Amplification of fast magnetosonic waves and the cut-off spectrum

1992 ◽  
Vol 48 (3) ◽  
pp. 345-357 ◽  
Author(s):  
I. M. Rutkevich ◽  
M. Mond
Keyword(s):  
Reflection Coefficient ◽  
Steady Flow ◽  
Inhomogeneous Medium ◽  
Wave Amplitude ◽  
Magnetosonic Wave ◽  
Wave Form ◽  
Critical Surface ◽  
Planar Flow ◽  
The Waves ◽  
Spectrum Of Eigenmodes

The propagation of fast magnetosonic waves in an inhomogeneous medium with planar flow in investigated. The equations describing the rays along which the waves propagate are derived, as well as the equations for the variations of the wave amplitude along the rays. These equations are solved for the case of steady flow that depends only on the radius. In addition, it is shown that a spectrum of eigenmodes may exist if the steady flow contains a shock. For that purpose, the reflection coefficient of a fast magnetosonic wave form a shock is derived, and it is shown that the waves can be localized in a region bounded by a shock and a critical surface. A criterion for stability of the spectrum is derived.

An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri

1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez
Keyword(s):  
Wave Length ◽  
Vertical Axis ◽  
The Other ◽  
Wave Form ◽  
Stationary Waves ◽  
Retrograde Motion ◽  
Time Signals ◽  
Group Form ◽  
Triangular Network ◽  
The Waves

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.

scholarly journals INTERACTION OF WAVES AND A TURBULENT CURRENT

1976 ◽  
Vol 1 (15) ◽  
pp. 22 ◽  
Author(s):  
J.D.A. Van Hoften ◽  
S. Karaki
Keyword(s):  
Experimental Investigation ◽  
Gravity Waves ◽  
Wave Amplitude ◽  
Current System ◽  
Bottom Shear Stress ◽  
Wave Dissipation ◽  
Wave Channel ◽  
Amplitude Attenuation ◽  
Current Interaction ◽  
The Waves

An experimental investigation was made to study wave-current interaction. Wave amplitude attenuation was measured along a laboratory wave channel to compare wave dissipation with and without flow. Mean, wave, and turbulent velocities were also measured to determine the modifications of the flow imposed by the gravity waves propogating with the current. The process of energy transfer in the wave current system was studied. Energy was found to be extracted from the waves, diffused downward and dissipated by an increase in bottom shear stress.

Deformation Analysis and Reliability Assessment of the Ship Hull in Irregular Waves

2013 ◽  
Author(s):  
Pengyao Yu ◽  
Guoqing Feng ◽  
Huilong Ren ◽  
Xiaodong Zhao
Keyword(s):  
Finite Element ◽  
Wave Amplitude ◽  
Ship Hull ◽  
Irregular Waves ◽  
Relative Deformation ◽  
Linear Potential ◽  
Regular Wave ◽  
Analysis Method ◽  
Deformation Response ◽  
The Waves

When the ship navigates in the sea, the dynamic deformation of the ship hull will be induced by the waves. The relative large deformation of the ship hull induced by the waves may affect the operation of some certain equipment. In order to keep the equipment operating normally, the influence of the ship deformation should be evaluated. The method for the calculation and analysis of the ship deformation is discussed here. The wave loads of the ship in unit regular wave amplitude are calculated based on 3-D linear potential flow theory. The sea pressure and inertial force of the ship are obtained and applied to the global finite element model of the ship. Under the quasi-static assumption, the structural deformation response in unit regular wave amplitude is calculated with the use of finite element analysis. Then, the amplitude frequency response of the relative deformation between two arbitrary positions in the hull is achieved. The history of the deformation can be obtained based on the simulation of deformation response in irregular waves or the modal superposition method. With the help of spectral analysis method, the spectrum of the relative deformation between two arbitrary positions in the hull may be obtained. The statistical analysis of ship hull deformation in the short-term sea state is realized. Considering the critical value of ship deformation, the reliability analysis method is adopted to assess the ability of hull to resist the deformation.

