Self-Similarity in Classical Fluids and MHD B.C. Low High Altitude Observatory National Center for Atmospheric Research Boulder, Colorado, USA The National.

Slides:

Advertisements

Similar presentations

Statistical Physics Approach to Understanding the Multiscale Dynamics of Earthquake Fault Systems Theory.

Advertisements

Prof. dr. A. Achterberg, Astronomical Dept., IMAPP, Radboud Universiteit.

Supernova Remnants Shell-type versus Crab-like Phases of shell-type SNR.

Cutnell/Johnson Physics 7th edition

“The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models” Papaloizou & Nelson 2003a, MNRAS 339, 923 Brian.

Cht. IV The Equation of Motion Prof. Alison Bridger 10/2011.

Reviewing the Summer School Solar Labs Nicholas Gross.

Modeling the Magnetic Field Evolution of the December Eruptive Flare Yuhong Fan High Altitude Observatory, National Center for Atmospheric Research.

1 MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 6 FLUID KINETMATICS.

An Analytical Solution for “EIT Waves” M. J. Wills-Davey, C. E. DeForest, Southwest Research Institute, Boulder, Colorado and J. O. Stenflo Southwest Research.

Center for Space Environment Modeling Ward Manchester University of Michigan Yuhong Fan High Altitude Observatory SHINE July.

Chapter 1. Introduction 1.1 Atmospheric Continuum –Continuous fluid medium –“mass point” = air parcel (or air particle) –Field variables: p, , T and their.

Onset of Coronal Mass Ejection Due to Loss of Confinement of Coronal Flux Ropes Y. Fan & S.E. Gibson HAO, National Center for Atmospheric Research High.

High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University.

A k-  model for turbulently thermal convection in solar like and RGB stars Li Yan Yunnan Astronomical Observatory, CAS.

Center for Space Environment Modeling W. Manchester 1, I. Roussev, I.V. Sokolov 1, 1 University of Michigan AGU Berkeley March.

The Effect of Sub-surface Fields on the Dynamic Evolution of a Model Corona Goals :  To predict the onset of a CME based upon reliable measurements of.

Enduring Understandings

1 Magnetic waves in sheared field regions E.J. Zita, The Evergreen State College, Olympia, WA Abstract How do magnetohydrodynamic (MHD) waves change.

Magnetic configurations responsible for the coronal heating and the solar wind Hwanhee Lee 1, Tetsuya Magara 1 1 School of Space research, Kyung Hee University.

Energy. What is Energy? Energy is defined as the ability to cause change. Anything that causes change must have energy to effect the change. To use energy.

Chapter 11 Angular Momentum.

Chapter 7 Linear Momentum. Chapter Momentum Linear Momentum- product of mass times velocity p=mvp=momentum units=kg.m/sec Restate Newton’s second.

Kinetic Effects on the Linear and Nonlinear Stability Properties of Field- Reversed Configurations E. V. Belova PPPL 2003 APS DPP Meeting, October 2003.

Semi-Empirical MHD Modeling of the Solar Wind Igor V. Sokolov, Ofer Cohen, Tamas I. Gombosi CSEM, University of Michigan Ilia I Roussev, Institute for.

Aerodynamics Linear Motion (Moving Air ).

Boundaries, shocks, and discontinuities. How discontinuities form Often due to “wave steepening” Example in ordinary fluid: –V s 2 = dP/d  m –P/  

Brookhaven Science Associates U.S. Department of Energy MUTAC Review April , 2004, LBNL Target Simulation Roman Samulyak, in collaboration with.

R. Oran csem.engin.umich.edu SHINE 09 May 2005 Campaign Event: Introducing Turbulence Rona Oran Igor V. Sokolov Richard Frazin Ward Manchester Tamas I.

Three-dimensional MHD simulation of a flux rope driven CME Manchester IV, W.B., Gombosi, T.I., Roussev, I., De Zeeuw, D.L., Sokolov, I.V., Powell, K.G.,

The Digital Demo Room One-Dimensional Hydrodynamics Simulator Conley “Lee” Ditsworth under the care and feeding of Dr. Charles F. Gammie and close supervision.

