We use numerical simulations to study the effect of nonlinear MHD waves in a stratified , self-gravitating molecular cloud that is bounded by a hot and tenuous external medium .
In a previous paper , we had shown the details of a standard model and studied the effect of varying the dimensionless amplitude \tilde { a } _ { d } of sinusoidal driving .
In this paper , we present the results of varying two other important free parameters : \beta _ { 0 } , the initial ratio of gas to magnetic pressure at the cloud midplane , and \tilde { \nu } _ { 0 } , the dimensionless frequency of driving .
Furthermore , we present the case of a temporally random driving force .
Our results demonstrate that a very important consideration for the actual level of turbulent support against gravity is the ratio of driving wavelength \lambda _ { 0 } to the the size of the initial non-turbulent cloud ; maximum cloud expansion is achieved when this ratio is close to unity .
All of our models yield the following basic results : ( 1 ) the cloud is lifted up by the pressure of nonlinear MHD waves and reaches a steady-state characterized by oscillations about a new time-averaged equilibrium state ; ( 2 ) after turbulent driving is discontinued , the turbulent energy dissipates within a few sound crossing times of the expanded cloud ; ( 3 ) the line-width–size relation is obtained by an ensemble of clouds with different free parameters and thereby differing time-averaged self-gravitational equilibrium states .
The best consistency with the observational correlation of magnetic field strength , turbulent line width , and density is achieved by cloud models with \beta _ { 0 } \approx 1 .
We also calculate the spatial power spectra of the turbulent clouds , and show that significant power is developed on scales larger than the scale length H _ { 0 } of the initial cloud , even if the input wavelength of turbulence \lambda _ { 0 } \approx H _ { 0 } , The cloud stratification and resulting increase of Alfvén speed toward the cloud edge allows for a transfer of energy to wavelengths significantly larger than \lambda _ { 0 } .
This explains why the relevant time scale for turbulent dissipation is the crossing time over the cloud scale rather than the crossing time over the driving scale .