Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measur...Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance. Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals.The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space. Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition. It is demonstrated that, at hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer.展开更多
In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there...In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis.展开更多
The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian c...The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.展开更多
基金supported by the National Natural Science Foundation of China (10832001,10872145)Opening subject of State Key Laboratory of Nonlinear Mechanics,Institute of Mechanics,Chinese Academy of Sciences
文摘Experimental investigation of hypersonic boundary layer instability on a cone is performed at Mach number 6 in a hypersonic wind tunnel. Time series signals of instantaneous fluctuating surface-thermal-flux are measured by Pt-thin-film thermocouple temperature sensors mounted at 28 stations on the cone surface in the streamwise direction to investigate the development of the unstable disturbance. Wavelet transform is employed as a mathematical tool to obtain the multi-scale characteristics of fluctuating surfacethermal-flux both in the temporal and spectrum space. The conditional sampling algorithm using wavelet coefficient as an index is put forward to extract the unstable disturbance waveform from the fluctuating surface-thermal-flux signals.The generic waveform for the second mode unstable disturbance is obtained by a phase-averaging technique. The development of the unstable disturbance in the streamwise direction is assessed both in the temporal and spectrum space. Our study shows that the local unstable disturbance detection method based on wavelet transformation offers an alternative powerful tool in studying the hypersonic unstable mode of laminar-turbulent transition. It is demonstrated that, at hypersonic speeds, the dominant flow instability is the second mode, which governs the course of laminar-turbulent transition of sharp cone boundary layer.
基金Supported by the National Natural Science Foundation of China(No.11461024)Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(No.NJZZ14310)National Higher-education Institution General Research and Development Project(No.2014YB023)
文摘In this paper, a diffusive predator-prey system of Holling type functional III is considered. For one hand, we considered the possibility of the occurrence of Turing patterns of the system. Our results show that there is no Turing patterns found in the system. On the other hand, we performed detailed Hopf bifurcation analysis to the systems, and showed that the system have multiple oscillatory patterns. Moreover, we also derived the conditions to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions. Computer simulations are included to support our theoretical analysis.
基金supported by the National Natural Science Foundation of China(Nos.11101044,11271051,11229101,11301083,11371065,11471134)the Fujian Provincial Natural Science Foundation of China(No.2014J01011)+1 种基金the National Basic Research Program(No.2011CB309705)the Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized problem.Then, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.
