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[...]... 144, 147, 148, 153, 166 , 171 boundary layer, 3–7, 161 –172, 218, 651, 687 ∼ equations, 159, 163 , 165 , 167 , 169 , 170, 218, 224, 225, 235, 238, 240, 349, 350 ∼ instability, 475 ∼ on free surface, 162 , 168 –172 ∼ on solid wall, 73, 162 167 , 591, 627, 629 ∼ separation, (see separation, boundary layer), 7 Blasius ∼, 166 , 167 , 476 Lagrangian ∼ equation, 241, 243 turbulent ∼, 541–548 boundary vorticity, 68, 143–145,... 671 vortex array, 291–295, 528 vortex breakdown, 8, 451, 502–515 AI/CI analysis of ∼, 511–515 conjugate flow theory of ∼, 507, 511 fold catastrophe theory of ∼, 506, 507 vorticity- dynamics mechanisms of ∼, 504–506 vortex collapse, 424 vortex core, 387–395, 485, 490, 496, 672, 673, 680 ∼ dynamics, 395–399, 559–561 vortex dipole, 289–291, 303–306 vortex dynamics, 1, 3–8, 56, 67, 94, 173, 451–698 vortex. .. 407–412 vortex force, 133, 601, 602, 619–621, 627–633 vortex identification (criteria), 310–320 vortex interaction, 532–535 ∼ with body, 435–441 ∼ with fluid interface, 441–445 ∼ with vortices, 418–434, 679 ∼ with wave, 524–525 vortex layer, 4, 6, 135, 165 , 173, 475, 515, 527 ∼ rolling up, 384–387, 527 Burgers ∼, 301 separated ∼, 232–234, 352 vortex merging, 680 vortex method, 187, 191, 194, 418 vortex. .. 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(Continued) normal vorticity continuity, 31 surface-force continuity, 30, 146 boundary enstrophy flux, 144, 147, 148, 153, 166 , 171 boundary layer, 3–7, 161 –172, 218, 651, 687 ∼ equations, 159, 163 , 165 , 167 , 169 , 170,. instability, 475 ∼ on free surface, 162 , 168 –172 ∼ on solid wall, 73, 162 167 , 591, 627, 629 ∼ separation, (see separation, boundary layer), 7 Blasius ∼, 166 , 167 , 476 Lagrangian ∼ equation, 241,. and transition to turbulence. In: Tatsumi T.(ed.) Turbulence and Chaotic Phenomena in fluids, North-Holland Amsterdam, 17–26. Stuart J.T. (1987) A critical review of vortex breakdown theory. Vortex