Energy transfer in compressible MHD turbulence

Transcription

1 Energy transfer in compressible MHD turbulence Philipp Grete Michigan State University in collaboration with Brian O Shea, Kris Beckwith, Wolfram Schmidt and Andrew Christlieb MIPSE Seminar University of Michigan, Ann Arbor, Nov 15, 2017 Philipp Grete Energy transfer in MHD turbulence Nov / 19

2 Motivation Motivation In many astrophysical systems turbulence compressibility magnetic fields e.g. dynamos, accretion disks, cosmic rays, star formation How do they interact? Study energy transfer [Image credit top: MPIfR and Newcastle University] [Image credit bottom: HST] Philipp Grete Energy transfer in MHD turbulence Nov / 19

3 Motivation More on energy transfer Total energy in an ideal MHD system is conserved Individual energy (and scale) budgets are not Different budgets and different interactions Regarding turbulence Energy cascade Inverse transfer Nonlocal transfer [Dynamo image credit: Vainshtein & Zel dovich 72] Philipp Grete Energy transfer in MHD turbulence Nov / 19

4 Transfer functions Formal description of energy transfer Nonlinear term in real space, e.g. B(x) (u(x) ) B(x) involves three wave vectors in spectral space, e.g. ( ) B(k) B(q) (u(p) p) that must form a triangle k + q + p = 0 triad interactions Philipp Grete Energy transfer in MHD turbulence Nov / 19

5 Transfer functions Interpretation of triad interactions ( ) B(k) B(q) (u(p) p) Field B at scale q gives energy to field B scale k by an interaction of type u Here, magnetic to magnetic via kinetic advection at at scale p Using shells rather than individual modes shell-to-shell transfer Local interactions: wavevectors with similar magnitudes Nonlocal interactions: wavevectors with dissimilar magnitude Locality is an important question in MHD, e.g. background fields Philipp Grete Energy transfer in MHD turbulence Nov / 19

6 Transfer functions Energy budgets in incompressible MHD E u (K) = Q w K (u ) w Q advection (kinetic cascade) + w K (v A ) B Q magnetic tension + dx E b (K) = Q B K (u ) B Q advection (magnetic cascade) + B K (v A w Q) magnetic tension + dx Philipp Grete Energy transfer in MHD turbulence Nov / 19

7 Transfer functions Energy budgets in compressible MHD [Grete+ PoP 2017] E u (K) = Q w K (u ) w Q advection (kinetic cascade) 1 2 wk w Q u compression E b (K) = Q + w K (v A ) B Q magnetic tension B K (u ) B Q advection (magnetic cascade) + B K (v A w Q) magnetic tension wk 2 ρ ( B B Q) magnetic pressure 1 2 BK B Q u compression ) ( w B K Q B 2 ρ } {{ } magnetic pressure + dx + dx Philipp Grete Energy transfer in MHD turbulence Nov / 19

8 Simulations Driven turbulence in a box ( ) [Grete+ PoP 2017] M0.5 Enzo M0.5 Athena M2.5 Enzo M2.5 Athena Compensated spectra Isothermal, isotropic, homogeneous Two codes: Enzo and Athena Two regimes: subsonic M s 0.5 and supersonic M s 2.5 Analyzed stationary regime (30 snapshots over 3 turnover times T ) Kin. energy Mag. energy wavenumber k Philipp Grete Energy transfer in MHD turbulence Nov / 19

9 Simulations Eddies at rest [Grete+ PoP 2017] How to define shells (eddies) Linear (thin) binning volume filling wave-like structures Logarithmic binning localized in real and spectral space Octave binning Linear binning k [2, 4] k [4, 8] k [8, 16] k [16, 32] k [32, 64] k [3, 4] k [7, 8] k [15, 16] k [31, 32] k [63, 64] Philipp Grete Energy transfer in MHD turbulence Nov / 19

10 Simulations Eddies in motion [Grete+ PoP 2017] movie plays here... maybe Philipp Grete Energy transfer in MHD turbulence Nov / 19