The Effect of Mass Flow Rate on the Reflection Behaviour of Small-Amplitude Pressure Waves from Duct Terminations

1978 ◽  
Vol 20 (4) ◽  
pp. 229-235 ◽  
Author(s):  
M. A. Ali ◽  
K. F. Gill ◽  
B. W. Imrie
Keyword(s):  
Reflection Coefficient ◽  
Steady Flow ◽  
Mass Flow ◽  
Small Amplitude ◽  
Binary Sequence ◽  
Low Flow ◽  
Correlation Technique ◽  
Pressure Waves ◽  
Flow Number ◽  
Wide Range

This paper describes an investigation of the reflection characteristics of small-amplitude pressure waves in the presence of steady flow in a duct. A correlation technique employing pseudo-random binary-sequence (p.r.b.s.) pulses is introduced. A theoretical model of the process is presented together with considerations of correlation analysis. The results show agreement between the experimental results and the model; they further indicate that, in the presence of a steady flow component, there is a significant effect on the reflection behaviour of plane pressure waves for a reduction in the area terminating a duct. The experimental technique is effective at very low flow velocities (Mach number = 0·02, Reynolds number = 30 times 103) and establishes a linear relationship between a reflection coefficient and a non-dimensional mass flow number. A reflection coefficient of flow is introduced as an appropriate parameter for such conditions. The procedure could be applied to a wide range of industrial processes to determine flow coefficients of duct elements in situ, to optimize flow processes and to locate leakage flows.

scholarly journals Instability of flow with suspended sediment in an inclined channel

1991 ◽  
Vol 13 (1) ◽  
pp. 1-8
Author(s):  
Nguyen Van Diep ◽  
Dang Huu Chung
Keyword(s):  
Nonlinear Analysis ◽  
Steady Flow ◽  
Suspended Sediment ◽  
Nonlinear Evolution ◽  
Sediment Concentration ◽  
Linear Analysis ◽  
Inclined Channel ◽  
Inclined Angle ◽  
The Waves ◽  
Unchanged Form

In this work the authors had studied the instability and nonlinear evolution of steady flow suspended sediment in inclined channel with fixed and plane bed. With the linear analysis- it has been shown that at the critical inclined angle, an arbitrary disturbance will be splinted in three modes 3F0/2, F0/2, F0, in which F0/2 and F0 propagate downstream and deaden while mode 3F0/2 propagates downstream and its form is unchanged. In particular the waves of sediment concentration always propagate downstream with velocity F0 and unchanged form. The nonlinear analysis has shown that the concentration waves propagate downstream with velocity F and deaden when the time t is large.

The front runner in roll waves produced by local disturbances

2021 ◽  
Vol 932 ◽  
Author(s):  
Boyuan Yu ◽  
Vincent H. Chu
Keyword(s):  
Shock Waves ◽  
Numerical Scheme ◽  
Wave Amplitude ◽  
Laboratory Data ◽  
Periodic Waves ◽  
Wave Group ◽  
Clear Water ◽  
Roll Waves ◽  
Simulation Results ◽  
The Waves

Roll waves produced by a local disturbance comprise a group of shock waves with steep fronts. We used a robust and accurate numerical scheme to capture the steep fronts in a shallow-water hydraulic model of the waves. Our simulations of the waves in clear water revealed the existence of a front runner with an exceedingly large amplitude – much greater than those of all other shock waves in the wave group. The trailing waves at the back remained periodic. Waves were produced continuously within the group due to nonlinear instability. The celerity depended on the wave amplitude. Over time, the instability produced an increasing number of shock waves in an ever-expanding wave group. We conducted simulations for three types of local disturbances of very different duration over a range of amplitudes. We interpreted the simulation results for the front runner and the trailing waves, guided by an analytical solution and the laboratory data available for the smaller waves in the trailing end of the wave group.

scholarly journals Head-on collision of internal waves with trapped cores

2017 ◽  
Vol 24 (4) ◽  
pp. 751-762 ◽  
Author(s):  
Vladimir Maderich ◽  
Kyung Tae Jung ◽  
Kateryna Terletska ◽  
Kyeong Ok Kim
Keyword(s):  
Wave Amplitude ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Class Iii ◽  
Navier Stokes Equations ◽  
Linear Waves ◽  
Non Linear ◽  
Conservation Of Momentum ◽  
Run Up ◽  
The Waves

Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier–Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly non-linear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

On steady non-breaking downstream waves and the wave resistance – Stokes’ method

2017 ◽  
Vol 815 ◽  
pp. 388-414
Author(s):  
Dmitri V. Maklakov ◽  
Alexander G. Petrov
Keyword(s):  
Integral Equations ◽  
Wave Amplitude ◽  
Wave Resistance ◽  
Quadratic System ◽  
System Of Equations ◽  
Two Dimensional ◽  
Method Of Integral Equations ◽  
Analytical Formulae ◽  
The Mean ◽  
The Waves

In this work, we have obtained explicit analytical formulae expressing the wave resistance of a two-dimensional body in terms of geometric parameters of nonlinear downstream waves. The formulae have been constructed in the form of high-order asymptotic expansions in powers of the wave amplitude with coefficients depending on the mean depth. To obtain these expansions, the second Stokes method has been used. The analysis represents the next step of the research carried out in Maklakov & Petrov (J. Fluid Mech., vol. 776, 2015, pp. 290–315), where the properties of the waves have been computed by a numerical method of integral equations. In the present work, we have derived a quadratic system of equations with respect to the coefficients of the second Stokes method and developed an effective computer algorithm for solving the system. Comparison with previous numerical results obtained by the method of integral equations has been made.

Padé approximants and nonlinear waves

1979 ◽  
Vol 21 (3) ◽  
pp. 549-571 ◽  
Author(s):  
F. J. Romerias ◽  
J. P. Dougherty
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Nonlinear Waves ◽  
Wave Amplitude ◽  
Plane Waves ◽  
Electron Plasma ◽  
Cold Electron ◽  
Small Wave ◽  
The Waves ◽  
Approximant Method

The perturbation solution of the ordinary differential equations that describe exact nonlinear travelling plane waves leads to asymptotic expansions in powers of the (small) wave amplitude for both the proffle and the frequency of the waves. This paper shows how the Padé approximant method can be used to extend the validity of those expansions to larger amplitudes. The method is applied to the Duffing equation and to two types of nonlinear waves in a cold electron plasma: longitudinal oscillations and coupled transverse–longitudinal relativistic waves.

Breaking and broadening of internal solitary waves

2000 ◽  
Vol 413 ◽  
pp. 181-217 ◽  
Author(s):  
JOHN GRUE ◽  
ATLE JENSEN ◽  
PER-OLAV RUSÅS ◽  
J. KRISTIAN SVEEN
Keyword(s):  
Solitary Waves ◽  
Wave Breaking ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Constant Density ◽  
Image Velocimetry ◽  
The Waves

Solitary waves propagating horizontally in a stratified fluid are investigated. The fluid has a shallow layer with linear stratification and a deep layer with constant density. The investigation is both experimental and theoretical. Detailed measurements of the velocities induced by the waves are facilitated by particle tracking velocimetry (PTV) and particle image velocimetry (PIV). Particular attention is paid to the role of wave breaking which is observed in the experiments. Incipient breaking is found to take place for moderately large waves in the form of the generation of vortices in the leading part of the waves. The maximal induced fluid velocity close to the free surface is then about 80% of the wave speed, and the wave amplitude is about half of the depth of the stratified layer. Wave amplitude is defined as the maximal excursion of the stratified layer. The breaking increases in power with increasing wave amplitude. The magnitude of the induced fluid velocity in the large waves is found to be approximately bounded by the wave speed. The breaking introduces a broadening of the waves. In the experiments a maximal amplitude and speed of the waves are obtained. A theoretical fully nonlinear two-layer model is developed in parallel with the experiments. In this model the fluid motion is assumed to be steady in a frame of reference moving with the wave. The Brunt-Väisälä frequency is constant in the layer with linear stratification and zero in the other. A mathematical solution is obtained by means of integral equations. Experiments and theory show good agreement up to breaking. An approximately linear relationship between the wave speed and amplitude is found both in the theory and the experiments and also when wave breaking is observed in the latter. The upper bound of the fluid velocity and the broadening of the waves, observed in the experiments, are not predicted by the theory, however. There was always found to be excursion of the solitary waves into the layer with constant density, irrespective of the ratio between the depths of the layers.

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