ć School of Physics, Georgia Institute
Coherent structures in stably stratified plane Couette flow
Coherent structures in stably stratified plane Couette flow D. Olvera * & R. R. Kerswell School of Mathematics, University of Bristol, Bristol, UK. * do2542@bristol.ac.uk Abstract A large body of recent
HOW STREAMWISE ROLLS AND STREAKS SELF-SUSTAIN IN A SHEAR FLOW: PART 2
HOW STREAMWISE ROLLS AND STREAKS SELF-SUSTAIN IN A SHEAR FLOW: PART 2 Fabian Waleffe and John Kim 2 Mathematics and Engineering Physics Departments, University of Wisconsin, Madison, WI 5376-33 2 Mechanical
ÉCOLE DE PHYSIQUE DES HOUCHES. Institut de Mécanique des Fluides Toulouse CNRS Université de Toulouse, also at
ÉCOLE DE PHYSIQUE DES HOUCHES STABILITY OF FLUID FLOWS Carlo COSSU Institut de Mécanique des Fluides Toulouse CNRS Université de Toulouse, also at Département de Mécanique, École Polytechinique http://www.imft.fr/carlo-cossu/
A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries
Center for Turbulence Research Annual Research Briefs 2006 41 A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries By D. You AND P. Moin 1. Motivation
Homotopy of exact coherent structures in plane shear flows
PHYSICS OF FLUIDS VOLUME 15, NUMBER 6 JUNE 2003 Homotopy of exact coherent structures in plane shear flows Fabian Waleffe a) Departments of Mathematics and Engineering Physics, University of Wisconsin
Introduction to Turbulence AEEM Why study turbulent flows?
Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.edu Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and
Exercise 5: Exact Solutions to the Navier-Stokes Equations I
Fluid Mechanics, SG4, HT009 September 5, 009 Exercise 5: Exact Solutions to the Navier-Stokes Equations I Example : Plane Couette Flow Consider the flow of a viscous Newtonian fluid between two parallel
Patterns of Turbulence. Dwight Barkley and Laurette Tuckerman
Patterns of Turbulence Dwight Barkley and Laurette Tuckerman Plane Couette Flow Re = U gap/2 ν Experiments by Prigent and Dauchot Re400 Z (Spanwise) 40 24 o Gap 2 Length 770 X (Streamwise) Examples: Patterns
4 Shear flow instabilities
4 Shear flow instabilities Here we consider the linear stability of a uni-directional base flow in a channel u B (y) u B = 0 in the region y [y,y 2. (35) 0 y = y 2 y z x u (y) B y = y In Sec. 4. we derive
Shear Turbulence: Onset and Structure
Shear Turbulence: Onset and Structure Fabian Waleffe notes by Martín Hoecker-Martínez and Chao Ma revised and massively expanded by FW WHOI GFD Lecture 1 June 20, 2011 1 Introduction Figure 1: Reynolds
Physics of irregularity flow and tumultuous conversion in shear flows
African Journal of Physics Vol. 1 (3), 15 pages, November, 2013. Available online at www.internationalscholarsjournals.org International Scholars Journals Full Length Research Paper Physics of irregularity
Stochastic excitation of streaky boundary layers. Luca Brandt, Dan Henningson Department of Mechanics, KTH, Sweden
Stochastic excitation of streaky boundary layers Jérôme Hœpffner Luca Brandt, Dan Henningson Department of Mechanics, KTH, Sweden Boundary layer excited by free-stream turbulence Fully turbulent inflow
Turbulent drag reduction by streamwise traveling waves
51st IEEE Conference on Decision and Control December 10-13, 2012. Maui, Hawaii, USA Turbulent drag reduction by streamwise traveling waves Armin Zare, Binh K. Lieu, and Mihailo R. Jovanović Abstract For
Σχηματισμός και εξισορρόπηση ζωνικών ανέμων σε πλανητικές τυρβώδεις ατμόσφαιρες
Σχηματισμός και εξισορρόπηση ζωνικών ανέμων σε πλανητικές τυρβώδεις ατμόσφαιρες Ναβίτ Κωνσταντίνου και Πέτρος Ιωάννου Τμήμα Φυσικής Εθνικό και Καποδιστριακό Παν/μιο Αθηνών Πανεπιστήμιο Κύπρου 7 Ιανουαρίου
