Skip to main content Accessibility help
×
  1. Home
  2. Publications
  3. Textbooks
  4. Content Listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

38615 results in Cambridge Textbooks

Page 1874 of 1931

  • COMMENTARY

  • Juvenal
  • Edited by Susanna Morton Braund, Yale University, Connecticut
  • Book:
    Juvenal: Satires Book I
    Published online:
    28 May 2018
    Print publication:
    07 March 1996, pp 75-308

  • Summary

    SATIRE 1

    1-6 The speaker plunges straight into his self-justification, declaring that he will take revenge for all the recitations he has sat through in the past. Implicit in this apologia is a recusatio, a ‘refusal’ to tackle epic, in favour of satire. He begins with a series of four rhetorical questions, the first two introduced by the antithetical extremes semper and numquam; the second two by anaphora of inpune which reiterates numquam … reponam. The increasing length of the questions conveys his vehemence.

    I ego auditor: supply ero or sim; the omission of the verb conveys indignation, egoindicates the speaker's self-centredness. He portrays himself as an auditor at a recitation (hence 3 recitauerit and 13 lectore), a regular social event in Rome ranging from the private dinner-party (Mart. 3.45, 11.52.16-18; J. 11.179-81) to grander affairs to which the educated public was invited (Plin. Ep. 1.13). The Romans tended to listen to ‘literature’ rather than simply read it as we do. tantum ‘only’. This prepares us for his desire for revenge. reponam ‘retaliate’, literally ‘repay (a debt)’, with no object expressed here. For the idea of taking revenge for recitations, cf. Hor. Ep. 1.19.39 ego nobilium scriptorum auditor et ultor.

    2, uexatus: the past participle has a concessive or causal force, ‘though harassed’ or ‘for having been harassed’ (Woodcock §92). Theseide Cordi: the poet Cordus is unknown to us and the name possibly fictitious. His poem is an epic about the Athenian hero Theseus (cf. Aeneas - Aeneid), a hackneyed subject; totiens and rauciy ‘hoarse’, imply that it is very long.

    3-4 inpune … recitauerit … consumpserit … : fut.perf.: ‘shall he have got away scot-free with reciting … with taking up … ’. ergo: on J.'s prosody see Introduction §8. togatas: i.e. fabulae togatae, comedies with a Roman setting, as opposed to fabulae palliatae, Latin comedies with a Greek setting, such as those of Plautus and Terence. elegos: the genre of Roman love elegy bloomed in the first century BC (Gallus, Tibullus, Propertius, Ovid), but elegies were still recited and written in J.'s time (Mart. 8.70.7; Plin. Ep. 6.15).

  • CHAPTER 9 - Further reading: a guided tour

  • Uriel Frisch, Observatoire de la Cote d'Azur
  • Book:
    Turbulence
    Published online:
    28 May 2018
    Print publication:
    30 November 1995, pp 195-254

  • Summary

    Introduction

    This chapter contains supplementary material beyond the scope of the previous chapters. The choice of topics is, of course, determined largely by the author's own interests and knowledge (or lack thereof). No attempt is made, for example, to discuss supersonic and magnetohydrodynamic turbulence or turbulent convection. As for numerical simulation of turbulence, one of the most important current tools in turbulence research, it defies being summarized and requires a book of its own. Some topics are presented rather briefly, either because there is no need to elaborate them (Section 9.2 on further reading in turbulence and fluid mechanics) or because very good reviews are easily found in the literature (Section 9.3 on mathematics and Section 9.4 on dynamical systems). Other topics require more detailed presentation for lack of suitable review or just because the author's viewpoint is somewhat unusual. Section 9.5 is an introduction, occasionally rather critical, to closure, functional and diagrammatic methods. Section 9.6 is devoted to eddy viscosity, multiscale methods and renormalization; it includes some little known historical material on nineteenth century turbulence research. Finally, Section 9.7 deals mostly with recent developments in two-dimensional turbulence.

    Books on turbulence and fluid mechanics

    One of the earliest reviews of (mostly homogeneous) turbulence, was written by von Neumann (1949) in the form of a report to the Office of Naval Research, after he had attended a conference in Paris on Problems of Motion of Gaseous Masses of Cosmical Dimensions, organized jointly by the International Union of Theoretical and Applied Mechanics and the International Astronomical Union.

  • CHAPTER 7 - Phenomenology of turbulence in the sense of Kolmogorov 1941

  • Uriel Frisch, Observatoire de la Cote d'Azur
  • Book:
    Turbulence
    Published online:
    28 May 2018
    Print publication:
    30 November 1995, pp 100-119

  • Summary

    Introduction

    In previous chapters we showed how it is possible to establish certain scaling laws for fully developed turbulence by starting from unproven but plausible hypotheses and then proceeding in a systematic fashion. By ‘phenomenology’ of fully developed turbulence one understands a kind of shorthand system whereby the same results can be recovered in a much simpler way, although, of course, at the price of less systematic arguments. Phenomenology of fully developed turbulence has some associated ‘mental images’, such as the ‘Richardson cascade’ (Section 7.3), which have played a very important role in the history of the subject. After recasting the K41 theory in phenomenological language and images, it also becomes possible to grasp intuitively some of the shortcomings which may be present. A considerable part of the existing work on turbulence rests on K41 phenomenology, particularly in applied areas such as the modeling of turbulent flow. Kolmogorov himself, with Ludwig Prandtl, was one of the pioneers of this important area of research, which is beyond the scope of this book (Kolmogorov 1942; see also Batchelor 1990, Spalding 1991 and Yaglom 1994). We shall give only some examples of what can be derived by phenomenology: counting degrees of freedom (Section 7.4), comparing macroscopic and microscopic length scales (Section 7.5), finding the probability distribution function of velocity gradients (Section 7.6) and finding the law of decay of the energy (Section 7.7).

