A First Course in Fluid Dynamics . By A. R. P ATERSON . Cambridge University Press, 1983. 528 pp. £37.50 (hb), £12.95 (pb). Inviscid Fluid Flows . By H. O CKENDON and A. B. T AYLER . Applied Mathematical Sciences, vol. 43. Springer, 1983. 146 pp. £10.85 (pb).

1985 ◽  
Vol 159 (-1) ◽  
pp. 533
Author(s):  
T. J. Pedley
2018 ◽  
Vol 25 (1) ◽  
pp. 125-127
Author(s):  
Ana M. Mancho ◽  
Emilio Hernández-García ◽  
Cristóbal López ◽  
Antonio Turiel ◽  
Stephen Wiggins ◽  
...  

Abstract. The third edition of the international workshop Nonlinear Processes in Oceanic and Atmospheric Flows was held at the Institute of Mathematical Sciences (ICMAT) in Madrid from 6 to 8 July 2016. The event gathered oceanographers, atmospheric scientists, physicists, and applied mathematicians sharing a common interest in the nonlinear dynamics of geophysical fluid flows. The philosophy of this meeting was to bring together researchers from a variety of backgrounds into an environment that favoured a vigorous discussion of concepts across different disciplines. The present Special Issue on Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics contains selected contributions, mainly from attendants of the workshop, providing an updated perspective on modelling aspects of geophysical flows as well as issues on prediction and assimilation of observational data and novel tools for describing transport and mixing processes in these contexts. More details on these aspects are discussed in this preface.


George Gabriel Stokes was one of the most significant mathematicians and natural philosophers of the nineteenth century. Serving as Lucasian professor at Cambridge he made wide-ranging contributions to optics, fluid dynamics and mathematical analysis. As Secretary of the Royal Society he played a major role in the direction of British science acting as both a sounding board and a gatekeeper. Outside his own area he was a distinguished public servant and MP for Cambridge University. He was keenly interested in the relation between science and religion and wrote extensively on the matter. This edited collection of essays brings together experts in mathematics, physics and the history of science to cover the many facets of Stokes’s life in a scholarly but accessible way.


1971 ◽  
Vol 17 ◽  
pp. 303-326 ◽  

Edward Armand Guggenheim was born on 11 August 1901 in Manchester; he was the elder brother of a family of three. His father, Armand Guggenheim, was of Swiss nationality but became a naturalized British subject at the age of forty-six in 1906. He was the senior partner in E. Spinner & Co., importers of Indian cotton and exporters of cotton cloth, especially khaki, and during the years 1917-1923 was also the Swiss Consul in Manchester. Edward after attending Terra Nova School, Birkdale, Southport, proceeded at the age of fourteen with a Junior Scholarship to Charterhouse. At first he was on the classical side but he switched to the science side where he came under the influence of two outstanding mathematics teachers, C. O. Tuckey and Alfred Lodge who was the brother of the more famous Oliver Lodge. His high intellectual qualities developed rapidly at Charterhouse, where he gained a Senior Scholarship in 1917 and was top of the sixth form in mathematical sciences for the period 1918-1920. His strong character and desire for authority were recognized by his election to the Head of House during his last year at School. Edward’s father died at the early age of 63, but his mother lived much longer and was an admirable hostess to Edward’s friends. After declining an Exhibition in the previous year, Edward won a Scholarship from Charterhouse to Cambridge University at Gonville and Caius College in 1920. One year later he obtained a first-class mathematical tripos in Part 1 and in 1923 a first-class in the natural science tripos, Part 2, in chemistry. One imagines that his theoretical papers were outstanding, since his practical ability at that time appears not to have been exceptionally high, particularly in preparative organic chemistry. After completion of an organic synthesis, which should have given a crystalline product, he was holding a test-tube containing a small volume of a viscous tarry material. It is reported that he contrived to collide with a perambulating demonstrator and, with studied carelessness, allowed the only record of his work to slip through his fingers with consequent breakage of the test-tube.


Acta Numerica ◽  
2016 ◽  
Vol 25 ◽  
pp. 567-679 ◽  
Author(s):  
Ulrik S. Fjordholm ◽  
Siddhartha Mishra ◽  
Eitan Tadmor

A standard paradigm for the existence of solutions in fluid dynamics is based on the construction of sequences of approximate solutions or approximate minimizers. This approach faces serious obstacles, most notably in multi-dimensional problems, where the persistence of oscillations at ever finer scales prevents compactness. Indeed, these oscillations are an indication, consistent with recent theoretical results, of the possible lack of existence/uniqueness of solutions within the standard framework of integrable functions. It is in this context that Young measures – parametrized probability measures which can describe the limits of such oscillatory sequences – offer the more general paradigm of measure-valued solutions for these problems.We present viable numerical algorithms to compute approximate measure-valued solutions, based on the realization of approximate measures as laws of Monte Carlo sampled random fields. We prove convergence of these algorithms to measure-valued solutions for the equations of compressible and incompressible inviscid fluid dynamics, and present a large number of numerical experiments which provide convincing evidence for the viability of the new paradigm. We also discuss the use of these algorithms, and their extensions, in uncertainty quantification and contexts other than fluid dynamics, such as non-convex variational problems in materials science.


2018 ◽  
Vol 75 (4) ◽  
pp. 1231-1241 ◽  
Author(s):  
Richard Rotunno ◽  
George H. Bryan

Abstract Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.


Author(s):  
Hilary Ockendon ◽  
Alan B. Tayler
Keyword(s):  

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