S5.4 secondary circulation and spin down 次级环流和旋转减弱 presentation演讲稿由刀豆文库小编整理，希望给你工作、学习、生活带来方便，猜你可能喜欢“circulation缈昏瘧”。
Good evening everyone.My topic is section five point four, secondary circulation and spin down.[click] There are five parts in my presentation, key words, secondary circulation, spin down, Physical meaning,and summary.[click]Firstly, let us see the key words.The secondary circulation is a circulation superposed on the primary circulation by the physical constraints of the system.And the spin down is a mechanism for destroying vorticity in a rotating atmosphere by losing angular momentum.The Angular momentum measures an object's tendency to continue to spin.And angular momentum is equal to the vector product among ma, velocity and distance(from point object is spinning or orbiting around)[click] Both the mixed-layer solution and the Ekman spiral solution indicate that in the planetary boundary layer the horizontal wind has a component directed toward lower preure.As the rad arrows shown in Fig.5.6, [click]this implies ma convergence in a cyclonic circulation and ma divergence in an anticyclonic circulation, which by ma continuity requires vertical motion out of and into the boundary layer, respectively.[click] In order to estimate the magnitude of this induced vertical motion, we note that if vg = 0 so that ug is independent of x, the cro isobaric ma transport per unit area at any level in the boundary layer is given by ρ0v.For the Ekman spiral, it is given by the equation five point thirty five, where De is equal to πdivide byγ, and is the Ekman layer depth defined in Section 5.3.4.[click]Integrating the mean continuity equation(5.13)through the depth of the boundary layer gives equation five point thirty six.Auming that w(0)= 0, and vg = 0 , and comparing with(5.35)that the ma transport at the top of the Ekman layer is given by equation five point thirty seven.[click]Noting that minus partial ug divide by partial y is just the geostrophic vorticity in this case.we find equation five point thirty eight after substituting into(5.36), where we have neglected the variation of density with height in the boundary layer and have aumed that one plus e to minus π is approximately equal to 1.Hence, we obtain the important result that the vertical velocity at the top of the boundary layer is proportional to the geostrophic vorticity.In this way the effect of boundary layer fluxes is communicated directly to the free atmosphere through a forced secondary circulation.This proce is often referred to as boundary layer pumping.It only occurs in rotating fluids and is one of the fundamental distinctions between rotating and nonrotating flow.For a typical synoptic-scale system , the vertical velocity given by(5.38)is of the order of a few millimeters per second.[click] An analogous boundary layer pumping is responsible for the decay of the circulation created when a cup of tea is stirre.Radial inflow takes place near the bottom of the cup.By continuity of ma, the radial inflow in the bottom boundary layer requires upward motion and a slow compensating outward radial flow throughout the remaining depth of the tea.This slow outward radial flow approximately conserves angular momentum, and by replacing high angular momentum fluid by low angular momentum fluid serves to spin down the vorticity in the cup far more rapidly than could mere diffusion.[click] For synoptic-scale motions the barotropic vorticity equation(4.24)can be written approximately as equation four point twenty four.where we have neglected ζg compared to f in the divergence term and have also neglected the latitudinal variation of f.Recalling that the geostrophic vorticity is independent of height in a barotropic atmosphere,(5.39)can be integrated easily from the top of the Ekman layer(z = De)to the tropopause(z = H)to give equation five point forty.Substituting for w(De)from(5.38), auming that w(H)= 0 and that H is much lager than De, the equation(5.40)may be written as equation five point forty one.This equation may be integrated in time to give equation five point forty two.where ζg(0)is the value of the geostrophic vorticity at time t = 0, and τe is the time that it takes the vorticity to decrease to e −1 of its original value.[click] This e-folding time scale is referred to as the barotropic spin-down time.Taking typical values of the parameters as follows, we find that τe approximates 4 days.Thus, for nidlatitude synoptic-scale disturbances in a barotropic atmosphere, the spin-down time is a few days.This decay time scale should be compared to the time scale for ordinary viscous diffusion.For viscous diffusion the time scale can be estimated from scale analysis of the diffusion equation five point forty three.So that for the above value of H and Km, the diffusion time scale is thus about 100 days.Hence, in the absence of convective clouds the spin-down proce is a far more effective mechanism for destroying vorticity in a rotating atmosphere than eddy diffusion.[click] Physically the spindown proce in the atmospheric case is primarily the Coriolis force that balances the preure gradient force away from the boundary.The Coriolis force for the outward-flowing fluid is directed clockwise, and this force thus exerts a torque opposite to the direction of the circulation of the vortex.In the case of boundary layer, viscosity is responsible for the presence of the secondary circulation.In a stably stratified baroclinic atmosphere, the buoyancy force will act to suppre vertical motion.So the interior secondary circulation will decrease with altitude, shown in Fig.five point eight.This flow will rather quickly spin down the vorticity at the top of Ekman layer that is enough to bring ζg to zero.The result is a baroclinic vortex with a vertical shear of the azimuthal velocity that is very strong.[click]This vertical shear of the geostrophic wind requires a radial temperature gradient that is in fact produced during the spin-down phase by adiabatic cooling of the air forced out of the Ekman layer.[click] Finally, let us see my summary.By the physical constraints of the system, a secondary circulation will occur.It only occurs in rotating fluids.And in boundary layer, viscosity is responsible for the presence of it.The secondary circulation can spin down an atmosphere vortex.The e-folding time is referred to as the barotropic spin-down time.The secondary circulation in the baroclinic atmosphere serves two purposes: it changes the azimuthal velocity field of the vortex through the action of the Coriolis force and it changes the temperature distribution so that a thermal wind balance is always maintained between the vertical shear of the azimuthal velocity and the radial temperature gradient.That’s all.Thanks four your attention, thank you!
