INTERNAL GRAVITY-SHEAR WAVES IN THE TROPOSPHERE: I. PHASE VELOCITIES

1966 ◽  
Vol 44 (10) ◽  
pp. 2259-2273 ◽  
Author(s):  
Keikichi Naito
Keyword(s):  
Internal Waves ◽  
Shear Waves ◽  
Horizontal Velocity ◽  
Long Wavelength ◽  
First Order ◽  
Phase Velocities ◽  
Air Density ◽  
Simple Models

The theory of internal gravity-shear waves in the troposphere is examined for two- and three-layer models of air density and horizontal velocity. It is shown that models having continuity in air density across the internal boundaries are not satisfactory for analysis involving first-order perturbations. The complexity of the analysis increases rapidly with the introduction of a gradient in the model density, and with additional layers in the model. The phase velocities of internal waves of wavelength between 100.m and 10 000 m are calculated for three simple models; the long-wavelength predictions agree favorably with observations by Gossard and Munk. No comparison is available for the shorter wavelengths.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

2007 ◽  
Vol 73 (6) ◽  
pp. 933-946
Author(s):  
S. PHIBANCHON ◽  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
First Order ◽  
Wave Solutions ◽  
Linear Waves ◽  
Weakly Nonlinear Waves

AbstractWe determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

scholarly journals The energetics of flow through a rapidly oscillating tube with slowly varying amplitude

2011 ◽  
Vol 369 (1947) ◽  
pp. 2989-3006 ◽  
Author(s):  
Robert J. Whittaker ◽  
Matthias Heil ◽  
Sarah L. Waters
Keyword(s):  
Flow Structure ◽  
Energy Budget ◽  
High Frequency ◽  
Axial Flow ◽  
Multiple Scale ◽  
Amplitude Equations ◽  
Long Wavelength ◽  
First Order ◽  
Collapsible Tubes ◽  
Flow Through

Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al . (Whittaker et al. 2010 J. Fluid Mech. 648 , 83–121. ( doi:10.1017/S0022112009992904 )) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems.

A numerical investigation of solitary internal waves with trapped cores formed via shoaling

2002 ◽  
Vol 451 ◽  
pp. 109-144 ◽  
Author(s):  
KEVIN G. LAMB
Keyword(s):  
Internal Waves ◽  
Mixed Layer ◽  
Propagation Speed ◽  
Horizontal Velocity ◽  
Buoyancy Frequency ◽  
Surface Mixed Layer ◽  
Near Surface ◽  
Flow Limit ◽  
Wave Propagation Speed ◽  
Solitary Internal Waves

The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave's propagation speed and as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

Plane Waves in Micropolar thermoelastic Materials with Voids

2016 ◽  
Vol 4 (2) ◽  
pp. 141-151 ◽  
Author(s):  
S.S. Singh ◽  
◽  
R. Lianngenga
Keyword(s):  
Linear Theory ◽  
Shear Waves ◽  
Plane Waves ◽  
Attenuation Coefficients ◽  
Phase Velocities ◽  
Dilatational Wave ◽  
Materials With Voids

The problem of plane waves in micropolar thermoelastic materials with voids has been investigated. Using the linear theory of micropolar thermoelastic materials with voids developed by Passarella [27], we come to know that there exist six waves, which are three coupled dilatational waves, two coupled shear waves and micropolar dilatational wave, in the materials. The phase velocities and their attenuation coefficients of the three coupled and micropolar dilatational and two coupled shear waves are obtained numerically and analytically.

A Lagrangian solution for internal waves

1985 ◽  
Vol 152 ◽  
pp. 191-202 ◽  
Author(s):  
Brian Sanderson
Keyword(s):  
Internal Waves ◽  
Breaking Waves ◽  
Stratified Fluid ◽  
Second Order ◽  
First Order ◽  
Lagrangian Equations ◽  
Lagrangian Solution ◽  
Lagrangian Coordinate ◽  
Sinusoidal Shape ◽  
The Difference

A perturbation procedure is used to obtain first- and second-order solutions for small-amplitude internal waves in a Lagrangian coordinate system. The first-order Lagrangian equations are formally accurate to the same order as the first-order Eulerian equations; however, they are different and the Lagrangian solution gives a more realistic wave shape. First-order Lagrangian solutions for internal waves in uniformly stratified fluid have a shape similar to that found in the second-order Eulerian solution. Wave profiles in uniformly stratified fluid exhibit broad crests and narrow troughs near the surface, a sinusoidal shape at mid-depth, and narrow crests and broad troughs near the bottom. The difference between the shape of crests and troughs grows as the wave amplitude is increased. Solutions obtained in a uniformly stratified fluid with a small bottom slope yield plausible shapes for breaking waves.

