Hydrodynamics of the atmosphere. equations of motion on rotating earth. Vorticity, potential vorticity, and divergence. Learning Goals 1) Develop a conceptual understanding of atmospheric dynamical processes; 2) Master the foundational mathematical and physical principles of atmospheric dynamics;
of planetary vorticity. Potential vorticity (PV) can be defined as the sum of the planetary vorticity and the vorticity component parallel to the rotation vector in the rotating frame. In an inviscid fluid, PV is materially con-served and is therefore well-mixed in strongly forced environments. This leads to the development of zones of
32 wake together with the vorticity generated at the tip edge. Using the fundamental vorticity 33 equation, we evaluated the convection, stretching and tilting of vorticity in the rotating wing 34 frame to understand the generation and evolution of vorticity. Based on these data, we
geostrophic equation for ﬂuid under a rigid lid, Dq Dt = 0, q= ∇2Ψ+ fh H, (2) where f is the Coriolis parameter and qis the quasigeostrophic potential vorticity. Here Ψ = ps/fρis the quasigeostrophic streamfunction, where ps is the pressure at the rigid lid and ρis the density of the ﬂuid. With this deﬁnition, Ψ satisﬁes u= − 1 r ∂Ψ ∂θ, v=
llow water equations that describe a thin inviscid ﬂuid layer above ﬁxed topography in a frame rotating about an arbitrary axis. Karelsky et al.  executed the generalization of clas-sical shallow water theory to the case of flows over an irregular bottom. They showed that the simple self-sim-
The change in wind speed is 50 - 30 = 20 knots = 10 m/s. The change in distance is 400,000 m. The change is wind speed over distance = 10/400,000 = 0.000025 s^-1. One unit of vorticityis equal to 0.00001 s-1 or 1*10^-5 s^-1. This produces a shear vorticity value of 2.5 units.
to measure rotation, we choose to consider the the average rotation of two lines Of the element that were mutually perpendicular at the beginning of the flow. Figures (a) and (b) shows a plane fluid element of sides and that lies on the — y plane. Consider Figure (a). The axis of rotation is the z axis and OA and 0B are the two
Derivation of the momentum equation in rotating coordinates Newton’s 2 nd law (i.e. the rate of change of momentum, measured relative to coordinates fixed in space, equals the sum of all forces) can be written symbolically as: F dt daVa =∑ v (1) which means that the rate of change of absolute velocity, Va r, following the motion in an inertial