Keiji 1)Kimura and Philip J. Morrison...

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Keiji Kimura 1) and Philip J. Morrison 2) 1) Kyoto University, 2) The University of Texas at Austin Geophysical Fluid Dynamics Program 2011 (20 th June 2011—26 th August 2011) Woods Hole Oceanographic Institution

Transcript of Keiji 1)Kimura and Philip J. Morrison...

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Keiji Kimura1) and Philip J. Morrison2)

1)Kyoto University, 2)The University of Texas at Austin

Geophysical Fluid Dynamics Program 2011

(20th June 2011—26th August 2011)

Woods Hole Oceanographic Institution

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京都大学数理解析研究所 博士課程2年 木村恵二 CPS セミナー，2011年 10月19日

惑星科学研究センター(CPS)

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Research Project in GFD Program 2011

Lectures in GFD Program 2011

Life at GFD

2011/10/19 CPS2011 3

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Keiji Kimura1) and Philip J. Morrison2)

1)Kyoto University, 2)The University of Texas at Austin

Geophysical Fluid Dynamics Program 2011

(20th June 2011—26th August 2011)

Woods Hole Oceanographic Institution

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Introduction

Linear Wave Modes

Energy Conservation

Equilibrium States

Conclusion

Future Works

2011/10/19 CPS2011 5

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Magnetohydrodynamic (MHD) approximation is well-used.

What are the limitations?

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(Wikipedia Sun)

(HP of Prof. Z. Yoshida)

(Glatzmeier and Roberts, 1995)

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Kinetic theory Two-fluid model (taking moments)

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Quasi-neutrality

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Kinetic theory Two-fluid model (taking moments)

One-fluid model (quasi-neutrality) (Lüst, 1959)

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: Continuity eqn.

: Momentum eqn.

: Generalized Ohm’s law

Collision (resistivity)

Hall term

Electron inertia

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Vasyliunas (1975)

Shay et al. (2001)

Fitzpatrick (2001)

Watson

Bhattacharjee et al. (1999)

There is no term in the momentum equation!

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(Ideal) MHD

Hall-MHD

Inertial-MHD (IMHD)

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Pre-Maxwell equations

: The characteristic timescale << the gyroperiod of electron

(Magnetic reconnection region?) Governing eqns.

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Comparing the linear wave modes between MHD and IMHD. Classifying some IMHD models in terms of the energy conservation. Considering the effect of electron inertia using IMHD, especially focusing on some equilibrium states.

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Introduction

Linear Wave Modes

Energy Conservation

Equilibrium States

Conclusion

Future Works

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Basic state (Shear) Alfven wave

Fast/Slow magnetosonic wave

Linearized compressible MHD

: uniform

: no flow

(Fitzpatrick)

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MHD

Inertial MHD

: Alfven speed

Higher wavenumber waves propagate more slowly!

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Introduction

Linear Wave Modes

Energy Conservation

Equilibrium States

Conclusion

Future Works

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Governing equations

Energy conservation

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Energy conservation

This is not a correct flux form… but total energy H is conserved!

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The epsilon term in the momentum equation is important!!

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Vasyliunas (1975)

Shay et al. (2001)

Fitzpatrick (2001)

Watson

Bhattacharjee et al. (1999)

There is no term in the momentum equation!

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Introduction

Linear Wave Modes

Energy Conservation

Equilibrium States

Conclusion

Future Works

2011/10/19 CPS2011 22

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With no flow 1. Grad-Shafranov equation

With flow (incompressible)

1. 2. Beltrami-“Jeltrami” flow

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Governing equation (no flow)

Axisymmetric solution

: Grad-Shafranov equation

What occurs with the electron inertia?

(Wikipedia)

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“Straight torus” = cylinder; torus with no curvature

“Axisymmetric” solution = z independent solution

: G-S in “straight torus”

When , then we find that and , and obtain

z

What occurs when epsilon and delta are finite?

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If the plasma is barotropic, i.e., ,

Modified Grad-Shafranov equation in “straight torus”

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Incompressible plasma

?? I did not get

any useful constraints…

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Straight torus Torus

Incompressible

3 constraints obtained

3 constraints obtained

Modified G-S obtained ??

Compressible

If barotropic, 3 (incomplete) constraints obtained.

?

If barotropic, modified GS

obtained. ???

Epsilon term is considered

Epsilon and delta term

are considered

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With no flow 1. Grad-Shafranov equation

With flow (incompressible)

1. 2. Beltrami-“Jeltrami” flow

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Governing equations (incompressible IMHD)

Assuming

If

quite similar!

