Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) descr...Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves(GCWs) are influenced by a linear shear flow(LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability(MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth,surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.展开更多
Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis me...Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of the NLSE is analyzed, and the region of the MI for gravity waves(the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive(negative)vorticity on MI can be balanced out by that of uniform down(up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.展开更多
Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability beh...Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.展开更多
The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered...The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered.All the obtained weakly non-linear equarions have clear physics concept. Basing on the analysis.the interaction between first order sound and vortex.and the creation of the secnd order vortex are studied and some.experiment phenomena of airfoil.flow control by sound are explained.展开更多
The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken ...The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.41830533)the National Key Research and Development Program of China(Grant Nos.2016YFC1401404 and 2017YFA0604102).
文摘Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves(GCWs) are influenced by a linear shear flow(LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability(MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth,surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2016YFC1401404 and 2017YFA0604102)the National Natural Science Foundation of China(Grant No.41830533)
文摘Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of the NLSE is analyzed, and the region of the MI for gravity waves(the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive(negative)vorticity on MI can be balanced out by that of uniform down(up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.
文摘Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.
文摘The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered.All the obtained weakly non-linear equarions have clear physics concept. Basing on the analysis.the interaction between first order sound and vortex.and the creation of the secnd order vortex are studied and some.experiment phenomena of airfoil.flow control by sound are explained.
基金supported by the National Natural Science Foundation of China (No. 51476152)
文摘The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.
