— saueys2aW Pmn|y eee Fluid Mechanics Third Revised English Edition Course of Theoretical Physics Volume 6 COURSE OF THEORETICAL PHYSICS Volume & FLUID MECTIANTCS OLB he Oat Tong f Fi Yok ust Race erste Te Nels Hattie Que Tso Vol Raabe Pe Youd arya Boy Yala Brame of Coun Mie FLUID MECHANICS ¥y L. D. LANDAU ano EM. LIBSHITZ Volume 6 0€ Course of Thevraiad Phiee “Tranalatd fm the Bastion by J.B. SYBES ow W, IL REID PERGAMON PRESS Oxford» London + Edinburgh » New York Torumto «Sydney + Paria * Hraunschweig Petpet Pua, Mend HL Ha, Old Pesgurse Drs SARL 3 Copyright ® 1989 Pesgumon Frees Led ire gosh én gl 1959 Second fpresion 1958 Thin ingress 1965 Sole diiron in he Ua klion Ferey Pals Comnpnoy, Tn Reading, Mistalvters* Pals Au" London “oa MMS, Ouro Eiteay of Conese Card Neon ®9-808 Pret ven oie iy 3. W. Aerih La rita CONTENTS Preface to the Fgh edition Notation 1. EAL FLUIDS "The eqnaton of eontinsiy Yale's eqeation Hiytroetates ‘The condition that sonvetion ia absent Bernall’ equation The energy thee ‘the momentary fax ‘The eoneervation of eizculation Porential tho Ineompressble dnida ‘The dag forse porental How putt a hody Geety mates Long grity es ‘Waves in an facommprenie Mid TL vigcors FLUIDS The equations of motion of a vztoes Mud Energy dissipation in an incompreasbs Maid How in pipe Flow hotweca rotating cinders ‘The la of weilarty Stokes fre The lamsar eke ‘The viseasiy af mugpensions sac sfutions of rte equations ef mnsiow fie 9 vteous Haid zeny motion in vss ald Dampieg uF grivity waves TH, YURUCLENCE, Sualiiny of ates how "The ome oF table Stabllty of New between totatng finders Stability af slew in » pipe Contents Tustabilty of angencieldiscoatinuitin Fully developed turbulenoe TLoeal mrbulence ‘Vhs velocity correlation “he turbulent reginn ate che phenemenen ef separation ‘The tobulent jet ‘The turbulent wake skys’ Nearer, Totanpe uctlenee TF, ROUNDARY LAYERS Suaiiy of low in he leminar boundary layer ‘The logaichnieveloeity pul: ‘Turholent flow in pipes he tuthutent boundary layer "rhe drag os lose post streamlined bodies Induced dong ‘The Bi a «tin wing ¥. THERMAL CONDUCTION IN FLUIDS “the genemd eywaton oF heac trator ‘Thermal emaacon ian incompressible uid ‘Thernal enndvedon ivan infiaite eiee “Thera conduction a nite medinca ‘The sitar Lae for hese tavalee Hee trazafer in a Bouruy Byer Heatiog of a body in a moving ece convection vi DIFFUSION “The xpations of tad dunes Fae a stsauce of suds Gacffiste of nes tprafer and theraaldifusion [Duhosion of particle empended ina uid VIL. SURVACE POFNOMENA ‘apices foxmula Capillary wenven "The effect of adeotbed fins on the ation a a quid Comcents YUL SOUND Sound waves The eazy and msnevtuna of round wares Ratcetion and eftaeden of sound weaves Goonnstiealsesnsten Propagation oF snund in # moving wedi Ghaneristie vibrations, Spherical wares Ghlindeicat waves "The genoal set of ths wave eyaation ‘The tcl wave ‘The emission of wond ‘The recipracity principle Propagation of sonad in arabe Scattering of sound Absoeplise of sound Second viseety 1x, SHOCK waves Propagation of disembances in 9 moving gts Btendy low of gan Surfaocs of discontinuity ‘The shoek adiabatic Weak shock waves, ‘The dicetion ef variation of quantities ina shack wave Shock waves ina petost gas Oblique shock reves ‘The thickaces of shock waves ‘The isothermal avon ‘Feak tisoonannitis X. ONE-DIMENSIONAL Gas FrOWw Flow of gas through a nose Flaw of a wiacous ga fan pipe Oneutimentonalsiilarey ewe Discontinue initial oon One-dieensemal exeling raves Fonatian of Sreoatiniiea i s'soond wave Characteritice ‘Riemann invarbnes Achivary ome-dimensonat go fore ‘The propagation of strong shack waves Shallowerter theory SL got flee bres. 04 $105, 306, jor. jus. sun. pu qu. gun. in, sty. juss. ius iia gus gue gn. pa. am uz. ize. 2s, 26, $77 Contes ‘TIL INTERSECTION OF SURFACES OF DISCONTINUYY arelction waves “the incesecton of shock seen ‘he interaction of shuck waves WU) a slid cusface Supersuvic fs rune! 38 angle lin pst rales abtacle NUL ‘UWO-DIMESSIONAL GAS FLOW Potential Roe of si" Steady spe weve Clmplygivs equation: the genera problem of seedy ww dimensional gea tow ‘Chaacteites ia ated teeimensinal Nex ‘Tho EnletTrieonat equatia, Teaoanic Toe ‘Solutions of the Biler Trisomi. equation near non-singua ln of the sone sata ‘Flow atthe velisity of ound ‘The intemeutivn af deeontinatice wich the tmasiton line MIL FLOW PAST FINITE BODIES “The formtion of shock waves in eupertoni Bow post bodies Supersunic fs pasta pointed body Subweie Now pase a thin wing Supersonic ow pat a ring ‘The lasr of transane sity “The lar of hypereeni srrits XIV. FID DYNAMICS OF COMBUSTION Slow comfuston Detoaation “Tis propagation of» derontion wate “The reac Teen he diferent modes nf camnbustion Cundedetion dscontinaities XV. RETALWIRTIC FLUID BYNAMTCS “The energy-tomentum tensor ‘The esuations of rlmvistie Neid dvoacsion Rolalnitc equations fur doaipadive procoses Page 309 ‘05 aw 43 aa