tailieunhanh - Fundamentals Of Geophysical Fluid Dynamics Part 2

Chất lỏng chuyển động là một môi trường liên tục do vô số phần tử chất lỏng chuyển động tạo nên, mỗi phần tử được đặc trưng bởi các đại lượng cơ bản của sự chuyển động, gọi là yếu tố chuyển động. Ví dụ như vận tốc u, áp suất thủy động p, khối lượng riêng ρ. | 58 t Fundamental Dynamics T z w Z W W y v Y V x u X U stationary coordinates rotating coordinates Fig. . A rotating coordinate frame with coordinates X Y Z T and a non-rotating frame with coordinates x y z t . The rotation vector is parallel to the vertical axis U Uz. Dt r dT UdX VdY Wdz . vs x dx ỳdy Zdz Vr X dx Y @Y Z dz . Similarly the incompressible continuity equation in preserves its form vs u vr U 0 implying that material parcel volume elements are the same in each frame with dx dX. The tracer equations in also preserve their form because of . The material acceleration transforms as Du Dt s x u yv Zw Dt X U - QY Y V QX ZW DU 2QZ X U vrP Dt r Po with P _ poQ2 X2 Y2 . 2 Earth s Rotation 59 The step from the first and second lines in is an application of . In the step to the third line use is made of and the relations DỊ OY D -nit D 0 Dt Dt Dt 1 that describe how the orientation of the transformed coordinates rotates. Since Vso VrỘ by the momentum equation in transforms into DU 20Z X U -Vrị Ộ - Z F . Dt r Po J Po After absorbing the incremental centrifugal force potential P p0 into a redefined geopotential function Ộ then has almost the same mathematical form as the original non-rotating momentum equation albeit in terms of its transformed variables except for the addition of the Coriolis force 20 X U. The Coriolis force has the effect of accelerating a rotating-frame horizontal parcel displacement in the horizontally perpendicular direction . to the right when 0 0 . This acceleration is only an apparent force from the perspective of an observer in the rotating frame since it is absent in the inertial-frame momentum balance. Hereafter the original notation . x will also be used for rotating coordinates and the context will make it clear which reference frame is being used. Alternative geometrical and heuristic discussions of this transformation are in Pedlosky Chap. .