Three dimensional simulations of nonlinear mhd wave propagation in the magnetosphere
This presentation is the property of its rightful owner.
Sponsored Links
1 / 28

Three-dimensional simulations of nonlinear MHD wave propagation in the magnetosphere PowerPoint PPT Presentation


  • 81 Views
  • Uploaded on
  • Presentation posted in: General

Three-dimensional simulations of nonlinear MHD wave propagation in the magnetosphere. Kyung- Im Kim¹, Dong-Hun Lee¹, Khan- Hyuk Kim ¹ , and Kihong Kim 2 1 School of Space Research, Kyung Hee Univ . 2 Division of Energy Systems Research, Ajou Univ.

Download Presentation

Three-dimensional simulations of nonlinear MHD wave propagation in the magnetosphere

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Three dimensional simulations of nonlinear mhd wave propagation in the magnetosphere

Three-dimensional simulations of nonlinear MHD wave propagation in the magnetosphere

Kyung-Im Kim¹, Dong-Hun Lee¹, Khan-Hyuk Kim¹,

and Kihong Kim2

1School of Space Research, Kyung Hee Univ.

2Division of Energy Systems Research, AjouUniv.


Three dimensional simulations of nonlinear mhd wave propagation in the magnetosphere

- Introduction: Effects of nonlinearity in a time-dependent system - Observations: e.g., Russell et al. (GRL, 2009) STEREO observations of shock formation in the solar wind - Theory: What kinds of exact nonlinear MHD solutions available? - Numerical approach 1. Theory vs. Numerical test2. check the profiles from ACE (Venus Express) to the Earth (STEREO)3. Apply to the 3-D homogeneous magnetosphere

- Conclusion


Introduction

Introduction

B

A

  • Propagation of nonlinear MHD waves is studied in the interplanetary space.

  • As realistic variations in the solar wind become often nonlinear,  it is important to investigate time-dependent behaviors of the solar wind fluctuations.


Introduction1

Introduction

  • If the disturbance is linear in a uniform space, f_A = f_B:

  • If the disturbance is linear in a nonuniform space, only

  • the effects of refraction/reflection are to change f_A & f_B:

A

A

B

B


Introduction2

Introduction

  • If the disturbance is nonlinear, f_A and f_B become differentiated even in a uniform space:

  • The disturbance in the SW rest frame can evolve in a time-dependent manner, which is far from the steady-state.

  • cf) Rankine-Hugoniot relations

A

A

B

B


Introduction3

Introduction

  • For instance, the eqof motion for adiabatic MHD:

: Linear MHD waves

: Steady-state cf) R-H relations

: Nonlinear MHD waves


Observations

Observations

Venus Express

0.72 AU

STEREO

1 AU

Russell et al., GRL, 2009


Theory

Theory

The assumption of simple waves (similarity flow) is often used to obtain a solution.

Exact solution for the nonlinear MHD wave is available

if it is a one-dimensional uniform system.


Theory1

Theory

Sources

Simple waves

Shock waves

* Simple waves

or


Theoretical solutions

Theoretical solutions

* Exact solution for the MHD wave [Lee & Kim, JGR, 2000]


Ex piston like motion

Ex) piston-like motion

V (Km/s)

V (Km/s)

V (Km/s)

V (Km/s)

Time (s)

Time (s)


Numerical test vs exact solutions

Numerical test vs. Exact solutions

V (Km/s)

V (Km/s)

V (Km/s)

V (Km/s)

Numerical solutions are corresponding to the exact solutions before the shock formation!


Numerical test vs exact solutions1

Numerical test vs. Exact solutions

V (Km/s)

X (Re)

Numerical solutions = Analytic solutions


Numerical effect test

Numerical effect test

Nx = 1000

Nx = 5000

Solution

Simulation

V (Km/s)

V (Km/s)

Time (s)

Time (s)


Numerical effect test1

Numerical effect test

B (nT)

Nx=2000

Time (Hr)

B (nT)

Nx=20000

Time (Hr)


Numerical model 1 small scale 300re

Numerical Model (1. Small scale : 300Re)

* 1-D Adiabatic MHD eqs

cf) Lx to ACE ~ 234 Re

* Impulse

V (Km/s)

