scholarly journals Analysis of a Generalized Lorenz–Stenflo Equation

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Fuchen Zhang ◽  
Rui Chen ◽  
Xiusu Chen
Keyword(s):  
Gravity Waves ◽  
Finite Amplitude ◽  
Functional Approach ◽  
Engineering Science ◽  
Hyperchaotic System ◽  
Numerical Examples ◽  
Acoustic Gravity Waves ◽  
Attractive Sets ◽  
Globally Attractive ◽  
Hyperchaotic Systems

Although the globally attractive sets of a hyperchaotic system have important applications in the fields of engineering, science, and technology, it is often a difficult task for the researchers to obtain the globally attractive set of the hyperchaotic systems due to the complexity of the hyperchaotic systems. Therefore, we will study the globally attractive set of a generalized hyperchaotic Lorenz–Stenflo system describing the evolution of finite amplitude acoustic gravity waves in a rotating atmosphere in this paper. Based on Lyapunov-like functional approach combining some simple inequalities, we derive the globally attractive set of this system with its parameters. The effectiveness of the proposed methods is illustrated via numerical examples.

scholarly journals Complex Dynamical Behaviors of Lorenz-Stenflo Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 513 ◽  
Author(s):  
Fuchen Zhang ◽  
Min Xiao
Keyword(s):  
Gravity Waves ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Acoustic Gravity Waves ◽  
Dynamical Behaviors ◽  
Lyapunov Function Method ◽  
Attractive Sets ◽  
Globally Attractive ◽  
Generalized Lyapunov Function ◽  
Theoretical Results

A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

Finite-amplitude acoustic-gravity waves: exact solutions

2015 ◽  
Vol 767 ◽  
pp. 52-64 ◽  
Author(s):  
Oleg A. Godin
Keyword(s):  
Gravity Waves ◽  
Wave Motion ◽  
Analytic Solutions ◽  
Finite Amplitude ◽  
Compressible Fluids ◽  
Acoustic Gravity Waves ◽  
Strongly Nonlinear ◽  
Exact Analytic Solutions ◽  
Nonlinear Hydrodynamics ◽  
Hydrodynamics Equations

AbstractWe consider strongly nonlinear waves in fluids in a uniform gravity field, and demonstrate that an incompressible wave motion, in which pressure remains constant in each fluid parcel, is supported by compressible fluids with free and rigid boundaries. We present exact analytic solutions of nonlinear hydrodynamics equations which describe the incompressible wave motion. The solutions provide an extension of the Gerstner wave in an incompressible fluid with a free boundary to waves in compressible three-dimensionally inhomogeneous moving fluids such as oceans and planetary atmospheres.

On the dynamics of a modified Lorenz–Stenflo system

2020 ◽  
Vol 31 (07) ◽  
pp. 2050104
Author(s):  
Paulo C. Rech
Keyword(s):  
Dynamical System ◽  
Gravity Waves ◽  
Cross Sections ◽  
Continuous Time ◽  
Periodic Structures ◽  
Finite Amplitude ◽  
Variable Formula ◽  
Acoustic Gravity Waves ◽  
Dynamical Behaviors ◽  
New System

The Lorenz–Stenflo system is a four-parameter four-dimensional autonomous nonlinear continuous-time dynamical system, derived to model the time evolution of finite amplitude acoustic gravity waves in a rotating atmosphere. In this paper, we propose a modified Lorenz–Stenflo system, where the variable [Formula: see text] in the fourth equation of the original Lorenz–Stenflo system was replaced by [Formula: see text]. We investigate cross-sections of the parameter-space of this new system, characterizing regions of different dynamical behaviors. We show that the aforementioned replacement may promote the emergence of organized periodic structures in places of these cross-sections, where they did not exist before modification.

Acoustic-Gravity Waves in Whirling Polar Thermosphere

2015 ◽  
Vol 47 (9) ◽  
pp. 10-22 ◽  
Author(s):  
Yuriy P. Ladikov-Roev ◽  
Oleg K. Cheremnykh ◽  
Alla K. Fedorenko ◽  
Vladimir E. Nabivach
Keyword(s):  
Gravity Waves ◽  
Acoustic Gravity Waves

scholarly journals Acoustic–gravity waves from multi-fault rupture

2021 ◽  
Vol 915 ◽  
Author(s):  
Byron Williams ◽  
Usama Kadri ◽  
Ali Abdolali
Keyword(s):  
Gravity Waves ◽  
Fault Rupture ◽  
Acoustic Gravity Waves

Abstract

Investigation of acoustic gravity waves in the upper atmosphere by the artificial periodic inhomogeneities method at Nizhny Novgorod

1996 ◽  
Vol 39 (3) ◽  
pp. 224-228
Author(s):  
N. V. Bakhmet'eva ◽  
V. V. Belikovich ◽  
E. A. Benediktov ◽  
V. N. Bubukina ◽  
N. P. Goncharov ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Upper Atmosphere ◽  
Acoustic Gravity Waves ◽  
Periodic Inhomogeneities

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

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