Stability Properties of Field-Reversed Configurations (FRC) E. V. Belova PPPL 2003 International Sherwood Fusion Theory Conference Corpus Christi, TX,

Charles Hakes Fort Lewis College1. Charles Hakes Fort Lewis College2 Chapter 9 The Sun.

Modeling of Materials Processes using Dimensional Analysis and Asymptotic Considerations Patricio Mendez, Tom Eagar Welding and Joining Group Massachusetts.

Physical Science. What is Physical Science Physics: the science of matter and energy and their interactions – Sciences such as physics, chemistry, astronomy,

Origin of solar systems 30 June - 2 July 2009 by Klaus Jockers Max-Planck-Institut of Solar System Science Katlenburg-Lindau.

Conical Flow induced by Quenched QCD Jets Jorge Casalderrey-Solana, Edward Shuryak and Derek Teaney, hep- ph/ SUNY Stony Brook.

Reconnection rates in Hall MHD and Collisionless plasmas

Jonathan L. Vigh and Wayne H. Schubert January 16, 2008.

Sun is NOT a normal gas B and plasma -- coupled (intimate, subtle) behaves differently from normal gas: 2. MHD Equations Sun is in 4th state of matter.

MHD Turbulence driven by low frequency waves and reflection from inhomogeneities: Theory, simulation and application to coronal heating W H Matthaeus Bartol.

High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University.

Dry Boundary Layer Dynamics Idealized theory Shamelessly ripped from Emanuel Mike Pritchard.

ERT 206/4 THERMODYNAMICS SEM 2 (2011/2012). light Energy can exist in numerous forms: Thermal Mechanical Kinetic Potential Electric Magnetic Chemical.

Wave propagation in a non-uniform, magnetised plasma: Finite beta James McLaughlin Leiden March 2005.

3D Spherical Shell Simulations of Rising Flux Tubes in the Solar Convective Envelope Yuhong Fan (HAO/NCAR) High Altitude Observatory (HAO) – National Center.

II. MAGNETOHYDRODYNAMICS (Space Climate School, Lapland, March, 2009) Eric Priest (St Andrews)

Structure and Stability of Phase Transition Layers in the Interstellar Medium Tsuyoshi Inoue, Shu-ichiro Inutsuka & Hiroshi Koyama 1 12 Kyoto Univ. Kobe.

CME-associated dimming regions Alysha Reinard 12, Doug Biesecker 1, Tim Howard 3 1 NOAA/SEC 2 University of Colorado 3 Montana State University SHINE 2006.

Simulation Study of Magnetic Reconnection in the Magnetotail and Solar Corona Zhi-Wei Ma Zhejiang University & Institute of Plasma Physics Beijing,

Stability of Expanding Jets Serguei Komissarov & Oliver Porth University of Leeds and Purdue University TexPoint fonts used in EMF. Read the TexPoint manual.

Hirophysics.com PATRICK ABLES. Hirophysics.com PART 1 TIME DILATION: GPS, Relativity, and other applications.

Black Hole Accretion, Conduction and Outflows Kristen Menou (Columbia University) In collaboration with Taka Tanaka (GS)

The Crucial Role of the Lewis No. in Jet Ignition Nika Rezaeyan, Luc Bauwens University of Calgary Matei Radulescu University of Ottawa Fernando Fachini.

1 Linear Wave Equation The maximum values of the transverse speed and transverse acceleration are v y, max =  A a y, max =  2 A The transverse speed.

-1- Solar wind turbulence from radio occultation data Chashei, I.V. Lebedev Physical Institute, Moscow, Russia Efimov, A.I., Institute of Radio Engineering.

A shock is a discontinuity separating two different regimes in a continuous media. –Shocks form when velocities exceed the signal speed in the medium.

Chapter 11 Angular Momentum. The Vector Product and Torque The torque vector lies in a direction perpendicular to the plane formed by the position vector.

Relativistic MHD Simulations of jets Relativistic MHD Simulations of jets Abstract We have performed 3D RMHD simulations to investigate the stability and.