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With no flow 1. Grad-Shafranov equation

With flow (incompressible)

1. 2. Beltrami-“Jeltrami” flow

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: Beltrami flow

: “Jeltrami” current

If similar to Bernoulli’s equation

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Modified Alfven wave in Inertial MHD is dispersive.

The epsilon term in the momentum equation is important in terms of energy conservation.

Modified Grad-Shafranov equation is obtained in “straight torus.” In the real torus, we obtained only some constraints.

Governing equations of equilibrium states with flow can be simplified in and in Beltrami-“Jeltrami”

flow.

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Physical interpretation of equilibrium state with delta term in modified Grad-Shafranov equation with curvature

Studying the stability with the effect of epsilon and delta term

Shocks

Magnetic reconnection

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Research Project in GFD Program 2011

Lectures in GFD Program 2011

Life at GFD

2011/10/19 CPS2011 35

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“Shear Turbulence: Onset and Structure”

Fabian Waleffe (University of

Wisconsin, Madison)

Richard Kerswell (Bristol University)

(2011) (1995)

(1990) (2011)

(1988)

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Canonical Laminar flow

“Turbulent” State

Transition occurs suddenly, noise-dependently and

dramatically!

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Canonical Flow Critical Reynolds number

Plane Couette ∞

Plane Poiseuille 5772 Hagen-

Poiseuille (Pipe) ∞?

“Turbulent” State

Transition can occur at lower Reynolds number!

Why? What occurs?

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1. General Introduction and Overview.

2. Viscous derivation of classic inviscid stability results for shear flows. Viscous instability.

3. Diffusion and damping in shear flows: a truly singular limit. Critical layers.

4. Origin and survival of 3D-ality.

5. Instability of streaky flows. Asymptotics of self-sustaining process.

6. Spatio-temporal complexity. Spots, puffs and slugs, snakes and spirals.

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Transition threshold i.e. the power law of the amplitude against Re

Structure (horseshoe vortex etc.) Linear and energy stabilities Squire’s theorem (linear) vs. streamwise roll (energy) How to sustain the turbulent state the feedback mechanism to the roll pattern Self-Sustaining Process (SSP) and SSP method finding the exact coherent structures The boundary of the laminar and turbulent states in phase space

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Waleffe (1997)

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Rolls V redistribute streamwise momentum

M U Streak U unstable to x-mode W

nonlinear interaction of W feeds back on

rolls V

Mean M shears W

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1. Transition scenarios: normality vs non-normality.

2. Edge tracking – walking the tightrope.

3. Triggering transition efficiently.

4. Turbulence: transient or sustained?

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Supercritical or subcritical scenarios Normal or Non-normal linear operator

Finding nonlinear solutions (e.g. Nagata’s solution)

Edge tracking

Finding Minimal Seeds

Is the turbulent state is a transient state or

sustained one? puff, localized pattern

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“Minimal seed”: the I.C. of smallest energy which can trigger transition to “turbulence”

Energy growth rate:

Can we identify the minimal seed by looking for an I.C. which experiences largest growth?

Linear transient growth Matrix-based SVD Matrix-free Variational principle (Euler-Lagrange eq.) this method can be used to study the nonlinear transient growth!

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Linearized Navier-Stokes eq.

Growth rate

Euler-Lagrange eqns.

Dual Linearized Navier-Stokes eqn.

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This method is easily extendable to the nonlinear problem!

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Linear

Nonlinear

Schmid and Henningson (1994)

Pringle and Kerswell (2010)

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Lectures in GFD Program 2011

Research Project in GFD Program 2011

Life at GFD

2011/10/19 CPS2011 50

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Giulio Mariotti (Boston Univ.)

Italian (27)

Martin Hoecker-Martinez (Oregon State Univ.)

American (32)

Chao Ma 馬超 (Univ. of Colorado,

Boulder) Chinese (28)

Matthew Chantry (Univ. of Bristol)

British (23)

Andrew Crosby (Univ. of Cambridge)

British (26)

Zhan Wang 王展 (Univ. of Wisconsin,

Madison) Chinese (28)

Lindsey Ritchie (Corson) (Univ. of Strathclyde)

British (27?)

Adele Morrison (Australian National Univ.)

Australian (29)

Samuel Potter (Princeton Univ.) American (29?)

Keiji Kimura (Kyoto Univ.) Japanese (25)

John Platt (Harvard Univ.)

