scholarly journals The Generation of Turbulence below Midlevel Cloud Bases: The Effect of Cooling due to Sublimation of Snow

2013 ◽  
Vol 52 (4) ◽  
pp. 819-833 ◽  
Author(s):  
Atsushi Kudo
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Vertical Shear ◽  
Cloud Base ◽  
Base Temperature ◽  
Sequence Of Events ◽  
Frontal Zones ◽  
The Stability

AbstractIn the author’s experience as a forecaster, commercial aircraft sometimes report turbulence beneath midlevel clouds that extend above upper frontal zones. Turbulence caused by Kelvin–Helmholtz instability occurs in upper frontal zones with strong vertical shear of horizontal winds. However, the turbulence seems to occur not only in the cloud bases (where upper frontal zones are) but also below the cloud bases where the vertical shear is not strong. Because those clouds are usually accompanied by precipitation that does not reach the ground, cooling by evaporation or sublimation seems to contribute to the generation of turbulence. In this paper, the mechanisms generating turbulence below midlevel cloud bases are examined by using observations and high-resolution three-dimensional numerical simulations with idealized initial conditions. The numerical simulations showed that the following sequence of events led to turbulence. Falling snow sublimated below cloud bases and cooled the air, which created absolute instability. This generated Rayleigh–Bénard convection cells. The vertical motion caused turbulence. The horizontal scale of the convection was about 800–1000 m, and the variations of vertical wind velocity were up to about 7 m s−1. The cloud base was accompanied by a virga-like distribution of snow. Sensitivity experiments showed the appropriate conditions to cause the turbulence: 1) the cloud-base temperature was between about 0° and −15°C, 2) the relative humidity in subcloud layers was sufficiently low, and 3) the stability in subcloud layers was weak. The results of the numerical simulations agreed well with the observations.

scholarly journals A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

scholarly journals Convective Instability Underneath Midlevel Clouds: Comparisons between Numerical Simulations and VHF Radar Observations

2015 ◽  
Vol 54 (11) ◽  
pp. 2217-2227 ◽  
Author(s):  
Atsushi Kudo ◽  
Hubert Luce ◽  
Hiroyuki Hashiguchi ◽  
Richard Wilson
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Radiosonde Data ◽  
Cloud Base ◽  
Very High Frequency ◽  
Vhf Radar ◽  
Turbulent Layer ◽  
Radar Observations ◽  
Mu Radar ◽  
Upper Level

AbstractDeep turbulent layers can sometimes be observed on the underside of clouds that extend above upper-level frontal zones. In a recent study based on 3D numerical simulations with idealized initial conditions, it was found that midlevel cloud-base turbulence (MCT) can result from Rayleigh–Bénard-like convection as a result of cooling by sublimation of precipitating snow into dry and weakly stratified subcloud layers. In the present study, numerically simulated MCT was compared with a turbulent layer detected by the very high-frequency (VHF) middle- and upper-atmosphere (MU) radar during the passage of an upper-level front topped by clouds. The simulations were initialized with thermodynamic parameters derived from simultaneous radiosonde data. It was found that some important features of the simulated MCT (such as the scale of convection and vertical wind velocity perturbations) agreed quantitatively well with those reported in radar observations. Even if the possibility of other generation mechanisms cannot be ruled out, the good agreement strongly suggests that the MU radar actually detected MCT.

The Role of Shearwise and Transverse Quasigeostrophic Vertical Motions in the Midlatitude Cyclone Life Cycle

2006 ◽  
Vol 134 (4) ◽  
pp. 1174-1193 ◽  
Author(s):  
Jonathan E. Martin
Keyword(s):  
Life Cycle ◽  
Vertical Motion ◽  
Development Stage ◽  
Life Cycles ◽  
Vertical Shear ◽  
Mature Stage ◽  
Motion Field ◽  
Initial Development ◽  
Frontal Zones ◽  
Oriented Parallel

