| 4 | | The shocked hydro clump vs the shocked magnetized clump. The magnetized clump develops a bump at the clump head.[[BR]][[BR]] |
| 5 | | [[Image(http://www.pas.rochester.edu/~shuleli/1121/ClumpShockInteraction.png, 50%)]][[BR]][[BR]] |
| | 8 | The important physics parameters are: [[BR]] |
| | 9 | The density contrast:[[BR]][[BR]] |
| | 10 | [[latex($\chi=\frac{\rho_{clump}}{\rho_{ambient}}$)]][[BR]][[BR]] |
| | 11 | The sonic Mach number:[[BR]][[BR]] |
| | 12 | [[latex($M=\frac{u_{wind}}{c_s}$)]][[BR]][[BR]] |
| | 13 | The Alfvenic Mach number:[[BR]][[BR]] |
| | 14 | [[latex($M_A =\frac{u_{wind}}{c_A}$)]][[BR]][[BR]] |
| | 15 | The magnetic beta:[[BR]][[BR]] |
| | 16 | [[latex($\beta =\frac{2 c_s^2}{\gamma c_A^2}$)]][[BR]][[BR]] |
| | 17 | The clump crushing time (defined by the time for the transmitted shocked to pass through the entire clump):[[BR]][[BR]] |
| | 18 | [[latex($\tau_{cc} = \frac{\chi^{1/2}r_{clump}}{M c_s}$)]][[BR]][[BR]] |
| | 19 | The paper Jones, T.W., Ryu, Dongsu, Tregillis, I.L. 1996 ApJ, 473, 365 studied the effect of 2-D magnetic field on a bullet passing through a uniform ambient medium.[[BR]] |
| | 20 | It also serves as an example on clumps getting shocked with 2-D uniform magnetic field.[[BR]] |
| | 21 | The image below shows the clump evolution when the uniform magnetic field is aligned with the shock direction.[[BR]][[BR]] |
| | 22 | |
| | 23 | |
| | 24 | In these simulations we notice:[[BR]] |
| | 25 | 1. No significant difference in terms of density evolution even for β = 1.[[BR]] |
| | 26 | 2. For the magnetic field to suppress the K-H instabilities at the boundary flows, one requires that the Alfven speed to be greater than the velocity difference of the shear layers [[BR]] |
| | 27 | at the boundary flows. This criterion can be translated to roughly: β < 1 along the clump edge. [[BR]] |
| | 28 | 3. When the clump is getting shocked, the clump is accelerating along the horizontal x axis, towards the lighter ambient material. This creates R-T instability whose bubbles will flow into [[BR]] |
| | 29 | and deform the shocked clump material. The magnetic field along the acceleration access has a less dramatic effect in suppressing the R-T instability comparing to that perpendicular [[BR]] |
| | 30 | to the acceleration axis. The criterion for the magnetic field to stabilize R-T instabilities is roughly: β < χ/M.[[BR]] |
| | 31 | 4. The field surrounding the clump is getting amplified due to compressing and stretching. But in the aligned field case, there is no place that the magnetic field becomes energetically [[BR]] |
| | 32 | dominant despite the amplification; that is, almost everywhere β >> 1. So the K-H and R-T instabilities are hardly suppressed. The clump density evolution is not dramatically different [[BR]] |
| | 33 | from the case when there is no field.[[BR]] |
| | 34 | 5. The stretching is the dominant magnetic field amplification mechanism. The "wing" shaped field encompassing the clump has the most stretching and thus the strongest amplification, which [[BR]] |
| | 35 | increases the flow coherence. [[BR]] |
| | 36 | 6. The low beta area is concentrated on the axis, behind the clump, which forms a "wake" of low density, high magnetic pressure region. [[BR]] |
| | 37 | |
| | 38 | |
| | 39 | The image below shows the clump evolution when the uniform magnetic field is perpendicular to the shock direction.[[BR]][[BR]] |
| | 40 | |
| | 41 | 1. The magnetic field is stretched and wrapped around the clump, which effectively confines the clump and prevents its fragmentation, even for moderately strong field β = 4. The clump [[BR]] |
| | 42 | embedded in the stretched field is compressed, but then, because of the strong confining effect of the field develops a streamlined profile and is not strongly eroded. [[BR]] |
| | 43 | 2. The field amplification is strong. One can observe some locations where the field strength is amplified by more than two orders of magnitude. The field is concentrated around the clump [[BR]] |
| | 44 | profile, which serves as a "shell", preventing the clump from fragmentation. The magnetic pressure at the clump head increases due to compression, which acts as a shock absorber.[[BR]] |
| | 45 | The magnetic pressure encompassing the clump increases due to stretching, which stabilizes the instabilities and gives the shocked material a more streamlined shape. [[BR]] |
| | 46 | 3. At later stage, the stretched field around the clump edge has β < 1 even for moderately strong initial field condition, indicating a much stronger amplification effect comparing to the [[BR]] |
| | 47 | aligned field case. [[BR]][[BR]] |
| | 48 | |
| | 49 | |
| | 50 | |
| | 51 | In AstroBEAR, the clump simulation is done using the clump object, the wind object and the cooling object. We also implement various multiphysics processes to make the situation [[BR]] |
| | 52 | more interesting. Below are snapshots of the clump density and magnetic pressure in a 3-D AMR simulation. Notice the field concentration at [[latex($\tau_{cc}$)]] is very different for [[BR]] |
| | 53 | the aligned and perpendicular field cases. [[BR]][[BR]] |
| | 54 | |
| | 55 | |
| | 56 | Here is a movie of the mentioned simulation. [[BR]][[BR]] |
| | 57 | |
| | 58 | |
| | 59 | The following images show the high resolution shocked clump problem with uniform magnetic field in AMR. [[BR]][[BR]] |
| | 60 | |
| | 61 | |
| | 62 | When resistivity is applied, the situation can be quite different since the field has a much higher reconnection rate and will be less likely to be amplified by compression. [[BR]] |
| | 63 | The reconnection will also convert the compressed magnetic energy into kinetic energy which disturbs the local flow pattern. Here, we show the shocked clumps with uniform perpendicular [[BR]] |
| | 64 | magnetic field with computational resistivity. [[BR]][[BR]] |
| | 65 | |
| | 66 | |
| | 67 | [[BR]][[BR]] |
| | 68 | |
| | 69 | |
| | 70 | == Clumps with contained magnetic field == |
| | 71 | |
| | 72 | Sometimes the clumps contain tangled magnetic field inside them. We put in the tangled magnetic field using the vector perturbation object. [[BR]] |
| | 73 | Here we show the shocked hydro clump vs the shocked magnetized clump. There is no pronounced difference between them.[[BR]][[BR]] |
| | 74 | [[Image(http://www.pas.rochester.edu/~shuleli/1121/ClumpShockInteraction.png, 30%)]][[BR]][[BR]] |
