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Astron. Astrophys. 338, 311-321 (1998)

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4. Conclusions

From our studies of nonlinear generation of longitudinal waves in solar magnetic flux tubes excited by the external turbulent velocities at various heights, the following conclusions can be drawn.

1. The time-averaged longitudinal wave energy fluxes [FORMULA] calculated for a single magnetic flux tube embedded in the solar atmosphere are of the order [FORMULA], which is roughly equal to the pure acoustic flux outside the tube. The calculated spectrum for longitudinal tube waves is broadly similar to that of the exciting turbulent velocity, namely, it is relatively constant at low frequencies and decreases rapidly for frequencies higher than [FORMULA].

2. The longitudinal wave energy spectra and the corresponding fluxes do not vary much with the height where the tube is squeezed. For large rms turbulent velocities ([FORMULA]) [FORMULA], the calculations stopped because rapid tube expansion led to very low tube temperatures ([FORMULA]) K.

3. The shape of the calculated wave energy spectra remains practically unchanged when the squeezing velocity is increased, but the longitudinal wave energy fluxes increase with the rms turbulent velocity [FORMULA] like [FORMULA].

4. Increasing the magnetic field strength in the tube does not change the shape of the wave energy spectrum, but increasing the field strength from [FORMULA] to [FORMULA], decreases the longitudinal wave flux by a factor of 3.6. It is found that [FORMULA].

5. The transverse wave fluxes of Huang et al. (1995) have to be revised upwards to values of the order of [FORMULA] [FORMULA], due to an error and by considering two orthogonal horizontal shaking directions. This is roughly similar to the fluxes estimated from observations of the proper motion of network bright points (Muller et al. 1994).

6. The obtained longitudinal wave energy fluxes are up to one order of magnitude higher than those found by using analytical methods (Musielak et al. 1995), but they are about a factor of 30 lower than the transverse wave fluxes. For the latter severe leakage out of the tube may occur.

There are several reasons that our approach has to be considered as idealized and simplified. First, the squeezing takes place only at a local height point and does not include the correlation effects which occur when the tube is squeezed over its entire length. Second, reflection and wave energy losses through nonlinear wave coupling, leakage, shock formation and atmospheric damping are not taken into account.

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© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998
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