scholarly journals On basic equations and kinematic-wave theory of separation processes in suspensions with gravity, centrifugal and Coriolis forces

2017 ◽  
Vol 229 (2) ◽  
pp. 779-794 ◽  
Author(s):  
Wilhelm Schneider
Keyword(s):  
Wave Theory ◽  
Kinematic Wave ◽  
Separation Processes ◽  
Coriolis Forces ◽  
Basic Equations

scholarly journals Mathematical analogies in physics. Thin-layer wave theory

2014 ◽  
Vol 57 (1) ◽  
Author(s):  
José M. Carcione ◽  
Vivian Grünhut ◽  
Ana Osella
Keyword(s):  
Quantum Mechanics ◽  
Thin Layer ◽  
Quantum Physics ◽  
Constitutive Relations ◽  
Normal Incidence ◽  
Wave Theory ◽  
Transverse Magnetic ◽  
Momentum Conservation ◽  
Tunnel Effect ◽  
Basic Equations

<p>Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law). In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies) between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect). The analogy is mainly illustrated with geophysical examples of propagation of S (shear), P (compressional), TM (transverse-magnetic) and TE (transverse-electric) waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.</p>

On kinematic waves I. Flood movement in long rivers

1955 ◽  
Vol 229 (1178) ◽  
pp. 281-316 ◽  
Keyword(s):  
Shock Waves ◽  
Equations Of Motion ◽  
Functional Relation ◽  
Wave Theory ◽  
Observation Point ◽  
Rate Of Change ◽  
Kinematic Wave ◽  
Unit Distance ◽  
Kinematic Waves ◽  
The Waves

In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k . In view of this, these waves are described as ‘kinematic’, as distinct from the classical wave motions, which depend also on Newton’s second law of motion and are therefore called ‘dynamic’. Kinematic waves travel with the velocity dq/dk , and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form ‘kinematic shock waves ’. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q ) terms neglected by the flow concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in §1. One example included in §1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (§2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (§3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the ‘Froude numbers’ appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in §3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the ‘monoclinal flood wave’ which is well known in the literature of this subject. The final sections (§§4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In §4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In §5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.

scholarly journals The Response Time of Glaciers in Iceland to Changes in climate

1986 ◽  
Vol 8 ◽  
pp. 100-101 ◽  
Author(s):  
Tómas Jóhannesson
Keyword(s):  
Response Time ◽  
Time Variation ◽  
Little Ice Age ◽  
Wave Theory ◽  
Warm Period ◽  
Ice Age ◽  
Kinematic Wave

Records of the time variation of the terminus position of Icelandic glaciers since 1700 show clear responses to the little ice age and to the warm period from 1930 to 1960. These data are used to deduce limits for the response time of the glaciers. The response time turns out to be of the order of one or two hundred years. This is much shorter than the “long response time” of Nye’s kinematic wave theory.

scholarly journals Response of valley glaciers to climate change and kinematic waves: a study with a numerical ice-flow model

1995 ◽  
Vol 41 (137) ◽  
pp. 142-152 ◽  
Author(s):  
R. S. W. van de Wal ◽  
J. Oerlemans
Keyword(s):  
Climate Change ◽  
Wave Velocity ◽  
Flow Model ◽  
Flow Direction ◽  
Wave Theory ◽  
Kinematic Wave ◽  
Kinematic Waves ◽  
Ice Velocity ◽  
Basal Shear ◽  
Wave Phenomena

AbstractA simple numerical flow model that couples mass divergence directly to basal shear stress as the only driving force is used to study kinematic waves. Kinematic waves that result from a perturbation of the ice thickness or mass balance are compared with the linear kinematic-wave theory of Nye/Weertman. The wave velocity is calculated as a function of the wavelength and amplitude of a perturbation. The modelled wave velocity is typically 6–8 times the vertically averaged velocity in the flow direction whereas linear theory predicts a factor of only 5.An experiment with the geometry of Hintereisferner, Austria, shows that the increase in the local ice velocity during a kinematic wave is about 10% but varies slightly depending on the position along the glacier and the amplitude of the kinematic wave. Kinematic waves are thus hard to detect from velocity measurements.The dynamics of simple continuity models are rich enough to support a variety of kinematic-wave phenomena. Such models are a useful tool to study the response of valley glaciers to climate change.

scholarly journals Response of valley glaciers to climate change and kinematic waves: a study with a numerical ice-flow model

1995 ◽  
Vol 41 (137) ◽  
pp. 142-152 ◽  
Author(s):  
R. S. W. van de Wal ◽  
J. Oerlemans
Keyword(s):  
Climate Change ◽  
Wave Velocity ◽  
Flow Model ◽  
Flow Direction ◽  
Wave Theory ◽  
Kinematic Wave ◽  
Kinematic Waves ◽  
Ice Velocity ◽  
Basal Shear ◽  
Wave Phenomena

AbstractA simple numerical flow model that couples mass divergence directly to basal shear stress as the only driving force is used to study kinematic waves. Kinematic waves that result from a perturbation of the ice thickness or mass balance are compared with the linear kinematic-wave theory of Nye/Weertman. The wave velocity is calculated as a function of the wavelength and amplitude of a perturbation. The modelled wave velocity is typically 6–8 times the vertically averaged velocity in the flow direction whereas linear theory predicts a factor of only 5.An experiment with the geometry of Hintereisferner, Austria, shows that the increase in the local ice velocity during a kinematic wave is about 10% but varies slightly depending on the position along the glacier and the amplitude of the kinematic wave. Kinematic waves are thus hard to detect from velocity measurements.The dynamics of simple continuity models are rich enough to support a variety of kinematic-wave phenomena. Such models are a useful tool to study the response of valley glaciers to climate change.

Use of kinematic wave theory to model irrigation on cracking soil

1997 ◽  
Vol 18 (1) ◽  
pp. 1-10 ◽  
Author(s):  
N. R. Austin ◽  
J. Bernard Prendergast
Keyword(s):  
Wave Theory ◽  
Kinematic Wave
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