11 Results What can we learn from the transfer functions T XYZ (Q, K)? Cross-scale transfer: Q k K>k T e.g. relevant for subgrid-scale turbulence modeling Total transfer: Q T e.g. relevant for the net effects cf. dynamos Shell-to-shell transfer: T helps to explain everything a lot Philipp Grete Energy transfer in MHD turbulence Nov / 19

12 Results Cross-scale transfer Cross-scale transfer overview [Grete+ PoP 2017] Not only one energy reservoir Transfer within and between Philipp Grete Energy transfer in MHD turbulence Nov / 19

13 Results Cross-scale transfer Mean cross-scale flux in the inertial range [Grete+ PoP 2017] Philipp Grete Energy transfer in MHD turbulence Nov / 19

14 Results Cross-scale transfer Mean cross-scale flux in the inertial range [Grete+ PoP 2017] Subsonic transfers match results of spectral code [Debliquy+ PoP 2011] Supersonic transfers are more dynamic Philipp Grete Energy transfer in MHD turbulence Nov / 19

15 Results Cross-scale transfer Cross-scale transfer versus scales [Grete+ PoP 2017] UUa UUc sum BUT BUP sum M0.5 Enzo M2.5 Enzo Individual fluxes are not constant Fluxes between regimes are similar (shape) vary in magnitude Total flux (all terms) is constant cross-scale flux cross-scale flux wavenumber k wavenumber k Philipp Grete Energy transfer in MHD turbulence Nov / 19

16 Results Total transfer Total transfer in (or out) a shell [Grete+ PoP 2017] Advection and compression work against each other Magnetic tension transfers energy to most scales total transfer total transfer M0.5 Enzo UUa UUc sum wavenumber k M2.5 Enzo BUT UBT sum wavenumber k Philipp Grete Energy transfer in MHD turbulence Nov / 19

17 Results Shell-to-shell transfer The energy cascades [Grete+ PoP 2017] Energy transfer is local Shell N receives energy from shell N 1 transfer energy to shell N + 1 Applies to (the stronger) magnetic cascade, too wavenumber K wavenumber K Kinetic cascade M0.5 Enzo M2.5 Enzo wavenumber Q wavenumber Q energy transfer energy transfer Philipp Grete Energy transfer in MHD turbulence Nov / 19

18 Results Shell-to-shell transfer Transfer mediated by magnetic tension [Grete+ PoP 2017] Mag. to kin. by magnetic tension Energy transfer is weakly local Velocity and magnetic field exchange most energy at K = Q Energy is received from few larger scales Q K and transferred to more smaller scales Q > K wavenumber K wavenumber K M0.5 Enzo M2.5 Enzo wavenumber Q wavenumber Q energy transfer energy transfer Philipp Grete Energy transfer in MHD turbulence Nov / 19

19 Results Shell-to-shell transfer Transfer mediated by magnetic pressure [Grete+ PoP 2017] Mag. to kin. by magnetic pressure Energy transfer is even less local Much stronger in the supersonic regime Similar shapes in both regimes wavenumber K wavenumber K M0.5 Enzo M2.5 Enzo wavenumber Q wavenumber Q energy transfer energy transfer Philipp Grete Energy transfer in MHD turbulence Nov / 19

20 Results Shell-to-shell transfer The compressive component in the magnetic cascade wavenumber K Magnetic cascade via compression M0.5 Enzo energy transfer Overall weak (few %) Very dissimilar between regimes wavenumber K M2.5 Enzo wavenumber Q wavenumber Q energy transfer Philipp Grete Energy transfer in MHD turbulence Nov / 19

21 Results Shell-to-shell transfer Conclusions [Grete+ PoP 2017] Established a method to analyze the compressible regime Underlying transfers between regimes are overall similar but can differ in their components and magnitudes Next: exploration of parameter space (in more realistic environments) Philipp Grete Energy transfer in MHD turbulence Nov / 19