Sarah C. Jones 1995 ¡  Understand mechanisms responsible for behavior of TCs in vertical shear ¡  Shear inhibits TC development ¡  Potential mechanism to oppose the tendency of shear to destroy a vortex: §  Vertical circulation – helps vortex remain vertically coupled (Flatau et al. 1994; Wang and Li 1992) ¡  Hydrostatic primitive-­‐equation model ¡  Initially barotropic vortex on an f-­‐plane §  i.e., no thermal structure ¡  Standard runs: §  vmax = 40 ms-­‐1, rmax = 100 km §  Shear profile: 10 km (0 ms-­‐1) Shear Vector Sfc (4 ms-­‐1) ¡  Hydrostatic primitive-­‐equation model ¡  Initially barotropic vortex on an f-­‐plane §  i.e., no thermal structure ¡  Standard runs: §  vmax = 40 ms-­‐1, rmax = 100 km §  Shear profile: 10 km (0 ms-­‐1) Shear Vector Sfc (4 ms-­‐1) 3. 
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Vortex motion and the development of the tilt The role of the vertical circulation Varying penetration depth and other parameters Vortex centers: minimum Φ’ Vortex centers: minimum Φ’ Vortex faster than environmental flow Vortex slower than environmental flow Vortex centers: minimum Φ’ Vortex faster than environmental flow Vortex slower than environmental flow 6 h 12 h 24 h Tilt Tilt Tilt 96 h Upper and lower PV rotate cyclonically Shear Vector Tilt 6 h 12 h Tilt Tilt What’s happening here? 24 h Tilt 96 h Upper and lower PV rotate cyclonically Shear Vector Tilt The shear is acting to reduce the tilt What’s happening here? 24 h Tilt 96 h Upper and lower PV rotate cyclonically Shear Vector Tilt 6 h 12 h 24 h Tilt Tilt Tilt 96 h Upper and lower PV rotate cyclonically Shear Vector Tilt What’s happening here? The shear is acting to increase the tilt, further separating the vortices 24 h Tilt 96 h Upper and lower PV rotate cyclonically Shear Vector Tilt What’s happening here? ¡  Shear tilts vortex ¡  Upper and lower anomalies begin to rotate cyclonically ¡  If vortex is tilted in same direction as shear, tilt increases and vortices separate ¡  If vortex is tilted in opposite direction of shear, tilt decreases and vortices align w θ’ Shear Vector 30 min Tilt z = 5 km Shear Vector 6 hrs Tilt w θ’ Shear Vector descent ascent warm cool 30 min Tilt z = 5 km Shear Vector 6 hrs Tilt w θ’ descent ascent warm cool 30 min What causes θ’ to rotate cyclonically? z = 5 km 6 hrs anticyclonic cyclonic What mechanisms contribute to this vertical circulation and potential temperature anomaly? w θ’ descent ascent warm cool 30 min What causes θ’ to rotate cyclonically? Horizontal advection of the anomaly by vortex flow z = 5 km 6 hrs anticyclonic cyclonic What mechanisms contribute to this vertical circulation and potential temperature anomaly? Mechanisms contributing to vertical circulation Adiabatic à cyclonic flow leads to ascent and decent along lines of constant θ descent ascent But how does that explain the θ anomalies? No diabatic processes, so these anomalies can only arise from advection Mechanisms contributing to vertical circulation Adiabatic à cyclonic flow leads to ascent and decent along lines of constant θ Vertical advection of the environmental θ descent warm ascent cool Mechanisms contributing to vertical circulation Adiabatic à cyclonic flow leads to ascent and decent along lines of constant θ Vertical advection of the environmental θ descent warm ascent cool Explains the 90° phase shift between w and θ’ Since the thermal anomalies rotate cyclonically and the phase shift remains constant, ascent is always DOWNTILT, not necessarily downshear! Shear Vector 24 h Since the thermal anomalies rotate cyclonically and the phase shift remains constant, ascent is always DOWNTILT, not necessarily downshear! Shear Vector Shear Vector descent ascent divergent wind 1 km 30 min Shear Vector descent ascent divergent wind 1 km Why is the inner core less tilted? 30 min Shear Vector descent ascent divergent wind 1 km Why is the inner core less tilted? Divergent winds advecting max PV westward, environmental flow advecting max PV eastward 30 min ¡  To maintain balance with a tilted vortex: §  Wavenumber-­‐one couplet with ascent downshear (initially) §  Potential temperature anomaly develops in association with vertical circulation ¡  θ’ and w have a 90° phase shift ¡  Thermal anomaly remains in phase with tilted vortex (ascent downTILT) ¡  Inner core vortex less tilted than outer region §  Stronger wavenumber-­‐one asymmetry in core Stronger Shear Rotation Rate Stronger Vortex Reduced Static Stability Higher Latitude Broader Vortex Stronger Shear Rotation Rate Decreases Tilt direction fairly constant Stronger Shear (8 ms-­‐1) Stronger Vortex Reduced Static Stability Higher Latitude Broader Vortex Stronger Shear Stronger Vortex Rotation Rate Decreases Increases Tilt direction fairly constant Stronger Shear (8 ms-­‐1) Reduced Static Stability Higher Latitude Broader Vortex Stronger Shear Stronger Vortex Reduced Static Stability Rotation Rate Decreases Increases Increases Tilt direction fairly constant Stronger Shear (8 ms-­‐1) Higher Latitude Broader Vortex Stronger Shear Stronger Vortex Reduced Static Stability Higher Latitude Rotation Rate Decreases Increases Increases Increases Tilt direction fairly constant Stronger Shear (8 ms-­‐1) Broader Vortex Stronger Shear Stronger Vortex Reduced Static Stability Higher Latitude Broader Vortex Rotation Rate Decreases Increases Increases Increases Increases Tilt direction fairly constant Increased penetration depth Vertical tilt smaller Broader vortex Stronger Shear (8 ms-­‐1) Stronger Shear Stronger Vortex Reduced Static Stability Higher Latitude Broader Vortex Rotation Rate Decreases Increases Increases Increases Increases Tilt direction fairly constant Increased penetration depth Vertical tilt smaller Penetration Depth Definition? Quasi-­‐Geostrophic Theory fL/N Stronger Shear (8 ms-­‐1) Nearly Axisymmetric Vortex [(f+2vT/r)(f+ζ)]1/2L/N Broader vortex Stronger Shear Stronger Vortex Reduced Static Stability Higher Latitude Broader Vortex Rotation Rate Decreases Increases Increases Increases Increases Tilt direction fairly constant Increased penetration depth Vertical tilt smaller Penetration Depth Definition? Quasi-­‐Geostrophic Theory fL/N Stronger Shear (8 ms-­‐1) Nearly Axisymmetric Vortex [(f+2vT/r)(f+ζ)]1/2L/N Broader vortex ¡  Rotation acts to oppose destructive action of shear, even in the absence of diabatic processes ¡  Vertical circulation develops to keep flow balanced §  Inner core smaller tilt than outer region ¡  Increase in penetration depth causes: §  Increase rotation rate §  Decrease vertical tilt magnitude