1 / 28

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 Kim ¹ , and Kihong Kim 2 1 School of Space Research, Kyung Hee Univ . 2 Division of Energy Systems Research, Ajou Univ.

jola
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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. - 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

  3. 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.

  4. 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

  5. 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

  6. Introduction • For instance, the eqof motion for adiabatic MHD: : Linear MHD waves : Steady-state cf) R-H relations : Nonlinear MHD waves

  7. Observations Venus Express 0.72 AU STEREO 1 AU Russell et al., GRL, 2009

  8. 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.

  9. Theory Sources Simple waves Shock waves * Simple waves or

  10. Theoretical solutions * Exact solution for the MHD wave [Lee & Kim, JGR, 2000]

  11. Ex) piston-like motion V (Km/s) V (Km/s) V (Km/s) V (Km/s) Time (s) Time (s)

  12. 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!

  13. Numerical test vs. Exact solutions V (Km/s) X (Re) Numerical solutions = Analytic solutions

  14. Numerical effect test Nx = 1000 Nx = 5000 Solution Simulation V (Km/s) V (Km/s) Time (s) Time (s)

  15. Numerical effect test B (nT) Nx=2000 Time (Hr) B (nT) Nx=20000 Time (Hr)

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 3D model (Homogeneous case)

  27. 3D model (Homogeneous case)

  28. 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.

More Related