Abstract The total quasigeostrophic (QG) vertical motion field is partitioned into transverse and shearwise couplets oriented parallel to, and along, the geostrophic vertical shear, respectively. The physical role played by each of these components of vertical motion in the midlatitude cyclone life cycle is then illustrated by examination of the life cycles of two recently observed cyclones. The analysis suggests that the origin and subsequent intensification of the lower-tropospheric cyclone responds predominantly to column stretching associated with the updraft portion of the shearwise QG vertical motion, which displays a single, dominant, middle-tropospheric couplet at all stages of the cyclone life cycle. The transverse QG omega, associated with the cyclones’ frontal zones, appears only after those frontal zones have been established. The absence of transverse ascent maxima and associated column stretching in the vicinity of the surface cyclone center suggests that the transverse ω plays little role in the initial development stage of the storms examined here. Near the end of the mature stage of the life cycle, however, in what appears to be a characteristic distribution, a transverse ascent maximum along the western edge of the warm frontal zone becomes superimposed with the shearwise ascent maximum that fuels continued cyclogenesis. It is suggested that use of the shearwise/transverse diagnostic approach may provide new and/or supporting insight regarding a number of synoptic processes including the development of upper-level jet/front systems and the nature of the physical distinction between type A and type B cyclogenesis events.

Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature

1978 ◽  
Vol 89 (3) ◽  
pp. 553-560 ◽  
Author(s):  
Frank M. Richter
Keyword(s):  
Rayleigh Number ◽  
Thermal Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Hexagonal Cell ◽  
Low Viscosity ◽  
Viscosity Increase ◽  
The Stability ◽  
Convection Rolls ◽  
Rayleigh Numbers

The stability of two-dimensional convection rolls has been studied as a function of the Rayleigh number, wavenumber and variation in viscosity. The experiments used controlled initial conditions for the wavenumber, Rayleigh numbers up to 25 000 and variations in viscosity up to a factor of about 20. The parameter range of stable rolls is bounded by a hexagonal-cell regime at small Rayleigh numbers and large variations in viscosity. Otherwise, the rolls are subject to the same transitions as have already been studied in fluids of uniform viscosity. The bimodal instability leading to a stable three-dimensional pattern occurs at smaller values of the average Rayleigh number as the variations in viscosity increase. This appears to be a consequence of the low viscosity of the warm thermal boundary layer associated with the original rolls.

scholarly journals Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Babatunde Idowu ◽  
Kehinde Oyeleke ◽  
Cornelius Ogabi ◽  
Olasunkanmi Olusola
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Scaling Factor ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Dimensional System

Introduction: In this work, the projective synchronization of two identical three dimensional chaotic system with quadratic and quartic non linearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factor was carried out for this category of system to show its feasibility in order to establish that no matter the type and number of nonlinearities, projective synchronization can be achieved. Numerical simulations was done to verify the above. In all kinds of chaos synchronization, projective synchronization (PS), characterized by a scaling factor that two systems synchronize proportionally, is one of the most interesting problems. It was first reported by Mainieri et al [1] , where it was stated that the two identical systems (master and slave) could be synchronized up to a scaling factor, . They further stated that the scaling factor was dependent on the chaotic evolution and initial conditions so that the ultimate state of projective synchronization was unpredictable. Aims: Is to achieve projective synchronization of two identical three Dimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling factor and also present the equilibrium and stability analysis of the system. This is to establish that projective synchronization can be achieved for varied systems with varied nonlinearities. Materials and Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, and the fourth order RungeKutta algorithm is used for numerical solutions. Results: In this work, the projective synchronization of two identical three dimensional systems with quadratic and quartic nonlinearities was achieved with the same and different scaling factor, . The equilibrium and stability analysis of the system was also presented. Numerical simulations was done to verify the above. Conclusion: The investigated projective synchronization behaviour of two identical three-dimensional system with two nonlinearities (quadratic and quartic) was achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.