* Simulation Parameters

- nx = 5000 , Lx = 300 Re

- Total time = 5000 s

- Sound speed = 50 Km/s

- Alfven speed = 49 Km/s

- Plasma density = 10

- Magnetic field Bz = 8 nT

t/t0


Shock formation 1 small scale 300re

Shock formation (1. Small scale : 300Re)

* Shock formations for different background magnetic fields (3nT, 5nT, 8nT) and impulse timescales ( 𝛕0 = 300s, 500s, 700s)

B0 = 3nT

B0 = 5nT

B0 = 8nT

B (nT)

Time (s)

Time (s)

Time (s)

Considered Solar Wind flow speed : 400 Km/s

: Timescale of the source motion

53Re

48Re

45Re

246Re

256Re

256Re


Shock formation 1 small scale 300re1

Shock formation (1. Small scale : 300Re)

* Shock formations for different amplitudes of impulse

45Re

256Re

B (nT)

v = v0

v = 2v0

v = 3v0

Time (s)

Time (s)

Time (s)

Considered Solar Wind flow speed : 400 Km/s

: Timescale of the source motion


Numerical model 2 large scale 0 28 au

Numerical Model (2. Large scale : 0.28 AU)

cf) ~ 6560 Re

* Impulse

* Simulation Parameters

- nx = 20000

- Total time = 105,000 s (~29.16 hr)

- Lx = 7000 Re (~0.28 AU)

- Sound speed = 60 Km/s

- Alfven speed = 66 Km/s

- Plasma density = 7

- Magnetic field Bz = 9 nT

V (Km/s)

t/𝛕0

Vx


Simulation box 2 large scale 0 28 au

Simulation Box (2. Large scale : 0.28 AU)

Simulation Box

z

I

II

x

Solar Wind (Vsw = 400 Km/s)

0.72 AU

1 AU

Sun

Venus Express

STEREO A


Shock formation 2 large scale 0 28 au

Shock formation (2. Large scale : 0.28 AU)

I (at 0.72 AU)

2 nT

B (nT)

Time (Hr)

II (at 1 AU)

2 nT

B (nT)

Time (Hr)

Considered Solar Wind flow speed : 400 Km/s, 𝛕0 : Timescale of the source motion


Shock formation 2 large scale 0 28 au1

Shock formation (2. Large scale : 0.28 AU)

I (at 0.72 AU)

B (nT)

Time (Hr)

II (at 1 AU)

B (nT)

Time (Hr)

Considered Solar Wind flow speed : 400 Km/s, 𝛕0 : Timescale of the source motion


Shock formation 2 large scale 0 28 au2

Shock formation (2. Large scale : 0.28 AU)

I (at 0.72 AU)

B (nT)

Time (Hr)

II (at 1 AU)

B (nT)

Time (Hr)

Considered Solar Wind flow speed : 400 Km/s, 𝛕0 : Timescale of the source motion


Shock formation 2 large scale 0 28 au3

Shock formation (2. Large scale : 0.28 AU)

I (at 0.72 AU)

B (nT)

Time (Hr)

II (at 1 AU)

B (nT)

Time (Hr)

Considered Solar Wind flow speed : 400 Km/s, 𝛕0 : Timescale of the source motion


3d model homogeneous magnetosphere

3D model (Homogeneous Magnetosphere)

* Simulation Parameters

- Total time = 140 s

- Sound speed = 60 Km/s

- Alfven speed = 600 Km/s

- Plasma density = 1

- Magnetic field Bz = 600 nT

V (Km/s)

t/t0

Z (20 Re)

Nz=512

B0

Y (10 Re)

Ny=64

X (40Re)

Nx=512


3d model homogeneous case

3D model (Homogeneous case)


3d model homogeneous case1

3D model (Homogeneous case)


Conclusion

Conclusion

  • Propagation of nonlinear MHD waves is studied in the interplanetary space. We examined how these fluctuations are changed by steepening process and/or shock formation.

  • The simulation results should be first validated by the exact analytical solution (Lee and Kim, 2000), which showed excellent correspondence between theory and simulation.

  • The profiles tend to significantly evolve at the different locations, which strongly depends on the given parameters.

  • The observations in the IP space (e.g., ACE) cannot directly deliver the SW condition around the earth unless it belongs to the linear case.


  • Login