scholarly journals Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 216
Author(s):  
Konstantin G. Zloshchastiev
Keyword(s):  
Turbulent Flows ◽  
Density Operator ◽  
Geometrical Optic ◽  
Kinetic Equations ◽  
Zonal Flow ◽  
Hamiltonian Operator ◽  
Statistical Ensembles ◽  
Mechanical Approach ◽  
Space Formulation ◽  
The Waves

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.

scholarly journals Wave Breaking in Undular Bores with Shear Flows

Water Waves ◽  
2021 ◽  
Author(s):  
Maria Bjørnestad ◽  
Henrik Kalisch ◽  
Malek Abid ◽  
Christian Kharif ◽  
Mats Brun
Keyword(s):  
Turbulent Flows ◽  
Wave Breaking ◽  
Vries Equation ◽  
Kdv Equation ◽  
Flow Depth ◽  
Present Contribution ◽  
Undular Bore ◽  
Wave Flume ◽  
The Kdv Equation ◽  
The Waves

AbstractIt is well known that weak hydraulic jumps and bores develop a growing number of surface oscillations behind the bore front. Defining the bore strength as the ratio of the head of the undular bore to the undisturbed depth, it was found in the classic work of Favre (Ondes de Translation. Dunod, Paris, 1935) that the regime of laminar flow is demarcated from the regime of partially turbulent flows by a sharply defined value 0.281. This critical bore strength is characterized by the eventual breaking of the leading wave of the bore front. Compared to the flow depth in the wave flume, the waves developing behind the bore front are long and of small amplitude, and it can be shown that the situation can be described approximately using the well known Kortweg–de Vries equation. In the present contribution, it is shown that if a shear flow is incorporated into the KdV equation, and a kinematic breaking criterion is used to test whether the waves are spilling, then the critical bore strength can be found theoretically within an error of less than ten percent.

Estimating Zonal Flow Contributions in Deep Water Assets From Pressure and Temperature Data

2017 ◽  
Author(s):  
A. Rashid Hasan ◽  
Rayhana N. Sohel ◽  
Xiaowei Wang
Keyword(s):  
Turbulent Flows ◽  
Deep Water ◽  
Fluid Pressure ◽  
Zonal Flow ◽  
Temperature Data ◽  
Sensitivity Analyses ◽  
Momentum Balance ◽  
Flow Profile ◽  
Flowing Fluid ◽  
Energy And Momentum

Producing hydrocarbon from deep water assets is extremely challenging and expensive. A good estimate of rates from multiple pay zones is essential for well monitoring, surveillance, and workover decisions. Such information can be gleaned from flowing fluid pressure and temperature; deep-water wells are often well instrumented that offers such data on a continuous basis. In this study a model is presented that estimates zonal flow contributions based on energy and momentum balances. Kinetic and heat energy coming from the reservoir fluid to the production tubing is accounted for in the model. The momentum balance for wellbore takes into account differing flow profile in laminar and turbulent flows. In addition, when sandface temperature data are not available, a recently developed analytical model to estimate the effect of Joule-Thompson expansion on sandface temperature was used to estimate sandface temperature from reservoir temperature. The model developed can be applied to any reservoir with multiple pay zones and is especially useful for deep-water assets where production logging is practically impossible. Available field data for multiphase flow was used to validate the model. Sensitivity analyses were performed that showed accurate temperature data is essential for the model to estimate zonal contribution accurately.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

scholarly journals Dynamics of Convectively Driven Banded Jets in the Laboratory

2007 ◽  
Vol 64 (11) ◽  
pp. 4031-4052 ◽  
Author(s):  
Peter L. Read ◽  
Yasuhiro H. Yamazaki ◽  
Stephen R. Lewis ◽  
Paul D. Williams ◽  
Robin Wordsworth ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flows ◽  
Large Scale ◽  
Zonal Flow ◽  
Inertial Range ◽  
Instability Criterion ◽  
Rossby Wave Breaking ◽  
Outer Planets ◽  
Zonal Jets ◽  
Geostrophic Turbulence

Abstract The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

scholarly journals Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay

2018 ◽  
Vol 32 (25) ◽  
pp. 1850276 ◽  
Author(s):  
Ludmila Praxmeyer ◽  
Konstantin G. Zloshchastiev
Keyword(s):  
Phase Space ◽  
Density Operator ◽  
Quantum Systems ◽  
Matrix Approach ◽  
Weyl Transform ◽  
Energy Eigenvalues ◽  
Decay Constants ◽  
Dissipative Effects ◽  
Mean Lifetime ◽  
Space Formulation

