简介：Usingtime-dependentcompressiblelaminarNavier-Stokesequationswithafinitevolumemethodincorporatingathird-order-accuratediscretizationscheme,theflowstructuresaroundaslenderatcertainincidencesarenumericalsimulatedandtypicalcrossflowpatternsarepresented.Atincidence10°,thesevorticalconfigurationsaredifferentatdissimilaraxiallocationsthoughtheyaresymmetric.At35°,thesymmetricvorticalstructuresstillmaintainovertheslender,yettheirinteractionatafterbodyisintensethanthatattheforebodysincethetwovorticeshavefullydevelopeddownstream.Theunstabletopologicalstructureoftrajectoryofsaddle-to-saddlepointsandmultiplelimitcyclearefurtherdiscussedintopologicalstabilitytheory.Thesestructureseasilyproducebifurcationwithperturbation.Theresultssupporttheviewofhydrodynamicinstabilityofvorticesflowfield.

简介：Lyapunov'ssecondmethodwasusedtostudythenonlinearstabilityofparallelshearflowsforstress-freeboundaries.Byintroducinganenergyfunctional,itwasshownthattheplaneCouetteandplanePoiseuilleflowsareconditionallyandasymptoticallystableforallReynoldsnumbers.Inparticular,totwo-dimensionalperturbations,bydefiningnewenergyfunctionalstheunconditionalstabilityofthebasicflowswasproved.