Curved jet streams University of Manchester弯喷流曼彻斯特大学.pptVIP

Vorticity Relative vorticity where U/R is the curvature term and -?U/?n the shear term Absolute vorticity where f is the Coriolis parameter. ξ written without a subscript normally refers to ξa. Potential vorticity: ratio of absolute vorticity to depth of an air column More formally we can derive Ertel’s formulation of PV: Vorticity equation We can derive the barotropic vorticity equation: Which relates stretching to changes in vorticity r Ω pt pb h Ω/h conserved Dines compensation In the stratosphere vertical motion is inhibited - so ω reaches a maximum in the mid-troposphere Divergence at jet stream level = Convergence at the surface This is how the jet stream drives the weather D D C C D C ground Tropopause Rossby waves A B C ξr 0 ξr 0 U Convergence Divergence Minimum in ξain ridge Maximum in ξa in trough So dξa/dt 0 – ξa increases as air goes from ridge to trough By conservation of PV, air columns must stretch. Stratosphere resists vertical motion so the columns stretch downwards – descending motion between A and B By Dines, this results in divergence at the surface – anticyclone tends to form. Example Upper tropospheric air flows at a speed of 30 ms-1 through a sinusoidal trough-ridge pattern at 50oN, of peak-to-peak amplitude 500 km and wavelength 3000 km. Calculate the change in absolute vorticity between ridge and trough, and derive the fractional change in the depth of an air column as it traverses the pattern. Draw a diagram to mark areas of upward and downward motion in the flow, and hence describe the effect of the pattern on the surface weather. (The radius of curvature of y = A sin(kx) is (Ak2)-1 at the crests). Example Upper tropospheric air flows at a speed of 30 ms-1 through a sinusoidal trough-ridge pattern at 50oN, of peak-to-peak amplitude 500 km and wavelength 3000 km. Calculate the change in absolute vorticity between ridge and trough, and derive the fractional change in the depth of an air column as it traverses the patter