The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and differe...The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.展开更多
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems.Many of these problems are characterized by high-dimensional dynamical systems which ...We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems.Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed.The computation of the critical conditions associated with these transitions,popularly referred to as‘tipping points’,is important for understanding the transition mechanisms.We describe the two basic classes of methods of numerical bifurcation analysis,which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system.The numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are given.To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems,we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.展开更多
基金supported in part by the German Research Foundation within FOR 1182
文摘The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. ＂Optimal＂ perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2D simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria： energy of the initial condition, energy dissipation of the initial condition, and amplitude of noise in a stochastic transition. We find that the states triggering the transition are different in the three cases, but show the same scaling with Reynolds number.
基金The workshop and the work of F.W.Wubs and H.A.Dijkstra was partially sponsored by the Netherlands Organization of Scientific Research(NWO)through the NWOCOMPLEXITY project PreKursThe participation of F.I.Dragomirescu to the workshop was partially supported by a Grant of the Romanian National Authority for Scientific Research,CNCS-UEFISCDI,project number PN-II-RU-PD-2011-3-0153,31/5.10.2011.Sandia National Laboratory is a multiprogram laboratory operated by Sandia Corporation,a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000The work of J.Sanchez-Umbria was supported by projects MTM2010-16930 and 2009-SGR-67.
文摘We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems.Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed.The computation of the critical conditions associated with these transitions,popularly referred to as‘tipping points’,is important for understanding the transition mechanisms.We describe the two basic classes of methods of numerical bifurcation analysis,which differ in the explicit or implicit use of the Jacobian matrix of the dynamical system.The numerical challenges involved in both methods are mentioned and possible solutions to current bottlenecks are given.To demonstrate that numerical bifurcation techniques are not restricted to relatively low-dimensional dynamical systems,we provide several examples of the application of the modern techniques to a diverse set of fluid mechanical problems.
