Application of a perturbation technique to the nonlinear equations of internal wave motion

1967 ◽  
Vol 72 (22) ◽  
pp. 5599-5611 ◽  
Author(s):  
Clement A. Griscom
Keyword(s):  
Internal Wave ◽  
Nonlinear Equations ◽  
Wave Motion ◽  
Perturbation Technique

Density Wave Measurements in a Rectangular Clarifier

1983 ◽  
Vol 18 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Mark K. Watson ◽  
R.R. Hudgins ◽  
P.L. Silveston
Keyword(s):  
Power Spectrum ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Motion ◽  
Wave Amplitude ◽  
Suspended Solids ◽  
Small Volume ◽  
Density Wave ◽  
Measure Concentration ◽  
Wave Measurements

Abstract Internal wave motion was studied in a laboratory rectangular, primary clarifier. A photo-extinction device was used as a turbidimeter to measure concentration fluctuations in a small volume within the clarifier as a function of time. The signal from this device was fed to a HP21MX minicomputer and the power spectrum plotted from data records lasting approximately 30 min. Results show large changes of wave amplitude as frequency increases. Two distinct regions occur: one with high amplitudes at frequencies below 0.03 Hz, the second with very small amplitudes appears for frequencies greater than 0.1 Hz. The former is associated with internal waves, the latter with flow-generated turbulence. Depth, velocity in the clarifier and inlet suspended solids influence wave amplitudes and the spectra. A variation with position or orientation of the probe was not detected. Contradictory results were found for the influence of flow contraction baffles on internal wave amplitude.

Internal wave motion in a periodic stratification

1979 ◽  
Vol 22 (10) ◽  
pp. 1862 ◽  
Author(s):  
Vincenzo Malvestuto
Keyword(s):  
Internal Wave ◽  
Wave Motion ◽  
Periodic Stratification

scholarly journals Modified Homotopy Perturbation Technique for the Approximate Solution of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Farooq Ahmed Shah
Keyword(s):  
Approximate Solution ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Perturbation Technique ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
New Methods ◽  
And Performance ◽  
Homotopy Perturbation Technique

We use a new modified homotopy perturbation method to suggest and analyze some new iterative methods for solving nonlinear equations. This new modification of the homotopy method is quite flexible. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations.

Internal wave motion in a non-homogeneous viscous fluid of variable depth

1971 ◽  
Vol 70 (1) ◽  
pp. 157-167 ◽  
Author(s):  
B. D. Dore
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Internal Wave ◽  
Surface Waves ◽  
Wave Motion ◽  
Variable Depth ◽  
Boundary Layer Analysis ◽  
Layer Analysis ◽  
Method Of Solution ◽  
Progressive Waves

AbstractA method of solution is given to the problem of internal wave motion in a non-homogeneous viscous fluid of variable depth. The approach is based on the inviscid theory of Keller and Mow(l) and on boundary-layer analysis. For internal progressive waves in uniform depths, it reduces essentially to the theory given by Dore(2). The present results are also applicable to surface waves when the fluid is homogeneous.

Application of Weakly Anisotropic Models of a Continuous Medium for Solving the Problems of Wave Dynamics

2000 ◽  
Vol 53 (3) ◽  
pp. 37-86 ◽  
Author(s):  
Yuriy A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Small Parameter ◽  
Wave Motion ◽  
Continuous Medium ◽  
Perturbation Technique ◽  
Anisotropic Models ◽  
Wave Dynamics ◽  
Theoretical Investigations ◽  
Anisotropic Elastic ◽  
Nonlinear Elastic ◽  
Wave Phenomena

A review of papers dealing with the investigation of wave phenomena occurring in weakly anisotropic elastic media is available in the present article. Several weakly anisotropic models of a continuous medium are presented and discussed which can be used to advantage both for solving the problems of wave dynamics and for carrying out comparison analysis of experimental data on measurements of elastic moduli of slightly anisotropic material by quasilongitudinal and quasitransverse waves with the results of the theoretical investigations. Based on these models, the behavior of harmonic and nonstationary bulk and surface waves and shock waves propagating in linear and nonlinear elastic isotropic and anisotropic media are examined. The problems are solved by the perturbation technique. The value characterizing the deviation of anisotropic elastic coefficients from isotropic moduli is chosen as a small parameter. Straight expansions of the desired values with respect to the small parameter are obtained, and the domains of nonuniformity of such expansions are indicated. For some of the problems under consideration, it has been possible to regularize the straight expansions of the values to be found by virtue of the especially selected manipulations of dilatation or translation of independent coordinates and to construct the uniformly valid solutions in the whole domain of wave motion existence. This review article contains 280 references.

Sign in / Sign up

Export Citation Format

Share Document