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Các tọa độ a,b,c của phần tử chất lỏng ở thời điểm ban đầu và thời gian t, gọi là biến số Lagrange. Có thể biết được chuyển động của phần tử và quỹ đạo của nó nếu biết được x,y,z và t. | 5.3 Turbulent Baroclinic Zonal Jet 203 Reynolds stress R divergence redistributes the zonal momentum in y increasing the eastward momentum in the jet core and decreasing it at the jet edges a.k.a. negative eddy viscosity since the Reynolds stress is an up-gradient momentum flux relative to the mean horizontal shear . However R it cannot have any integrated effect since L dy@R r L Jo y Io 5.89 0 due to the meridional boundary conditions cf. Sec. 5.4 . In the bottom layer eastward momentum is transmitted downward by the isopycnal form stress i.e. D2.5 and it is balanced almost entirely by the topographic and turbulent bottom stress because the abyssal RN is quite weak. The shape for R y can be interpreted either in terms of radiating Rossby waves Sec. 5.4 or as a property of the linearly unstable eigenmodes for un y not shown here cf. Sec. 3.3.3 for barotropic eigenmodes . When Ly LT Lp R multiple jet cores can occur through the up-gradient fluxes by R each with a meridional scale near Lp. The scale relation Ly Lp is only marginally satisfied for the westerly winds but it is more likely true for the ACC and some observational evidence indicates persistent multiple jet cores there. 5.3.4 Potential Vorticity Homogenization From 5.27 5.84 and 5.88 the mean zonal momentum balance 5.82 can be rewritten more concisely as ý ũ. @. 0 vnqQG n x Fn 5.90 after doing zonal integrations by parts. This shows that the eddy-mean interaction for a baroclinic zonal-channel flow is entirely captured by the meridional eddy potential vorticity flux that combines the Reynolds stress and isopycnal form stress divergences T 1--- _ D1.5 @R1 vn qQ G.n - Hy - iiy- n 1 _ Dn-.5 Dn .s @Rn 1 ----- 2 n N - 1 Hn J @y _ DN-.5 -Dbot dRN _ N n N 5.91 Hn J @y In the vertical interior where Fn is small 5.90 indicates that v nqQG n 204 Baroclinic and Jet Dynamics is also small. Since qQG is approximately conserved following parcels in 5.26 a fluctuating Lagrangian meridional parcel displacement ry .