  • CHAPTER 6 - The Kolmogorov 1941 theory

  • Uriel Frisch, Observatoire de la Cote d'Azur
  • Book:
    Turbulence
    Published online:
    28 May 2018
    Print publication:
    30 November 1995, pp 72-99

  • Summary

    There is presently no fully deductive theory which starts from the Navier–Stokes equation and leads to the two basic experimental laws reported in Chapter 5. Still, it is possible to formulate hypotheses, compatible with these laws and leading to additional predictions. This was the purpose of the celebrated Kolmogorov 1941 theory (in short K41). It will here be reformulated rather freely. In Section 6.1 we shall present a modern viewpoint with emphasis on postulated symmetries rather than on postulated universality, i.e. independence on the particular mechanism by the turbulence is generated. We thereby obtain a scaling theory with an undetermined scaling exponent. The latter is determined in Section 6.2 from the ‘four-fifths’ law, an exact relation derived by Kolmogorov, also in 1941. The main results of the K41 theory are presented in Section 6.3.

    Kolmogorov 1941 and symmetries

    In Section 2.2 we made a list of known symmetries for the Navier–Stokes equation (time- and space-translations, rotations, Galilean transformations, scaling transformations, etc). What are their implications for turbulence?

    Let us begin with time-translations. At low Reynolds numbers, if the boundary conditions and any external driving force are time-independent, the flow is steady and thus does not break the time-invariance symmetry. When the Reynolds number is increased, an Andronov–Hopf bifurcation may occur. This makes the flow time-periodic and turns the continuous time-invariance symmetry into a discrete one. When the Reynolds number is increased further the flow will usually, at some point, become chaotic.

  • CHAPTER 3 - Why a probabilistic description of turbulence?

  • Uriel Frisch, Observatoire de la Cote d'Azur
  • Book:
    Turbulence
    Published online:
    28 May 2018
    Print publication:
    30 November 1995, pp 27-39

  • Summary

    There is something predictable in a turbulent signal

    In Chapter 1 we presented some pictures chosen to prompt the study of the symmetries of the Navier–Stokes equation. However important flow visualizations may be, experimental data on turbulence also include a considerable body of quantitative results. Velocimetry, the measurement of the flow velocity (or one component thereof) at a given point as a function of time, is by far the most common way of getting quantitative information. There are many different techniques of velocimetry which we shall not review here.

    Let us turn directly to an example. Fig. 3.1(a) shows a one-second signal obtained from a hot-wire probe placed in the very large wind tunnel SI of ONERA. The signal is the ‘streamwise’ velocity (component parallel to the mean flow). It is sampled five thousand times per second (5 kHz). The mean flow has been subtracted so that the signal appears to fluctuate around zero.

    What strikes us when looking at this signal?

  • (i) The signal appears highly disorganized and presents structures on all scales.

  • (ii) The signal appears unpredictable in its detailed behavior.

  • (iii) Some properties of the signal are quite reproducible.

    • Regarding item (i), we observe that in contrast to the signal shown in Fig. 2.2 which had only two scales present, the signal shown here displays structures on all scales: the eye directly perceives structures with time-scales of the order of one second, of one-tenth of a second, of one-hundredth of a second, and possibly smaller.

  • Preface

  • Uriel Frisch, Observatoire de la Cote d'Azur
  • Book:
    Turbulence
    Published online:
    28 May 2018
    Print publication:
    30 November 1995, pp xi-xiv

  • Summary

    Andrei Nikolaevich Kolmogorov's work in 1941 remains a major source of inspiration for turbulence research. Great classics, when revisited in the light of new developments, may reveal hidden pearls, as is the case with Kolmogorov's very brief third 1941 paper ‘Dissipation of energy in locally isotropic turbulence’ (Kolmogorov 1941c). It contains one of the very few exact and nontrivial results in the field, as well as very modern ideas on scaling, ideas which cannot be refuted by the argument Lev Landau used to criticize the universality assumptions of the first 1941 paper.

    Revisiting Kolmogorov's fifty-year-old work on turbulence was one goal of the lectures on which this book is based. The lectures were intended for first-year graduate students in ‘Turbulence and Dynamical Systems’ at the University of Nice–Sophia–Antipolis. My presentation deliberately emphasizes concepts which are central in dynamical systems studies, such as symmetry-breaking and deterministic chaos. The students had some knowledge of fluid dynamics, but little or no training in modern probability theory. I have therefore included a significant amount of background material. The presentation uses a physicist's viewpoint with more emphasis on systematic arguments than on mathematical rigor. Also, I have a marked preference for working in coordinate space rather than in Fourier space, whenever possible.

    Modern work on turbulence focuses to a large extent on trying to understand the reasons for the partial failure of the 1941 theory.

Page 1874 of 1931