## 3. Results and discussion## 3.1. Calculation of stochastic hydrodynamic modelsFor my study, I start with a monochromatic wave having a period of s. In order to increase the stability of the hydrodynamic wave solutions, the radiation damping is switched on over a timespan of s. The wave computation is continued over 3500 time steps, corresponding to s. During that time 129 shocks are inserted into the atmosphere. The hydrodynamic atmosphere has then reached a dynamical steady state given by the balance of shock wave heating and radiative cooling. Then I start to introduce shock waves with stochastically changing wave periods. I have selected two different wave period distributions. Both distributions are assumed to be Gaussian and centered at s. The first distribution (Spectrum 1) has a standard deviation of s, whereas the standard deviation of the second distribution (Spectrum 2) is s (see Fig. 1). The spectrum has been cut off to avoid "negative periods." Periods below s have also been excluded due to the limited hydrodynamic resolution in the wave models. The peak values of the wave period distributions have been chosen according to results from traditional acoustic energy generation models (Bohn 1984; Ulmschneider et al. 1996). As comparison to these stochastic wave models, I also calculate a monochromatic wave model with s. Contrary to waves considering period distributions, monochromatic waves rely on a fixed wave period only. The above-given wave period has been selected to ensure that shock overtaking events are avoided, which are found to occur even in monochromatic wave computations with sufficiently small wave periods (Theurer et al. 1997).
Cuntz (1992a, b) already obtained some results concerning the behavior of stochastic wave models. He found that these models are characterized by shock-shock interaction due to the fact that a broad range of frequencies exists. The stochasticity of the wave field leads to episodic energy and momentum input to the atmosphere, which controls the temperature, the flow speed, and the thermodynamic quantities. The models are also characterized by a complicated hydrodynamic structure determined by a nonuniform distribution of shocks. The shock strengths and the shock speeds differ substantially and change non-monotonically with height. This result gives insight into the basic physics going on: after allowing the wave period to change stochastically, shocks with different strengths are introduced into the atmosphere. Different shock strengths cause different shock speeds leading to interacting, overtaking and merging of shocks ("shock-cannibalism"). Since the strength of an overtaking shock combines with the shocks it engulfs, its speed increases, so it overtakes more and more shocks in front of it and attains an even greater strength. Consequently, the amount of momentum and energy deposition that occurs varies drastically with time and atmospheric height. The direction of the flow alternates between outwardly and inwardly directed motions depending on the strengths of the shocks and the radiation-hydrodynamic history of the flow. An example of that behavior is given in Fig. 2. It shows the
temperature structure of a stochastic shock wave model at
s and s
after acoustic frequency spectra have been employed. It is found that
the second and third shock (counted from lower to higher mass column
densities) merge as the speed of the third shock is 11.5 km
s
## 3.2. Evaluation of chromospheric velocity fieldsThe main goal of this paper is to explore the consequences of
shock-shock interaction for the generation of stochastic chromospheric
velocity fields in Ori in a systematic
manner. Therefore, I evaluate the behavior of the flow at different
atmospheric heights corresponding to distinct values of the mass
column density First of all, I evaluate the results for Spectrum 1. In order
to minimize the impact of the starting model, which is the
monochromatic wave model obtained at time step IT = 3500, I ignore the
following s for the statistical analysis.
The wave computation is then continued over a timespan of
s. During that period of time, 51 shocks
are inserted into the atmosphere. Due to overtaking and merging of
shocks, strong atmospheric inflows and outflows are initiated. It is
found that at relatively low mass column densities (i.e., farther out
in the atmosphere) the likelihood for larger inflows and outflows
increases (see Fig. 3). At log
In the case of Spectrum 2, the results obtained are quite
similar. It is found again that at log Now I investigate the flow velocity © European Southern Observatory (ESO) 1997 Online publication: April 28, 1998 |