Wyniki wyszukiwania - BazTech

1

Anisotropic turbulent viscosity and large-scale motive force in thermally driven turbulence at low Prandtl number

Mizerski K. A.

Archives of Mechanics

|

2022

|

Vol. 74, nr 5

409-436

EN

The fully developed turbulent Boussinesq convection is known to form large-scale rolls, often termed the ‘large-scale circulation’ (LSC). It is an interesting question how such a large-scale flow is created, in particular in systems when the energy input occurs at small scales, when inverse cascade is required in order to transfer energy into the large-scale modes. Here, the small-scale driving is introduced through stochastic, randomly distributed heat source (say radiational). The mean flow equations are derived by means of simplified renormalization group technique, which can be termed a ‘weakly nonlinear renormalization procedure’ based on consideration of only the leading order terms at each step of the recursion procedure, as full renormalization in the studied anisotropic case turns out unattainable. The effective, anisotropic viscosity is obtained and it is shown that the inverse energy cascade occurs via an effective ‘motive force’ which takes the form of transient negative, vertical diffusion.

2

Vertical heat transport at infinite Prandtl number for micropolar fluid

Caggio M., Kalita P., Łukaszewicz G., Mizerski K. A.

Archives of Mechanics

|

2020

|

Vol. 72, nr 6

525--553

EN

We investigate the upper bound on the vertical heat transport in the fully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number for a micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh number, with a logarithmic correction. The derived bound is compared with the optimal known one for the Newtonian fluid. It follows that the (optimal) upper bound for the micropolar fluid is less than the corresponding bound for the Newtonian fluid at the same Rayleigh number. Moreover, strong microrotational diffusion effects can entirely suppress the heat transfer. In the Newtonian limit our purely analytical findings fully agree with estimates and scaling laws obtained from previous theories significantly relying on phenomenology.

3

Subtle structure of streamers under conditions resembling those of Transient Luminous Events

Błęcki J. S., Mizerski K. A.

Archives of Mechanics

|

2018

|

Vol. 70, nr 6

535--550

EN

The paper presents a brief review of the observational facts related to plasma filamentation in astrophysics and the subtle structures of plasma in Transient Luminous Events (TLE’s) and an analysis of the physical mechanism that could contribute to formation of filaments in plasma inside streamers. The values of physical parameters are assumed such as to resemble the physical conditions in streamers of the TLE’s. Estimates of the typical spatial scales of these structures and temporal characteristics of filament formation are given. The analysis concerns a non-magnetic mechanism based on a form of non-relativistic dissipative instability and the electron-nitrogen collisional 2Πg resonance. It is argued that the influence of the magnetic field is negligible at the leading order at least up to the altitudes of about 65–70 km. Under the conditions related to those in plasma inside the TLE’s, derived based on the current knowledge of physical parameters within the electric discharges, the identified dissipative-resonant instability is demonstrated to be the only/most vigorous linear instability developing in the system. It results in periodic plasma density distribution in the direction transverse to the electric field. The obtained time scales of the instability development are quick and proportional to the inverse of the ion-neutral collision frequency, 1/νi, whereas the proposed spatial scale of the density stripes/filaments is proportional to the electron temperature and inversely proportional to the speed of the discharge.