Tham khảo tài liệu 'fundamentals of geophysical fluid dynamics part 6', khoa học tự nhiên, vật lý phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 174 Baroclinic and Jet Dynamics or for continuous height modes 1 iH H Jo dz Gp z Gq z with ỗp q 1 if p q and ỗp q 0 if p q . Ỗ is a discrete delta function . This is a mathematically desirable property for a set of vertical basis functions because it assures that the inverse transformation for is well defined as or sN Hh ýn Gm n m H dz-f z Gm z . m The physical motivation for making this transformation comes from measurements of large-scale atmospheric and oceanic flows that show that most of the energy is associated with only a few of the gravest vertical modes . ones with the smallest m values and correspondingly largest vertical scales . So it is more efficient to analyze the behavior of I m x y t for a few m values than of x y z t at all z values with significant energy. A more theoretical motivation is that the vertical modes can be chosen as explained in the rest of this section so each mode has a independent . decoupled from other modes linear dynamics analogous to a single fluid layer barotropic or shallow-water . In general a full dynamical decoupling between the vertical modes cannot be achieved but it can be done for some important behaviors . the Rossby wave propagation in Sec. . For specificity consider the 2-layer quasigeostrophic equations N 2 to illustrate how the Gm are calculated. The two vertical modes are referred to as barotropic m 0 and baroclinic m 1 . For a N-layer model each mode with m 1 is referred to as the mth baroclinic mode. To achieve the linear-dynamical decoupling between layers it is sufficient to diagonalize the relationship between the potential vorticity and streamfunction. That is determine the 2x2 matrix Gm n such that each modal potential vorticity contribution apart from the planetary vorticity term . qQGm py H n 1Hn qQG n py Gm n Layered Hydrostatic Model 175 depends only on its own modal streamfunction field m H n 1 HnlnGm n and not on any other I m0 with m m. This is .