Understanding and Controlling Turbulent Shear Flows
Understanding and Controlling Turbulent Shear Flows Bassam Bamieh Department of Mechanical Engineering University of California, Santa Barbara http://www.engineering.ucsb.edu/ bamieh 23rd Benelux Meeting
Boundary-Layer Theory
Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
Low-speed streak instability in near wall turbulence with adverse pressure gradient
Journal of Physics: Conference Series Low-speed streak instability in near wall turbulence with adverse pressure gradient To cite this article: U Ehrenstein et al 2011 J. Phys.: Conf. Ser. 318 032027 View
Using Statistical State Dynamics to Study the Mechanism of Wall-Turbulence
Using Statistical State Dynamics to Study the Mechanism of Wall-Turbulence Brian Farrell Harvard University Cambridge, MA IPAM Turbulence Workshop UCLA November 19, 2014 thanks to: Petros Ioannou, Dennice
Topics in Fluid Dynamics: Classical physics and recent mathematics
Topics in Fluid Dynamics: Classical physics and recent mathematics Toan T. Nguyen 1,2 Penn State University Graduate Student Seminar @ PSU Jan 18th, 2018 1 Homepage: http://math.psu.edu/nguyen 2 Math blog:
Application of wall forcing methods in a turbulent channel flow using Incompact3d
Application of wall forcing methods in a turbulent channel flow using Incompact3d S. Khosh Aghdam Department of Mechanical Engineering - University of Sheffield 1 Flow control 2 Drag reduction 3 Maths
Chapter 6: Incompressible Inviscid Flow
Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational
The mean velocity profile in the smooth wall turbulent boundary layer : 1) viscous sublayer
The mean velocity profile in the smooth wall turbulent boundary layer : 1) viscous sublayer u = τ 0 y μ τ = μ du dy the velocity varies linearly, as a Couette flow (moving upper wall). Thus, the shear
Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions
Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,
Résonance et contrôle en cavité ouverte
Résonance et contrôle en cavité ouverte Jérôme Hœpffner KTH, Sweden Avec Espen Åkervik, Uwe Ehrenstein, Dan Henningson Outline The flow case Investigation tools resonance Reduced dynamic model for feedback
ON TRANSITION SCENARIOS IN CHANNEL FLOWS
ON TRANSITION SCENARIOS IN CHANNEL FLOWS FABIAN WALEFFE Abstract. [Cha2] has proposed scaling estimates for the magnitude of the smallest perturbations that could trigger turbulence in channel flows. Those
1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows
Published in Phys. Fluids 14, L73-L76 (22). Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Koji Fukagata, Kaoru Iwamoto, and Nobuhide Kasagi Department of Mechanical
The Enigma of The Transition to Turbulence in a Pipe
4th Brooke Benjamin Lecture The Enigma of The Transition to Turbulence in a Pipe T. Mullin Manchester Centre for Nonlinear Dynamics The University of Manchester, UK Joint work with: A.G. Darbyshire, B.
(1) Transition from one to another laminar flow. (a) Thermal instability: Bernard Problem
Professor Fred Stern Fall 2014 1 Chapter 6: Viscous Flow in Ducts 6.2 Stability and Transition Stability: can a physical state withstand a disturbance and still return to its original state. In fluid mechanics,
very elongated in streamwise direction
Linear analyses: Input-output vs. Stability Has much of the phenomenology of boundary la ut analysis of Linearized Navier-Stokes (Cont.) AMPLIFICATION: 1 y. z x 1 STABILITY: Transitional v = (bypass) T
Turbulence Modeling I!
Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!
Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity
Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity Tobias Knopp D 23. November 28 Reynolds averaged Navier-Stokes equations Consider the RANS equations with
Basic Fluid Mechanics
Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible
Chapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
Fundamentals of Fluid Dynamics: Elementary Viscous Flow
Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research
LOW SPEED STREAKS INSTABILITY OF TURBULENT BOUNDARY LAYER FLOWS WITH ADVERSE PRESSURE GRADIENT
LOW SPEED STREAKS INSTABILITY OF TURBULENT BOUNDARY LAYER FLOWS WITH ADVERSE PRESSURE GRADIENT J.-P. Laval (1) CNRS, UMR 8107, F-59650 Villeneuve d Ascq, France (2) Univ Lille Nord de France, F-59000 Lille,
The Turbulent Rotational Phase Separator
The Turbulent Rotational Phase Separator J.G.M. Kuerten and B.P.M. van Esch Dept. of Mechanical Engineering, Technische Universiteit Eindhoven, The Netherlands j.g.m.kuerten@tue.nl Summary. The Rotational
Transition in shear flows: non-linear normality versus non-normal linearity
Transition in shear flows: non-linear normality versus non-normal linearity Fabian Waleffe MIT, Department of Mathematics, Room 2-378, Cambridge, MA 02139 Physics of Fluids 7, pp. 3060-3066. Abstract A
Fluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
UNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes
arxiv:physics/ v2 [physics.flu-dyn] 3 Jul 2007
![arxiv:physics/ v2 [physics.flu-dyn] 3 Jul 2007](/thumbs/86/93477096.jpg "arxiv:physics/ v2 [physics.flu-dyn] 3 Jul 2007")
Leray-α model and transition to turbulence in rough-wall boundary layers Alexey Cheskidov Department of Mathematics, University of Michigan, Ann Arbor, Michigan 4819 arxiv:physics/6111v2 [physics.flu-dyn]
COHERENT STATES IN TRANSITIONAL PIPE FLOW
COHERENT STATES IN TRANSITIONAL PIPE FLOW Maria Isabella Gavarini 1, Alessandro Bottaro 2 and Frans T.M. Nieuwstadt 1 1 J.M. Burgers Centre, Delft University of Technology, The Netherlands 2 DIAM, Università
Bifurcations and multistability in turbulence
Bifurcations and multistability in turbulence VKS team A. Chiffaudel L. Marié F. Ravelet F.Daviaud CEA/Saclay, France O. Dauchot A. Prigent Conceptual Aspects of turbulence, Vienna, February 28 1 Bifurcations
Systems Theory and Shear Flow Turbulence Linear Multivariable Systems Theory is alive and well
Systems Theory and Shear Flow Turbulence Linear Multivariable Systems Theory is alive and well Dedicated to J. Boyd Pearson Bassam Bamieh Mechanical & Environmental Engineering University of California
Applied Mathematics and Mechanics (English Edition)
Appl. Math. Mech. -Engl. Ed., 39(9), 1267 1276 (2018) Applied Mathematics and Mechanics (English Edition) https://doi.org/10.1007/s10483-018-2364-7 Direct numerical simulation of turbulent flows through
FLUID MECHANICS. Atmosphere, Ocean. Aerodynamics. Energy conversion. Transport of heat/other. Numerous industrial processes
SG2214 Anders Dahlkild Luca Brandt FLUID MECHANICS : SG2214 Course requirements (7.5 cr.) INL 1 (3 cr.) 3 sets of home work problems (for 10 p. on written exam) 1 laboration TEN1 (4.5 cr.) 1 written exam
Turbulent-laminar patterns in plane Couette flow
Turbulent-laminar patterns in plane Couette flow Dwight Barkley Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom Laurette S. Tuckerman LIMSI-CNRS, BP 133, 91403 Orsay, France
Physical Properties of Fluids
Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel
Chapter 9: Differential Analysis
9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control
Generation of initial fields for channel flow investigation
Generation of initial fields for channel flow investigation Markus Uhlmann Potsdam Institut für Klimafolgenforschung, D-442 Potsdam uhlmann@pik-potsdam.de (Mai 2) In the framework of the DFG-funded research
Localized vortex/tollmien-schlichting wave interaction states in plane Poiseuille flow