A Numerical Study of the Breakout Model for Coronal Mass Ejection Initiation P. MacNeice, S.K. Antiochos, A. Phillips, D.S. Spicer, C.R. DeVore, and K.

Data-constrained Simulation of CME Initiation and Propagation Antonia Savcheva ESPM 2014 September 11, 2014 Collaborators: R. Evans, B. van der Holst,

4.3 Energy and Conservation Laws. Kinetic energy is the energy associated with motion. KE = ½ mv 2 m = mass, v = velocity Types of Energy – Kinetic Energy.

Particle Kinematics Direction of velocity vector is parallel to path Magnitude of velocity vector is distance traveled / time Inertial frame – non accelerating,

T HE VORTICAL MECHANISM OF GENERATION & COLLIMATION OF THE ASTROPHYSICAL JETS M.G. A BRAHAMYAN Yerevan State University, Armenia.

Chapter 3: Conservation of Energy. Important Notation 2.

Heliosphere: Solar Wind

Spectral and Algebraic Instabilities in Thin Keplerian Disks: I – Linear Theory Edward Liverts Michael Mond Yuri Shtemler.

The Sun: close-up of a spectral class G main sequence star

Abstract We simulate the twisting of an initially potential coronal flux tube by photospheric vortex motions. The flux tube starts to evolve slowly(quasi-statically)

Wave Propagation Over a Boltzmann Shock Profile

Presentation transcript:

Self-Similarity in Classical Fluids and MHD B.C. Low High Altitude Observatory National Center for Atmospheric Research Boulder, Colorado, USA The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

1-D Thermal Pulse

Reduction from pde to ode

Spherically-Symmetric Flows

Sedov-Taylor Point Explosion Initial state: Similarity variable: The solution:

A Realistic “Point” Explosion Energy released: Fireball radius: Warm medium: Length scales: Time scales: Similarity regime:

Intermediate Asymptotics Barenblatt & Zel’dovich (1972, Ann.Rev. Fluid Mech. 4, 285) Self-similar solutions are the intermediate asymptotic forms of a solution in a local space time region away from boundaries and its initial state. Self-similar solutions often turn out to be the “preferred” end state of a diversity of possible evolutions originating from very different initial states.

CME Kinetic Properties Typical CME mass ~ Median Speed ~ Range ~ G-escape Speed ~ Coronal Sound Speed ~ Coronal Alfven Speed ~

Time-Dependent Ideal MHD

Darnell & Burkepile 2002

Homologous Expansion

Time-Dependent Ideal MHD

Homologous Radial Flow: Zero-Force Flow

Homologous Radial Flow: Mass Conservation

A Simple Class of Self-Similar MHD Solutions

A More Sophisticated Class of Self-Similar MHD Solutions

A Non-Galilean Transformation A non-Galiliean transformation introduces inertial forces, e.g., the Coriolis force in a uniformly rotating frame of reference. The similarity space introduces a pure radial force of magnitude - the net force driving the flow.

Stability Problems in Similarity Space With no loss of generality: Time-dependent linear perturbations about a static state in space – a classic stability problem.

A More Sophisticated Class of Self-Similar MHD Solutions

Velocity vs Distance

A More Sophisticated Class of Self-Similar MHD Solutions

Squeezing a 3D Solution out of a 2D Solution

Unsqueezed Solution

Squeezed Solution

A Theoretical 3-Part CME Gibson & Low (1998, 2000)

Summary Similarity solutions as long-time end-states. Compatible scaling laws of the thermal energy of a polytropic gas of 4/3 index with gravitational and magnetic energy. Observed broad range of CME speeds. The 3-part structure of CMEs has its origin in the initial state. Do similarity flows occur in CMEs?

Movies from Gibson & Low Frot~1 shows a time sequence of the magnetic field of the CME making its way out surrounded by the global open magnetic field of the corona. Sigmoid shows the 3 D magnetic field of the CME from different perspective. Pb3 shows a time sequence of the CME in simulated Thomson-scattered light.