The Wigner–Weyl transform and phase space formulation of a density matrix approach are applied to a non-Hermitian model which is quadratic in positions and momenta. We show that in the presence of a quantum environment or reservoir, mean lifetime and decay constants of quantum systems do not necessarily take arbitrary values, but could become functions of energy eigenvalues and have a discrete spectrum. It is demonstrated also that a constraint upon mean lifetime and energy appears, which is used to derive the resonance conditions at which long-lived states occur. The latter indicate that quantum dissipative effects do not always lead to decay but, under certain conditions, can support stability of a system.

HIGH-ORDER OPTICAL HARMONIC GENERATION ON CARBON NANOTUBES: QUANTUM-MECHANICAL APPROACH

2004 ◽  
Vol 03 (03) ◽  
pp. 343-354 ◽  
Author(s):  
G. Ya. SLEPYAN ◽  
A. A. KHRUTCHINSKII ◽  
A. M. NEMILENTSAU ◽  
S. A. MAKSIMENKO ◽  
J. HERRMANN
Keyword(s):  
Harmonic Generation ◽  
High Harmonic ◽  
Kinetic Equations ◽  
Laser Pulses ◽  
Femtosecond Laser Pulses ◽  
High Order ◽  
Mechanical Approach ◽  
Optical Harmonic Generation ◽  
The Time Domain ◽  
Quantum Mechanical Approach

The high harmonic generation by a single-wall carbon nanotube (CNT) due to the interaction with femtosecond laser pulses is investigated. The analysis utilizes the quantum kinetic equations for π-electrons with both intra-band and inter-band transitions. Nonperturbative approach using numerical solution of the quantum kinetic equations in the time domain has been developed and the density of the axial electric current in CNT has been calculated. The amplitude of this current and the conversion efficiency in dependence on the number of the high-order harmonics, the CNT type, the frequency and the intensity of the driving field have been investigated.

scholarly journals On the Instability of the African Easterly Jet and the Generation of African Waves: Reversals of the Potential Vorticity Gradient

2008 ◽  
Vol 65 (7) ◽  
pp. 2130-2151 ◽  
Author(s):  
Jen-Shan Hsieh ◽  
Kerry H. Cook
Keyword(s):  
Potential Vorticity ◽  
Climate Model ◽  
Regional Climate ◽  
Baroclinic Instability ◽  
Lower Troposphere ◽  
Zonal Flow ◽  
Shear Instability ◽  
Unstable Region ◽  
African Easterly Jet ◽  
The Waves

Abstract The relationship between the generation of African easterly waves and instability growing in regions with reversed potential vorticity gradients is studied using a regional climate model. Results indicate that the convective generation of potential vorticity (PV) due to the meridional and vertical gradients of diabatic heating in the upper and lower troposphere causes a vertically elongated PV anomaly on the southern flank of the African easterly jet. This PV maximum at 9°N in the midtroposphere, together with a PV minimum near 15°N at lower levels because of dry convection over the Sahara, reverses the meridional PV gradient between 9° and 15°N, which suggests that the zonal flow may be unstable in this region. Analysis of the seasonal mean Eliassen–Palm flux for African waves indicates that wave energy generated convectively through baroclinic overturning in the upper troposphere propagates downward and triggers barotropic conversions south of the jet and baroclinic conversions below and north of the jet. The barotropic conversion of the jet initiates primarily outside of the region of strengthened reversed potential vorticity (q) gradients, suggesting that this barotropic conversion is a result of convectively induced eddies extracting energy from the zonal flow rather than the release of zonal kinetic energy to the waves in the unstable region. In contrast, the residual barotropic conversion occurs inside the region of reversed q gradients during the waves’ decaying stage when ITCZ convection weakens. The baroclinic instability in the unstable region becomes distinguishable from that due to surface temperature gradients when the surface heat flux is weak, a condition under which the African easterly jet better acts as an internal jet. Thus, this analysis indicates that the shear instability of the jet occurs to sustain the waves at the decaying stage rather than to initiate the waves, since it does not appear strong enough to reenergize the waves.

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