Accepted for publication in the Journal of Fluid Mechanics Localized vortex/tollmien-schlichting wave interaction states in plane Poiseuille flow L. J. Dempsey, K. Deguchi, P. Hall and A. G. Walton Department
The behaviour of high Reynolds flows in a driven cavity
The behaviour of high Reynolds flows in a driven cavity Charles-Henri BRUNEAU and Mazen SAAD Mathématiques Appliquées de Bordeaux, Université Bordeaux 1 CNRS UMR 5466, INRIA team MC 351 cours de la Libération,
Math background. Physics. Simulation. Related phenomena. Frontiers in graphics. Rigid fluids
Fluid dynamics Math background Physics Simulation Related phenomena Frontiers in graphics Rigid fluids Fields Domain Ω R2 Scalar field f :Ω R Vector field f : Ω R2 Types of derivatives Derivatives measure
Polymer maximum drag reduction: A unique transitional state
Center for Turbulence Research Annual Research Briefs 47 Polymer maximum drag reduction: A unique transitional state By Y. Dubief, C. M. White, E. S. G. Shaqfeh AND V. E. Terrapon. Motivation and objectives
( ) Notes. Fluid mechanics. Inviscid Euler model. Lagrangian viewpoint. " = " x,t,#, #
Notes Assignment 4 due today (when I check email tomorrow morning) Don t be afraid to make assumptions, approximate quantities, In particular, method for computing time step bound (look at max eigenvalue
OPTIMUM SUCTION DISTRIBUTION FOR TRANSITION CONTROL *
OPTIMUM SUCTION DISTRIBUTION FOR TRANSITION CONTROL * P. Balakumar* Department of Aerospace Engineering Old Dominion University Norfolk, Virginia 23529 P. Hall Department of Mathematics Imperial College
On the feasibility of merging LES with RANS for the near-wall region of attached turbulent flows
Center for Turbulence Research Annual Research Briefs 1998 267 On the feasibility of merging LES with RANS for the near-wall region of attached turbulent flows By Jeffrey S. Baggett 1. Motivation and objectives
Regularity diagnostics applied to a turbulent boundary layer
Center for Turbulence Research Proceedings of the Summer Program 208 247 Regularity diagnostics applied to a turbulent boundary layer By H. J. Bae, J. D. Gibbon, R. M. Kerr AND A. Lozano-Durán Regularity
BOUNDARY LAYER ANALYSIS WITH NAVIER-STOKES EQUATION IN 2D CHANNEL FLOW
Proceedings of,, BOUNDARY LAYER ANALYSIS WITH NAVIER-STOKES EQUATION IN 2D CHANNEL FLOW Yunho Jang Department of Mechanical and Industrial Engineering University of Massachusetts Amherst, MA 01002 Email:
Lecture 1. Hydrodynamic Stability F. H. Busse NotesbyA.Alexakis&E.Evstatiev
Lecture Hydrodynamic Stability F. H. Busse NotesbyA.Alexakis&E.Evstatiev Introduction In many cases in nature, like in the Earth s atmosphere, in the interior of stars and planets, one sees the appearance
DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING
DIRECT NUMERICAL SIMULATION OF SPATIALLY DEVELOPING TURBULENT BOUNDARY LAYER FOR SKIN FRICTION DRAG REDUCTION BY WALL SURFACE-HEATING OR COOLING Yukinori Kametani Department of mechanical engineering Keio
FLOW-NORDITA Spring School on Turbulent Boundary Layers1
Jonathan F. Morrison, Ati Sharma Department of Aeronautics Imperial College, London & Beverley J. McKeon Graduate Aeronautical Laboratories, California Institute Technology FLOW-NORDITA Spring School on
FLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions
June 30 - July 3, 2015 Melbourne, Australia 9 P-26 Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions Jungwoo Kim Department of Mechanical System Design Engineering
Hydrodynamic Turbulence in Accretion Disks
Hydrodynamic Turbulence in Accretion Disks Banibrata Mukhopadhyay, Niayesh Afshordi, Ramesh Narayan Harvard-Smithsonian Center for Astrophysics, 6 Garden Street, MA 38, USA Turbulent viscosity in cold
Chapter 8 Flow in Conduits
57:00 Mechanics of Fluids and Transport Processes Chapter 8 Professor Fred Stern Fall 013 1 Chapter 8 Flow in Conduits Entrance and developed flows Le = f(d, V,, ) i theorem Le/D = f(re) Laminar flow:
