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.

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 An Iterative Method for Time-Fractional Swift-Hohenberg Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjin Li ◽  
Yanni Pang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Cauchy Problems ◽  
Initial Value ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

We study a type of iterative method and apply it to time-fractional Swift-Hohenberg equation with initial value. Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations.

scholarly journals Nonlinear Formation of the Three-Dimensional Spectrum of Mesoscale Wind Velocity and Temperature Fluctuations in a Stably Stratified Atmosphere

2018 ◽  
Vol 75 (10) ◽  
pp. 3447-3467 ◽  
Author(s):  
Igor Chunchuzov
Keyword(s):  
Wind Velocity ◽  
Internal Waves ◽  
Large Scale ◽  
Temperature Fluctuations ◽  
Time Spectrum ◽  
Analytic Form ◽  
Approximate Solutions ◽  
Horizontal Wind ◽  
Relative Temperature ◽  
Velocity Fluctuations

The theory of formation of the space–time spectrum of the mesoscale fluctuations in the horizontal wind velocity and vertical displacements (or relative temperature fluctuations) in a stably stratified atmosphere is developed. The nonlinear mechanism of the formation of the finescale layered inhomogeneities in the internal wave fields associated with the nonresonant wave–wave and wave–vortical mode interactions is described. The 3D spatial spectra of the layered inhomogeneities are obtained from the approximate solutions of Lagrangian motion equations for internal waves and subsequent transition to the Eulerian coordinate system. Because of such transition, the advection of internal waves by the wind induced by the waves and vortical modes is taken into account. The contributions from the large-scale wind disturbances and finescale layered inhomogeneities to the horizontal wavenumber spectrum of the velocity fluctuations are found. Using an analytic form obtained for the 3D spectrum, the comparison is made between the modeled one-dimensional (1D) wavenumber spectra (vertical and horizontal) of the fluctuations with the observed spectra in the upper troposphere and lower stratosphere. The observed 1D (horizontal and vertical) wavenumber spectra of the horizontal velocity fluctuations with a −3 power-law decay are explained.

EULER AND TAYLOR POLYNOMIALS METHOD FOR SOLVING VOLTERRA TYPE INTEGRO DIFFERENTIAL EQUATIONS WITH NONLINEAR TERMS

2021 ◽  
Vol 21 (2) ◽  
pp. 395-406
Author(s):  
DENİZ ELMACI ◽  
NURCAN BAYKUŞ SAVAŞANERİL ◽  
FADİME DAL ◽  
MEHMET SEZER
Keyword(s):  
Differential Equations ◽  
Matrix Equation ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Mean Value Theorem ◽  
Euler Polynomials ◽  
Algebraic Equations ◽  
Volterra Type ◽  
Collocation Points ◽  
The Matrix

In this study, the first order nonlinear Volterra type integro-differential equations are used in order to identify approximate solutions concerning Euler polynomials of a matrix method based on collocation points. This method converts the mentioned nonlinear integro-differential equation into the matrix equation with the utilization of Euler polynomials along with collocation points. The matrix equation is a system of nonlinear algebraic equations with the unknown Euler coefficients. Additionally, this approach provides analytic solutions, if the exact solutions are polynomials. Furthermore, some illustrative examples are presented with the aid of an error estimation by using the Mean-Value Theorem and residual functions. The obtained results show that the developed method is efficient and simple enough to be applied. And also, convergence of the solutions of the problems were examined. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB.

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

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Fractional Differential Equations ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Variable Order ◽  
Polynomial Solutions ◽  
Fractional Differential ◽  
Approximate Polynomial

AbstractIn this paper a new way to compute analytic approximate polynomial solutions for a class of nonlinear variable order fractional differential equations is proposed, based on the Polynomial Least Squares Method (PLSM). In order to emphasize the accuracy and the efficiency of the method several examples are included.

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