The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature PDF
Preview The Essence of Turbulence as a Physical Phenomenon: With Emphasis on Issues of Paradigmatic Nature
Arkady Tsinober The Essence of Turbulence as a Physical Phenomenon With Emphasis on Issues of Paradigmatic Nature Second Edition The Essence of Turbulence as a Physical Phenomenon Arkady Tsinober The Essence of Turbulence as a Physical Phenomenon With Emphasis on Issues of Paradigmatic Nature Second Edition 123 Arkady Tsinober Schoolof MechanicalEngineering TelAviv University TelAviv, Israel ISBN978-3-319-99530-4 ISBN978-3-319-99531-1 (eBook) https://doi.org/10.1007/978-3-319-99531-1 LibraryofCongressControlNumber:2018960751 1stedition:©SpringerScience+BusinessMediaDordrecht2014 2ndedition:©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To my wife Preface to the Second Edition Themainissueofconcernandemphasisofthepresenteditionremainsthesameas in the first edition and which is termed same way—the essence of turbulence. Likewise, the main premises for this version remain as for the first edition. These are the absence of theory based on first principles, the long-standing paradigmatic crisis and inadequate tools to handle both the problems, and the phenomenon of turbulence.Therefore,allthedifficultiesandthelikewerethesameasdescribedin the Preface to the First Edition. Moreover, the structure and the outlay remained basically the same mostly for the reader convenience. However, the motivation and the reasons to go for a second edition although similarareconsiderablydifferent.Apartfromanupdating,theseareduetotheneed for the extensions/amendments and clarifications, and reiterations in specific con- texts of key points and similar. The text of the first edition appeared to be too laconic as the book is not an introduction for the novice—the readers need a reasonable theoretical background in spite of the absence of theory and even becauseofthisasthereisnoguidingtheorybasedonfirstprinciples.Alsojudging by responses, the first edition appeared to be not an “easy reading”—but who can taketheriskofclaimingthatturbulenceiseasyespeciallywithcontinuingincrease oftheamountofpublicationsintotheexistingocean,thoughasbeforewithoutany considerable progress as concerns fundamental aspects. Moreover, many new publications belong to the category of “interpretational abuse” and alike which are “aided” by the absence of theory based on first principles. Consequently, the revision was made throughout most of the text to one degree or another. The emphasisisgiventowhatisrelatedtotheissueof“essence”includingitsmeaning and issues of paradigmatic nature and related also with special attention to the Epilogue with a triple increase in its volume. All this along with fighting the most difficult temptation of considerably increasing the volume of the book as there are manyremaininginterestingissuesworthtobeaddressed.Thevolumeofthepresent editionisincreasedby50%ascomparedtothepreviouseditionwithoutaddingany “water.”Thisalongwiththeadditionofsomeissuesnottouchedinthefirstedition. The savings in the volume are also due to the increase of the emphasis on vii viii PrefacetotheSecondEdition constructive aspects and issues of general nature, i.e. in part due to qualitative reprocessing without quantitative changes due to added pages. Finally, many of the existing texts tend to avoid most of the controversies, contradicting views, and unresolved questions (in turbulence, there are more ofthemthan“solutions”)attemptingto“smooththeangles”asmuchaspossible,in waysthatare,tomyview,bothinappropriateandmisleading.Consequently,some interpretations/views expressed in this book may appear to some as flagrant/ egregious. My apologies. Asbefore,theemphasisonthefundamentalissuesisaconsequenceoftheview that without corresponding progress in the fundamental aspects, there is little chance for progress in any applications. More generally, there is a desperate need for the physical fundamentals of a great variety of processes in nature and tech- nology in which turbulence plays a central role. For this reason, the book is of interest for the widest audience as turbulence is omnipresent indeed throughout natural sciences and technology. Tel Aviv, Israel Arkady Tsinober July 2018 Preface to the First Edition One of my hopes is that this small book will aid the readers, especially the young ones,todeveloptheirownjudgmentonthehugeliteratureinthefieldandtomake some distinction between the “essence” and “the water”. It is also among the reasons that the main themes of this small book are about fundamental issues of paradigmatic nature. The reasons for using the term “issues ofparadigmaticnature”insteadof,say,just“paradigmsinturbulence”isduetothe question on the very existence of the latter (so far). Themainpremisesandthereasons/causesthatitwaspossibletomakethisbook shortaretheabsenceoftheorybasedonfirstprinciplesandinadequatetoolstohandle boththeproblemandthephenomenonofturbulence.Obviously,forthisreasonthe “essence”appearsimplicativelyratherthanexplicitly.Thisstateofmatterswasandis continuously stressed in the community including many prominent scientists and among them by Batchelor (1962), Kolmogorov (1985), Liepmann (1979), Lumley and Yaglom (2001), von Neumann (1949), Ruelle (1990), Saffman (1978, 1991), Wiener(1938),seeAppendixforessentialquotations. Indeed,theheaviestandthemostambitiousarmoryfromtheoreticalphysicsand mathematicswastriedformorethanfiftyyears,butwithoutmuchsuccess:genuine turbulence, the big T-problem, as a physical and mathematical problem remains unsolved. Itisnotatrivialtasktoaddressthingslikeparadigmaticissues(as,infact,there are no real paradigms in fundamental research of turbulence) in a field which–in wordsofLiepmannisthegraveyardoftheories,sothatonehastorelaymainlyon theempiricalevidence.Thetaskisnotmadeeasierinviewofnoconsensusonwhat is (are) the problem(s) of turbulence, neither is there an agreement on what are/should be the aims/goals of turbulence research/theories and what would con- stitute its (their) solution. The basic properties of turbulence of fundamental nature and the essential mathematicalcomplicationsofthesubjectwereonlydisclosedbyactualexperience with the physical (and numerical) counterparts of these equations (von Neumann 1949) and of the theoretical objects in question many of which still await to be found and properly defined. Today, as before, observations remain the major ix x PrefacetotheFirstEdition exploratory tool in elucidating the properties of turbulence as a physical phe- nomenon. This is not to claim absence of theory(ies). On the contrary, there are plenty–many with qualitatively different and even contradictory premises–all agreeing well with some experimental data and even claiming rigor, but not nec- essarily for the right reasons and not based on first principles with few exceptions havingnodirectbearingontheNavier—Stokesequationsandtherebybeingmostly out of scope of this book. Paradoxically, due to the alarming overabundance and continuing major over- productionofpublicationsoftheoreticalnatureclaiming“theory”orexploitingthe term turbulence in one way or another, the above task is made easier. This is because most of such publications did not bring any real breakthrough in under- standing and have not much to do with the essence of turbulence without con- tributing to alleviating the long-lasting and continuing paradigmatic crisis in the basic research of turbulence. There was still a need for the “Saffman’s criterion” (Saffman 1978), in order to reduce the amount of references but complemented by typicallygivingsomeearlyandlatestreferences.Thebookbytheauthor(Tsinober 2009),containsmorethanonethousandreferencesonbasicissues,sothatitmaybe of help also in the context of this small book as the former is devoted also exclusively to the basic issues. Stillinsuchasituationonehastomakedifficultchoicesonwhatonehastoput on paper. It is obvious, however, that the choice has to be made out of issues of fundamental/basic nature which are based on fundamental observations/facts and closely related issues. The book islimited by incompressible flows and consists offour parts. Part I is devoted to main aspects of what is both the nature of the phenomenon and the problem of turbulence, what equations describe turbulence adequately, and also inadequately,alongwithsomecloselyrelatedissues.PartIIisaboutbriefdescription ofwhataretheoriginsofturbulenceandinabitmoredetailaboutthenatureofboth thephenomenonandtheproblemwiththeemphasisondiscussionofvariousfacets of the “undeniably statistical nature” contrasted to the “deterministic origin” of turbulenceasdescribedbypurelydeterministicnon-integrableequationsandrelated issues. This includes a discussion of the consequences of complex behavior of systemsdescribedbypurelydeterministicequationssuchasthenecessityofchange of the paradigmatic meaning of apparent randomness, stochasticity of turbulence which is roughly just the complexity due to a large number of strongly interacting degrees offreedomgoverned by the NavierStokes equations. Part III is a continu- ation of the previous part, and covers more specific issues, but not less important. What follows comprises or are related to the second part of the major qualitative universal features of turbulent flows briefly described in Chap. 1. A distinction is also made between the issues of paradigmatic nature and those which are apparently/seemingly, i.e. pseudo-paradigmatic such as the most popular cascades. Part IV consists of an The Epilogue which is a brief reiteration of the main points PrefacetotheFirstEdition xi with different more general accents and reminding that all ideas/theories, etc. pro- posed so far did fall/failed belong to the category of misconceptions and/or ill definedconcepts,seeChap.9inTsinober(2009).Thesearefollowedbyremarkson what next andan Appendix. Essential Quotations. Tel Aviv, Israel Arkady Tsinober March 2013
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