Stability Control of a Three-Dimensional Passive Walker by Periodic Input Based on the Frequency Entrainment

2011 ◽  
Vol 23 (6) ◽  
pp. 1100-1107 ◽  
Author(s):  
Soichiro Suzuki ◽  
◽  
Masamichi Takada ◽  
Yuta Iwakura ◽  
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Stability Control ◽  
Human Gait ◽  
Mechanical Oscillator ◽  
Frequency Entrainment ◽  
Passive Walking ◽  
Periodic Input ◽  
The Stability ◽  
Human Gait Analysis

This study proposes a new control that stabilizes a three-dimensional (3D) passive walker without torque input at knees and ankles joints by using entrainment and a mechanical oscillator. It is difficult to stabilize a 3D biped passive walker in different environments because the range of initial conditions for stable walking is limited, so we designed a 3D biped passive walker as a passive walking platform by considering the results of human gait analysis to make the success of passive walking high. The stability of this platform was analytically determined by analyzing the frontal movement limit cycle. In the new control, the frontalmovement period is synchronized with the swing-leg period by a mechanical oscillator on the top of the walker. The mechanical oscillator controller generates a target path to synchronize oscillatormovement with swing-leg movement using frequency entrainment. The walker is stabilized when the frontal movement period was synchronized with the swing-leg period by periodic input generated by the mechanical oscillator. It was experimentally found consequently that the walker was stabilized on different slopes and flat floors.

Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability

2018 ◽  
Vol 838 ◽  
pp. 478-500 ◽  
Author(s):  
Mathieu Marant ◽  
Carlo Cossu
Keyword(s):  
Initial Conditions ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Basic Flow ◽  
Sensitivity Analyses ◽  
Mean Flow ◽  
Helmholtz Instability ◽  
Flow Distortion ◽  
Streamwise Streaks ◽  
The Stability

The optimal energy amplifications of streamwise-uniform and spanwise-periodic perturbations of the hyperbolic-tangent mixing layer are computed and found to be very large, with maximum amplifications increasing with the Reynolds number and with the spanwise wavelength of the perturbations. The optimal initial conditions are streamwise vortices and the most amplified structures are streamwise streaks with sinuous symmetry in the cross-stream plane. The leading suboptimal perturbations have opposite (varicose) symmetry. When forced with finite amplitudes these perturbations modify the characteristics of the Kelvin–Helmholtz instability. Maximum temporal growth rates are reduced by optimal sinuous perturbations and are slightly increased by varicose suboptimal ones. In contrast, the onset of absolute instability is delayed by varicose suboptimal perturbations and is slightly promoted by sinuous optimal ones. We show that if, instead of the computed fully nonlinear basic-flow distortions, the stability analysis is based on a shape assumption for the flow distortions, then opposite effects on the flow stability are predicted in most of the considered cases. These strong differences are attributed to the spanwise-uniform component of the nonlinear basic-flow distortion which, we conclude, should be systematically included in sensitivity analyses of the stability of two-dimensional basic flows to three-dimensional basic-flow perturbations. We finally show that the leading-order quadratic sensitivity of the eigenvalues to the amplitude of the streaks is preserved if the effects of the mean flow distortion are included in the sensitivity analysis.

scholarly journals Stability of the Triangular Lagrangian Solutions of the Photo Gravitational Restricted Three-Body Problem in the Three-Dimensional Case

1993 ◽  
Vol 132 ◽  
pp. 291-308
Author(s):  
Md. Ghulam Murtuza ◽  
Vijay Kumar ◽  
R.K. Choudhry
Keyword(s):  
Body Problem ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
The Stability ◽  
Three Body

AbstractThe stability of the triangular Lagrangian solutions for the photo-gravitational restricted three-body problem in the three-dimensional case is investigated for the case when the resonances are absent and also when the resonances are present. Stability is proved for most (in the sense of Lebesgue) initial conditions for all μ < μ0 except for the resonance cases.

Sign in / Sign up

Export Citation Format

Share Document