Computer Science – Sound
Scientific paper
Apr 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006phdt........11t&link_type=abstract
Ph.D. Thesis
Computer Science
Sound
Scientific paper
Velocity shear induced phenomena in solar and astrophysical flows
This thesis has concentrated on a non-modal analysis of flows with velocity inhomogeneities. Various astrophysical applications have been considered.
In Chapter 2 we have studied a simple shear flow in order to demonstrate the non-modal method as well as basic properties of flows with inhomogeneous velocity fields. We illustrated the mathematical formalism on a parallel flow with a constant linear velocity shear. The effect of the shearing background on the different types of modes was demonstrated separately.
In Chapter 3 we studied linear mode conversion and sound production in uniform shear flows. The flows under consideration were two dimensional, planar, inviscid, unbounded, and had uniform density/pressure and constant shear of velocity. We studied the aerodynamic production of acoustic waves in inhomogeneous hydrodynamic flows. A qualitative analysis of the wave excitation amplitudes in wave-number space are followed by direct numerical simulations on the vortex package dynamics in shear flows. We have derived the formalism for the separation of linear modes in flows with constant velocity shear. Hence, we carried out numerical analysis to study the wave generation and confirm the theoretical results obtained with the non-modal method.
In Chapter 4 we have extended the theory of Chapter 3 to the MHD waves. We have studied 2D linear perturbations in 3D unbounded ideal MHD shear flows. In this case the linear spectrum consists of the magnetosonic wave mode and two aperiodic modes with zero frequency. These modes are a vortex mode with intrinsic vortical perturbations and a magneto-mechanical mode which has transient vortical characteristics in the sheared medium. Both aperiodic modes are able to excite magnetosonic waves with similar wave-numbers when the wave-number in the direction of the velocity shear becomes zero. It turns out that the vortex modes are the main source of the waves in flows with weak or moderate magnetic fields. The magneto-mechanical mode may generate more waves in strongly magnetized plasma for stronger velocity shear.
In Chapter 5 we have studied compressible convection in shear flows. In particular we have focused on linear small-scale perturbations in unstably stratified flows with constant shear of velocity. We have found that the mode conversion originates from the velocity shear of the flow. Exponentially growing perturbations of convection are able to excite acoustic waves. At particular wave-numbers g-mode perturbations (perturbations of buoyancy) feed the acoustic radiation of the turbulent convection. The generated oscillations are spatially correlated with the source flow. This process may be important for convection in astrophysical objects. We discussed the solar convective envelope as an example. Generating waves in high shear regions of a stratified turbulent flow, this non-resonant phenomenon can contribute to the production of sound in the solar convection zone.
In Chapter 6 we have investigated non-axisymmetric perturbations in differentially rotating hydrodynamic flows in a gravitational field. The aim here was twofold: Firstly, shear flows commonly occur in many astrophysical situations and they are thought to be the key to the explanation of accretion disk phenomena. Secondly, it gives us an opportunity to study vortex-wave mode conversion in a medium, where two intrinsically different wave modes are present: sound waves as well as internal gravity-spiral waves.
We found that vortices are able to generate gravity-spiral waves in flows with Keplerian shear. Higher shear rates are necessary to trigger the double excitation of density spiral and acoustic waves.
We have analyzed the dynamics of accretion disks and based on our results promote the hydrodynamic model of the turbulence. Firstly, we describe the general balances in the rotating disk flows in 2D and show that the stabilizing effect of the Coriolis force can be overcome by a substantial increase of the Reynolds number. Secondly we study 3D perturbations where we contribute to the bypass transition scenario and derive a possible mechanism for the hydrodynamic turbulence in accretion disks.
In Chapter 7 we have studied the resonant interactions of the MHD wave modes in shear flows. We have shown that the reciprocal transformation of the MHD wave modes may occur symmetrically. Depending on the wave-numbers, the mutual transformation of the Alfven and fast magnetosonic waves is possible in strongly magnetized plasmas. Transformations of the Alfven and the slow magnetosonic waves are expected in weakly magnetized plasmas. Plasmas with equal magnetic and thermal pressure (beta=1) may exhibit the transformations of all three MHD waves simultaneously. An important property is that this process is resonant by nature: in contrast with the mode conversion phenomenon described in Chapters (3-6) the amplitude of waves generated during transformations do not generally grow when the shear parameter increases. It is quite the opposite. The resonance and effective exchange of energy between the MHD wave modes require low value of shear parameters. We have discussed astrophysi!
cal consequences of our study. Among these are applications in the solar atmosphere and wind, galactic spiral arms, pulsar magnetosphere and Earth's atmosphere.
Overall, the main frame of investigation throughout this thesis lies on the non-modal analysis of perturbations, recovering short time transient phenomena that originate from the non-normal character of the shear flows. We hope that our efforts contribute to a better understanding of the kinematically inhomogeneous astrophysical objects. The aim here was twofold: Firstly, shear flows commonly occur in many astrophysical situations and they are thought to be the key to the explanation of accretion disk phenomena. Secondly, it gives us an opportunity to study vortex-wave mode conversion in a medium, where two intrinsically different wave modes are present: sound waves as well as internal gravity-spiral waves.
We found that vortices are able to generate gravity-spiral waves in flows with Keplerian shear. Higher shear rates are necessary to trigger the double excitation of density spiral and acoustic waves.
We have analyzed the dynamics of accretion disks and based on our results promote the hydrodynamic model of the turbulence. Firstly, we describe the general balances in the rotating disk flows in 2D and show that the stabilizing effect of the Coriolis force can be overcome by a substantial increase of the Reynolds number. Secondly we study 3D perturbations where we contribute to the bypass transition scenario and derive a possible mechanism for the hydrodynamic turbulence in accretion disks.
In Chapter 7 we have studied the resonant interactions of the MHD wave modes in shear flows. We have shown that the reciprocal transformation of the MHD wave modes may occur symmetrically. Depending on the wave-numbers, the mutual transformation of the Alfven and fast magnetosonic waves is possible in strongly magnetized plasmas. Transformations of the Alfven and the slow magnetosonic waves are expected in weakly magnetized plasmas. Plasmas with equal magnetic and thermal pressure (beta=1) may exhibit the transformations of all three MHD waves simultaneously. An important property is that this process is resonant by nature: in contrast with the mode conversion phenomenon described in Chapters (3-6) the amplitude of waves generated during transformations do not generally grow when the shear parameter increases. It is quite the opposite. The resonance and effective exchange of energy between the MHD wave modes require low value of shear parameters. We have discussed astrophysi!
cal consequences of our study. Among these are applications in the solar atmosphere and wind, galactic spiral arms, pulsar magnetosphere and Earth's atmosphere.
Overall, the main frame of investigation throughout this thesis lies on the non-modal analysis of perturbations, recovering short time transient phenomena that originate f
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