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.

scholarly journals Internal Acoustic Gravity Waves

1968 ◽  
Vol 23 (10) ◽  
pp. 1459-1470
Author(s):  
Alden Mclellan ◽  
F. Winterberg
Keyword(s):  
Fluid Dynamics ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Wave Motion ◽  
Ideal Gas ◽  
Acoustic Gravity Waves ◽  
Dissipative Effects ◽  
Isothermal Medium ◽  
Particle Orbits ◽  
Penetration Depths

An exhaustive analysis of wave motion in a compressible isothermal medium under the influence of gravity is presented. The dispersion relation governing the wave propagation is derived from the linearized equations of fluid dynamics and thermodynamics, and it is arranged in a nondimensional form. Penetration depths, frequency cutoffs, and particle orbits are calculated under the assumption of an ideal gas. With the nondimensional form of the dispersion relation these data can be expressed in a form independent of the constants describing a particular atmosphere. The results can be conventiently displayed on a number of diagrams valid for monatomic and diatomic gases. Dissipative effects arising from viscosity and heat conduction are neglected.

The focusing of surface waves by internal waves

1999 ◽  
Vol 384 ◽  
pp. 27-58 ◽  
Author(s):  
A. N. DONATO ◽  
D. H. PEREGRINE ◽  
J. R. STOCKER
Keyword(s):  
Surface Waves ◽  
Internal Waves ◽  
Gravity Waves ◽  
Initial Conditions ◽  
Surface Current ◽  
Analytic Solutions ◽  
Ray Theory ◽  
Linear Waves ◽  
Exact Analytic Solutions ◽  
The Waves

The surface current generated by internal waves in the ocean affects surface gravity waves. The propagation of short surface waves is studied using both simple ray theory for linear waves and a fully nonlinear numerical potential solver. Attention is directed to the case of short waves with initially uniform wavenumber, as may be generated by a strong gust of wind. In general, some of the waves are focused by the surface current and in these regions the waves steepen and may break. Comparisons are made between ray theory and the more accurate solutions. For ray theory, the occurrence of focusing is examined in some detail and exact analytic solutions are found for rays on currents with linear and quadratic spatial variation – only the latter giving focusing for our initial conditions. With regard to interpretation of remote sensing of the sea surface, we find that enhanced wave steepness is not necessarily associated with a particular phase of the internal wave, and simplistic interpretations may sometimes be misleading.

Single shock and periodic sawtooth-shaped waves in media with non-analytic nonlinearities

2018 ◽  
Vol 13 (2) ◽  
pp. 18
Author(s):  
O.V. Rudenko ◽  
C.M. Hedberg
Keyword(s):  
Mathematical Models ◽  
Nonlinear Waves ◽  
Analytic Solutions ◽  
Strongly Nonlinear ◽  
The Past ◽  
Exact Analytic Solutions ◽  
Multiphase Systems ◽  
Qualitative Level ◽  
Propagation Of Waves ◽  
Physical Phenomena

The review of new mathematical models containing non-analytic nonlinearities is given. These equations have been proposed recently, over the past few years. The models describe strongly nonlinear waves of the first type, according to the classification introduced earlier by the authors. These models are interesting because of two reasons: (i) equations admit exact analytic solutions, and (ii) solutions describe the real physical phenomena. Among these models are modular and quadratically cubic equations of Hopf, Burgers, Korteveg-de Vries, Khokhlov-Zabolotskaya and Ostrovsky-Vakhnenko type. Media with non-analytic nonlinearities exist among composites, meta-materials, inhomogeneous and multiphase systems. Some physical phenomena manifested in the propagation of waves in such media are described on the qualitative level of severity.

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.

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.

THE REFLECTION AND DUCTING OF ATMOSPHERIC ACOUSTIC–GRAVITY WAVES

1965 ◽  
Vol 43 (12) ◽  
pp. 2222-2243 ◽  
Author(s):  
M. L. V. Pitteway ◽  
C. O. Hines
Keyword(s):  
Differential Equations ◽  
Wind Velocity ◽  
Gravity Waves ◽  
Simple Form ◽  
Wave Reflection ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Horizontal Wind ◽  
Acoustic Gravity Waves ◽  
Group Velocities

A simple form is derived for the differential equations governing the propagation of acoustic–gravity waves in an atmosphere whose temperature and horizontal wind velocity vary in an arbitrary manner with height. The condition for wave reflection is discussed in some detail, and the W.K.B. approximate solutions are derived and examined. Analytic solutions are obtained for exponential and for linear variations of temperature with height, and group velocities for ducted modes are studied with these models.

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

CRYSTALLINE GRAVITY

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT
Keyword(s):  
Finite Number ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Holonomy Group ◽  
Discrete Subgroup ◽  
Analytic Solutions ◽  
Space Time ◽  
Exact Analytic Solutions ◽  
Finite Domains ◽  
Dimensional Crystal

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

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