The background to the work is described at

Dynamics of the Solar Atmosphere Generated by the Eigen Modes of Solar Global Oscillations

Theoretical background to this work is described in

Our Wobbling Star!

and

The Solar Global Eigenmodes of Oscillation

Source code used for the runs including the input files may be obtained from github https://github.com/mikeg64/smaug_pmode/

We have performed two series of simulations delivering the same quantity of energy into the solar atmosphere with the extended driver across the lower boundary of the model.

The series are;

- Normal modes for a given value for the speed of sound in the solar atmosphere
- Mode series for drivers corresponding to the 5 minute and 3 minute oscillation

The series for the normal modes are calculated from the following expressions for a given of the speed of sound c and a value for the length of the simulation box of 4Mm. The frequency is computed using

The series of normal modes are computed such that the modes satisfy the following condition

The speed of sound for the VALIIc solar atmosphere is shown in the plot below

Variation of Sound Speed with height above the Photosphere Calculated from the VALIIC and McWhirter Model of the Solar Atmosphere |

The simulations are tabulated below. The tables indicate the mode, the period for the driver, the driver amplitude and the label used for each of the data sets (for the input files and the configuration outputs). Remember that for both series the amplitudes have been set so that the same amount of energy is delivered by the driver. For the normal modes we have

For sound speed 20km/s

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 282.84 | 500 | spic_2p82_0_0_3d |

(0,1) | 200.0 | 200 | spic_2p00_0_1_3d |

(0,2) | 133.33 | 100 | spic_1p33_0_2_3d |

(0,3) | 100.0 | 58.8 | spic_1p00_0_3_3d |

For sound speed 13km/s

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 435.1 | 500 | spic_4p35_0_0_3d |

(0,1) | 307.7 | 200 | spic_3p07_0_1_3d |

(0,2) | 205.1 | 100 | spic_2p05_0_2_3d |

(0,3) | 153.8 | 58.8 | spic_1p53_0_3_3d |

For sound speed 8.4km/s

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 673.4 | 500 | spic_6p7_0_0_3d |

(0,1) | 425.9 | 200 | spic_4p3_0_1_3d |

(0,2) | 301.2 | 100 | spic_3p0_0_2_3d |

(0,3) | 147.1 | 58.8 | spic_2p3_0_3_3d |

For sound speed 31.43km/s

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 179.98 | 500 | spic_1p79_0_0_3d |

(0,1) | 127.27 | 200 | spic_1p27_0_1_3d |

(0,2) | 84.84 | 100 | spic_0p84_0_2_3d |

(0,3) | 63.63 | 58.8 | spic_0p63_0_3_3d |

The series for the five and three minute modes are as follows

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 300.0 | 1250 | spic5b0_3d_rep_3d |

(0,1) | 300.0 | 500 | spic5b0_1_3d |

(0,2) | 300.0 | 250 | spic5b0_2_3d |

(0,3) | 300.0 | 147.06 | spic5b0_3_3d |

Mode | Driver Period (s) | Amplitude (m/s) | Label |

(0,0) | 180.0 | 1250 | spic6b0_3d_rep_3d |

(0,1) | 180.0 | 500 | spic6b0_1_3d |

(0,2) | 180.0 | 250 | spic6b0_2_3d |

(0,3) | 180.0 | 147.06 | spic6b0_3_3d |

We present below distance-time plots, plots of the energy flux and the variation of the energy flux for the different modes.

The plots below compare the distance time plots for the vertical component of the plasma velocity with the (0,0),(0,1),(0,2) and (0,3) modes.

Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Chromosphere at 1.06Mm. |

Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Transition Layer at 2Mm. |

Distance Time plot for 180s Driver the d-t plot has been taken through a horizontal section through the model in the Solar Corona at 4.3Mm. |

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Chromosphere at 1.06Mm. |

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Transition Layer at 2Mm. |

Distance Time plot for 300s Driver the d-t plot has been taken through a horizontal section through the model in the Solar Corona at 4.3Mm. |

The plots below show the integrated energy across a section of the computational model for different heights through the solar atmosphere the variation with time is shown.

Integrated Energy Variation for 180s Driver |

Integrated Energy Variation for 300s Driver |

The plots below compare the integrated time averaged flux for the solar atmosphere and the transition layer. For each mode the plots illustrate the variation of the integrated flux with the driver period.

Time Averaged Flux Variation for the Solar Corona |

Time Averaged Flux Variation for the Transition Layer |

The full set of results (images) is available from the following link

http://bit.ly/1TUMfOf

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