Kinematic Waves

1989 ◽  
pp. 30-33
Author(s):  
Cornelis B. Vreugdenhil
Keyword(s):  
Kinematic Waves

scholarly journals Glacier elevation and mass changes over the central Karakoram region estimated from TanDEM-X and SRTM/X-SAR digital elevation models

2016 ◽  
Vol 57 (71) ◽  
pp. 273-281 ◽  
Author(s):  
Melanie Rankl ◽  
Matthias Braun
Keyword(s):  
High Resolution ◽  
Snow Cover ◽  
Digital Elevation Models ◽  
Mass Balances ◽  
Freshwater Resources ◽  
Digital Elevation ◽  
Glacier Changes ◽  
Kinematic Waves ◽  
Elevation Changes ◽  
River Communities

AbstractSnow cover and glaciers in the Karakoram region are important freshwater resources for many down-river communities as they provide water for irrigation and hydropower. A better understanding of current glacier changes is hence an important informational baseline. We present glacier elevation changes in the central Karakoram region using TanDEM-X and SRTM/X-SAR DEM differences between 2000 and 2012. We calculated elevation differences for glaciers with advancing and stable termini or surge-type glaciers separately using an inventory from a previous study. Glaciers with stable and advancing termini since the 1970s showed nearly balanced elevation changes of -0.09 ±0.12 m a-1 on average or mass budgets of -0.01 ±0.02Gt a-1 (using a density of 850 kg m-3). Our findings are in accordance with previous studies indicating stable or only slightly negative glacier mass balances during recent years in the Karakoram. The high-resolution elevation changes revealed distinct patterns of mass relocation at glacier surfaces during active surge cycles. The formation of kinematic waves at quiescent surge-type glaciers could be observed and points towards future active surge behaviour. Our study reveals the potential of the TanDEM-X mission to estimate geodetic glacier mass balances, but also points to still existing uncertainties induced by the geodetic method.

scholarly journals Map-based methods for estimating glacier equilibrium-line altitudes

2003 ◽  
Vol 49 (166) ◽  
pp. 329-336 ◽  
Author(s):  
Katherine C. Leonard ◽  
Andrew G. Fountain
Keyword(s):  
Mass Balance ◽  
Sea Level ◽  
Equilibrium Line ◽  
Topographic Maps ◽  
Kinematic Waves ◽  
The Mean

AbstractWe examine the validity of two methods for estimating glacier equilibrium-line altitudes (ELAs) from topographic maps. The ELA determined by contour inflection (the kinematic ELA) and the mean elevation of the glacier correlate extremely well with the ELA determined from mass-balance data (observed ELA). However, the range in glacier elevations above sea level is much larger than the variation in ELA, making this correlation unhelpful. The data were normalized and a reasonable correlation (r2 = 0.59) was found between observed and kinematic ELA.The average of the normalized kinematic ELAs was consistently located down-glacier from the observed ELA, consistent with theory. The normalized mean elevation of the glacier exhibited no correlation and suggests that the toe–headwall altitude ratio is not a good approximation for the ELA. Kinematic waves had no effect on the position of the kinematic ELA. Therefore, topographic maps of glacier surfaces can be used to infer the position of the ELA and provide a method for estimating past ELAs from historic topographic maps.

On kinematic waves II. A theory of traffic flow on long crowded roads

1955 ◽  
Vol 229 (1178) ◽  
pp. 317-345 ◽  
Keyword(s):  
Traffic Flow ◽  
Functional Relationship ◽  
Vehicle Speed ◽  
Main Road ◽  
The Road ◽  
Traffic Distribution ◽  
Kinematic Waves ◽  
The Subject ◽  
The Mean ◽  
Starting Flow

This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.

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.

Kinematic waves and draw resonance in film casting process

2001 ◽  
Vol 101 (1-3) ◽  
pp. 43-54 ◽  
Author(s):  
Joo Sung Lee ◽  
Hyun Wook Jung ◽  
Hyun-Seob Song ◽  
Kwan-Young Lee ◽  
Jae Chun Hyun
Keyword(s):  
Casting Process ◽  
Film Casting ◽  
Draw Resonance ◽  
Kinematic Waves

scholarly journals On the flow of polythermal glaciers. II. Surface wave analysis

1980 ◽  
Vol 370 (1741) ◽  
pp. 155-171 ◽  
Keyword(s):  
Surface Wave ◽  
Hyperbolic Equation ◽  
Large Scale ◽  
Reduced Model ◽  
Nonlinear Hyperbolic Equation ◽  
Wave Analysis ◽  
Valley Glacier ◽  
Kinematic Waves ◽  
Surface Disturbance ◽  
Formation And Evolution

We show how the ‘reduced’ model developed in part I of this paper may be used to derive a nonlinear hyperbolic equation which describes the passage of kinematic waves along the surface of a valley glacier. Qualitative descriptions of large-scale snout movements and the formation and evolution of surface shocks are found from this approach, and earlier results of Nye (1960) are reproduced in the limit where surface disturbance amplitudes are ‘small’.

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