Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids
We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potenti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/6/11/216 |
| _version_ | 1797547298679422976 |
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| author | Konstantin G. Zloshchastiev |
| author_facet | Konstantin G. Zloshchastiev |
| author_sort | Konstantin G. Zloshchastiev |
| collection | DOAJ |
| description | We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system’s stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations. |
| first_indexed | 2024-03-10T14:41:21Z |
| format | Article |
| id | doaj.art-cf82ca62b7e24181b2391da8aa413798 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T14:41:21Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-cf82ca62b7e24181b2391da8aa4137982023-11-20T21:45:48ZengMDPI AGUniverse2218-19972020-11-0161121610.3390/universe6110216Density Operator Approach to Turbulent Flows in Plasma and Atmospheric FluidsKonstantin G. Zloshchastiev0Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South AfricaWe formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system’s stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.https://www.mdpi.com/2218-1997/6/11/216plasma turbulenceplanetary atmosphereflow instabilityzonal flowdrift waveRossby wave |
| spellingShingle | Konstantin G. Zloshchastiev Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids Universe plasma turbulence planetary atmosphere flow instability zonal flow drift wave Rossby wave |
| title | Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids |
| title_full | Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids |
| title_fullStr | Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids |
| title_full_unstemmed | Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids |
| title_short | Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids |
| title_sort | density operator approach to turbulent flows in plasma and atmospheric fluids |
| topic | plasma turbulence planetary atmosphere flow instability zonal flow drift wave Rossby wave |
| url | https://www.mdpi.com/2218-1997/6/11/216 |
| work_keys_str_mv | AT konstantingzloshchastiev densityoperatorapproachtoturbulentflowsinplasmaandatmosphericfluids |