Bounds on Surface Stress Driven Flows
Bounds on Surface Stress Driven Flows George Hagstrom Charlie Doering January 1, 9 1 Introduction In the past fifteen years the background method of Constantin, Doering, and Hopf has been used to derive
Fluid Mechanics II Viscosity and shear stresses
Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small
Hydrodynamics. l. mahadevan harvard university
Thermodynamics / statistical mechanics : Hydrodynamics N>>1; large number of interacting particles! Hydrodynamics : L >> l; T >> t; long wavelength, slow time - average over (some) microscopic length and
INTRODUCTION OBJECTIVES
INTRODUCTION The transport of particles in laminar and turbulent flows has numerous applications in engineering, biological and environmental systems. The deposition of aerosol particles in channels and
DAY 19: Boundary Layer
DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence
The need for de-aliasing in a Chebyshev pseudo-spectral method
The need for de-aliasing in a Chebyshev pseudo-spectral method Markus Uhlmann Potsdam Institut für Klimafolgenforschung, D-442 Potsdam uhlmann@pik-potsdam.de (March 2) Abstract In the present report, we
Introduction to Fluid Mechanics
Introduction to Fluid Mechanics Tien-Tsan Shieh April 16, 2009 What is a Fluid? The key distinction between a fluid and a solid lies in the mode of resistance to change of shape. The fluid, unlike the
Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition
Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow
Compressible turbulent channel flow with impedance boundary conditions
Center for Turbulence Research Proceedings of the Summer Program 2014 305 Compressible turbulent channel flow with impedance boundary conditions By C. Scalo, J. Bodart, S. K. Lele AND L. Joly We have performed
Getting started: CFD notation
PDE of p-th order Getting started: CFD notation f ( u,x, t, u x 1,..., u x n, u, 2 u x 1 x 2,..., p u p ) = 0 scalar unknowns u = u(x, t), x R n, t R, n = 1,2,3 vector unknowns v = v(x, t), v R m, m =
J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and
J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883
Vorticity and Dynamics
Vorticity and Dynamics In Navier-Stokes equation Nonlinear term ω u the Lamb vector is related to the nonlinear term u 2 (u ) u = + ω u 2 Sort of Coriolis force in a rotation frame Viscous term ν u = ν
CONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 3 LAMINAR BOUNDARY LAYER FLOW LAMINAR BOUNDARY LAYER FLOW Boundary
Lecture 9: Triggering Transition: Towards Minimal Seeds
Lecture 9: Triggering Transition: Towards Minimal Seeds Rich Kerswell Notes by Andrew Crosby, Keiji Kimura 3 June 11 1 Introduction In the previous lecture we discussed the edge and tracking it forward
Optimum algorithm for channel flow analysis in direct numerical simulation method
International Journal of Civil Engineering Optimum algorithm for channel flow analysis in direct numerical simulation method M. R. Kavianpour,*, E. Rajabi Received: May 0, Revised: February 0,Accepted:
WALL PRESSURE FLUCTUATIONS IN A TURBULENT BOUNDARY LAYER AFTER BLOWING OR SUCTION
WALL PRESSURE FLUCTUATIONS IN A TURBULENT BOUNDARY LAYER AFTER BLOWING OR SUCTION Joongnyon Kim, Kyoungyoun Kim, Hyung Jin Sung Department of Mechanical Engineering, Korea Advanced Institute of Science
Turbulence - Theory and Modelling GROUP-STUDIES:
Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence
The large-scale organization of autonomous turbulent wall regions
Center for Turbulence Research Annual Research Briefs 21 317 The large-scale organization of autonomous turbulent wall regions By Javier Jiménez, Oscar Flores AND Manuel García Villalba 1. Introduction
Given the water behaves as shown above, which direction will the cylinder rotate?
water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0