Measurement of the Propagation of Long-Wavelength Disturbances Through Turbulent Flow in Tubes

1976 ◽  
Vol 98 (1) ◽  
pp. 70-78 ◽  
Author(s):  
D. L. Margolis ◽  
F. T. Brown
Keyword(s):  
Small Amplitude ◽  
Eddy Viscosity ◽  
Flow Model ◽  
Transition Band ◽  
Low Frequencies ◽  
Long Wavelength ◽  
Phase Velocities ◽  
Eddy Viscosity Model ◽  
Turbulence Production ◽  
Factor Data

Phase velocities and attenuation factors for the propagation of small amplitude long wavelength sinusoidal disturbances, measured in a tube with turbulent liquid flow, are reported. Three frequency bands are delineated. A quasi-steady-flow model, based primarily on friction-factor data, is corroborated at low frequencies. An eddy-viscosity model, in which the energy of turbulence fails to respond in quasi-steady fashion to the sinusoidal disturbances, is corroborated at higher frequencies. In a predicted transition band unexpected and dramatic peaks in attenuation and phase velocity were found. A discussion suggests that the phenomenon may be related to deterministic aspects of turbulence production.

scholarly journals Effects of Convective Conditions and Chemical Reaction on Peristaltic Flow of Eyring-Powell Fluid

2014 ◽  
Vol 11 (4) ◽  
pp. 221-233 ◽  
Author(s):  
T. Hayat ◽  
Anum Tanveer ◽  
Humaira Yasmin ◽  
A. Alsaedi
Keyword(s):  
Reynolds Number ◽  
Chemical Reaction ◽  
Peristaltic Flow ◽  
Convective Conditions ◽  
Soret And Dufour Effects ◽  
Long Wavelength ◽  
First Order ◽  
Symmetric Channel ◽  
Order Chemical Reaction ◽  
First Order Chemical Reaction

This paper addresses the peristaltic flow of Eyring-Powell fluid in a symmetric channel with convective conditions. The Soret and Dufour effects are considered. Impact of first order chemical reaction is seen. The channel walls are of compliant nature. Long wavelength and low Reynolds number concepts are implemented. Resulting problems are solved for the stream function, temperature and concentration. Graphical results are presented and discussed in detail for various pertinent parameters.

scholarly journals Spontaneous generation of inertial waves from boundary turbulence in a librating sphere

2013 ◽  
Vol 728 ◽  
Author(s):  
Alban Sauret ◽  
David Cébron ◽  
Michael Le Bars
Keyword(s):  
Boundary Layer ◽  
Internal Waves ◽  
Stratified Flows ◽  
Rotating Flow ◽  
Spontaneous Generation ◽  
Inertial Waves ◽  
First Order ◽  
Ekman Boundary Layer ◽  
Key Features ◽  
Boundary Turbulence

AbstractIn this work, we report the excitation of inertial waves in a librating sphere even for libration frequencies where these waves are not directly forced. This spontaneous generation comes from the localized turbulence induced by the centrifugal instabilities in the Ekman boundary layer near the equator and does not depend on the libration frequency. We characterize the key features of these inertial waves in analogy with previous studies of the generation of internal waves in stratified flows from localized turbulent patterns. In particular, the temporal spectrum exhibits preferred values of excited frequency. This first-order phenomenon is generic to any rotating flow in the presence of localized turbulence and is fully relevant for planetary applications.

scholarly journals Effect of Structure of Internal Waves on Energy Transfer and Flow Control Between South and Middle Basins of Caspian Sea

2016 ◽  
Vol 10 (3) ◽  
pp. 33
Author(s):  
Ashrafoalsadat Shekarbaghani
Keyword(s):  
Energy Transfer ◽  
Internal Waves ◽  
Caspian Sea ◽  
Density Ratio ◽  
Vertical Direction ◽  
Horizontal Velocity ◽  
Theoretical Studies ◽  
Exchange Flow ◽  
Vertical Movements ◽  
Stratified Structure

In this study, role of internal waves in controlling stratified exchange flows between south and middle basins of Caspian Sea and energy transfer have been studied. The studies have been conducted based on field and theoretical studies based on numerical calculations. In this investigation, Caspian Sea has been considered as stratified and Boussinesq approximation has been considered. In equations governing the movement, cohesion and compressibility have been neglected. In the field studies, investigation of density profiles indicate signs of stratified structure which so far has been attributed to dual distribution convection phenomenon, but by considering density ratio profile and values of density ratio which are mostly negative numbers, the factor causing stratified structure of Caspian Sea can be attributed to existence of internal waves. Density field in these two basins indicate that the middle basin has higher average density compared to the south basin, this fact can cause creation of a gravity exchange flow. This exchange flow causes creation of internal waves in this sea that can have a modal structure towards vertical direction. In theoretical studies, the two middle and south basins of Caspian Sea are networked in two dimension x-z systems and equations governing movement are solved through a numerical method by using finite difference method and the vertical velocity values obtained in 290 points of the network was almost 10<sup>-6</sup> to 10<sup>-4</sup> m/s, meaning that vertical movements are much smaller. Values obtained for horizontal velocity are almost 10<sup>-3</sup> to 10<sup>-1</sup> m/s. Vertical and horizontal velocity profiles obtained from solution of these equations and also density profile obtained in four integration periods indicate that as a result of passage of gravity flow between the two basins, density in various points of the two basins change. The structure created from internal waves on the crest causes creation of shear strata observed. This structure can be effective in exchange of the two basins. Therefore, in transfer and energy conversion, identification of the created strata is of a high importance.

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