British (24)

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British: 4 American: 2 Chinese: 2 Australian: 1 Italian: 1 Japanese: 1 Univ. in USA: 6 in British: 3 in Australia: 1 in Japan: 1

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Genta Kawahara, “Structures of low-Reynolds number turbulence in a rectangular duct” Friedrich Busse, “Generation of magnetic fields by convection in rotating spherical fluid shells” Jesse Ausubel, “Self-sinking capsules to investigate Earth’s interior and dispose of radioactive waste” Tomoaki Itano, “Coherent vortices in plane Couette flow – bifurcation, symmetry and visualization” Predrag Cvitanovic, “What Phil Morrison would not teach us: how to reduce the symmetry of pipe flows”

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Martin Hoecker-Martinez: Constraints on low order models: the cost of simplicity Keiji Kimura: A One-fluid MHD Model with Electron Inertial Matthew Chantry: Traversing the edge: how turbulence decays Giulio Mariotti: A low dimensional model for shear turbulence in Plane Poiseuille Flow: an example to understand the edge Adele Morrison: Upstream basin circulation of rotating, hydraulically controlled flows Samuel Potter: Islands in locally-forced basin circulations Zhan Wang: Tow-layer viscous fluid in an inclined closed tube: Kelvin-Helmholtz instability Andrew Crosby: Chaotic interaction of vortex patches with boundaries Chao Ma: On Brownian motion in a Fluid with a Plane Boundary John Platt: Localized Solutions for Plane Couette flow: a continuation method study Lindsey Ritchie: Ascending the ridge: Maximizing the heat flux in steady porous medium convection

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5勝3敗!!

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得たもの

生活力，料理の技術 アメリカ人の人生の楽しみ方 スポーツの重要性 度胸（英語力）

Shear Turbulence の知識

MHD の知識

失ったもの 体重 (-5kg)

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林先生をはじめ，北大・神戸大GCOE，CPS

関係者の皆様に深く感謝申し上げます

2011/10/19 CPS2011 61

(1984)


岡崎 桂二 Keiji Okazaki

岡崎 桂二 Keiji Okazaki

Release Fernando Kimura

Release Fernando Kimura

PENYAKIT KIMURA - kankertht- · PDF fileLaporan kasus PENYAKIT KIMURA Gde ... Pilihan terapi penyakit Kimura dengan reseksi tumor, ... Gambar 4. CT Scan kepala potongan aksial dan

PENYAKIT KIMURA - kankertht- · PDF fileLaporan kasus PENYAKIT KIMURA Gde ... Pilihan terapi penyakit Kimura dengan reseksi tumor, ... Gambar 4. CT Scan kepala potongan aksial dan

Tough Mudder: Kimura Team

Tough Mudder: Kimura Team

005 Keiji Morokuma

005 Keiji Morokuma

Lowside, Shinya Kimura

Lowside, Shinya Kimura

Keiji Yoshimura Jalta

Keiji Yoshimura Jalta

Hommage à Takeo Kimura

Hommage à Takeo Kimura

OSCAR API for Low-Power Multicores and Manycores, and … · OSCAR API for Low-Power Multicores and Manycores, and API Standard Translator Keiji Kimura, Waseda University 1 MPSoC2012/Keiji

OSCAR API for Low-Power Multicores and Manycores, and … · OSCAR API for Low-Power Multicores and Manycores, and API Standard Translator Keiji Kimura, Waseda University 1 MPSoC2012/Keiji

Kimura Disease

Kimura Disease

Kimura - Dragão completa

Kimura - Dragão completa

Dragon by Yoshihisha Kimura

Dragon by Yoshihisha Kimura

 · Egberto Gismonti Frevo Mari Kimura Eigenspace Mari Kimura Canon Elastique Joaõ Bosco Coisa Feita Mari Kimura Breuer Vivant Hermeto Pascoal Bebê Mari Kimura (The Wind) 5:53 4:48

 · Egberto Gismonti Frevo Mari Kimura Eigenspace Mari Kimura Canon Elastique Joaõ Bosco Coisa Feita Mari Kimura Breuer Vivant Hermeto Pascoal Bebê Mari Kimura (The Wind) 5:53 4:48

Takahiro Kimura

Takahiro Kimura

Gamification por Juliano Kimura

Gamification por Juliano Kimura

Artur Borger Kimura

Artur Borger Kimura

Kimura Method

Kimura Method

of Registered Voters April... · moody, linda d. morrison, morrison, morrison, morrison, morrison, morrison, morrison, alberta j. ... judy nolt rep rep rep rep rep dem rep rep rep

of Registered Voters April... · moody, linda d. morrison, morrison, morrison, morrison, morrison, morrison, morrison, alberta j. ... judy nolt rep rep rep rep rep dem rep rep rep

keiji kitamura - origami treasure chest.pdf

keiji kitamura - origami treasure chest.pdf

A Short Story by Keiji

A Short Story by Keiji