Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of ...Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapbunoff norm can still be obtained on the basis of variational consideration.展开更多
After my paper (Zeng, 1986b) was published and another (Zeng, 1989) was submitted to the journal, I found two papers written by Arnold (1966) and McIntyre et al. (1987) and received some reprints of Ripa’s papers (19...After my paper (Zeng, 1986b) was published and another (Zeng, 1989) was submitted to the journal, I found two papers written by Arnold (1966) and McIntyre et al. (1987) and received some reprints of Ripa’s papers (1983; 1984; 1987; 1988) in the same field. I thank Drs. Mu Mu and Pedro Ripa very much for showing and sending me these interesting papers.展开更多
An overview of hydrodynamic problems related to the broad variety of ships and sea structures involved in transportation, oil and gas exploration and production, marine operations, recovery of oil-spill, renewable ene...An overview of hydrodynamic problems related to the broad variety of ships and sea structures involved in transportation, oil and gas exploration and production, marine operations, recovery of oil-spill, renewable energy, infrastructure and aquaculture is given. An approximate hydroelastic model for wave and current induced response of a floating fish farm with circular plastic collar and net cage is discussed. Weakly nonlinear potential-flow problems such as slow-drift motions and stationkeeping, springing of ships and ringing are given special attention. Body-fixed coordinate system is recommended in weakly nonlinear potential-flow analysis of bodies with sharp corners. Dynamic ship instabilities, Mathieu-type instabilities, chaos and two-phase flow involving interface instabilities are discussed. It is advocated that slamming must be coupled with structural mechanics in order to find important time scales of the many physical effects associated with slamming and that both water entry and exit matter in describing the global wetdeck slamming effects. Further, sloshing-induced slamming in prismatic LNG tanks is perhaps the most complicated slamming problem because many fluid mechanic and thermodynamic parameters as well as hydroelasticity may matter.展开更多
文摘Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapbunoff norm can still be obtained on the basis of variational consideration.
文摘After my paper (Zeng, 1986b) was published and another (Zeng, 1989) was submitted to the journal, I found two papers written by Arnold (1966) and McIntyre et al. (1987) and received some reprints of Ripa’s papers (1983; 1984; 1987; 1988) in the same field. I thank Drs. Mu Mu and Pedro Ripa very much for showing and sending me these interesting papers.
基金supported by the Research Council of Norway through the Centres of Excellence funding scheme AMOS (Grant No. 223254)
文摘An overview of hydrodynamic problems related to the broad variety of ships and sea structures involved in transportation, oil and gas exploration and production, marine operations, recovery of oil-spill, renewable energy, infrastructure and aquaculture is given. An approximate hydroelastic model for wave and current induced response of a floating fish farm with circular plastic collar and net cage is discussed. Weakly nonlinear potential-flow problems such as slow-drift motions and stationkeeping, springing of ships and ringing are given special attention. Body-fixed coordinate system is recommended in weakly nonlinear potential-flow analysis of bodies with sharp corners. Dynamic ship instabilities, Mathieu-type instabilities, chaos and two-phase flow involving interface instabilities are discussed. It is advocated that slamming must be coupled with structural mechanics in order to find important time scales of the many physical effects associated with slamming and that both water entry and exit matter in describing the global wetdeck slamming effects. Further, sloshing-induced slamming in prismatic LNG tanks is perhaps the most complicated slamming problem because many fluid mechanic and thermodynamic parameters as well as hydroelasticity may matter.
