Geostrophic and thermal wind Reminder Geostrophic wind in
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Geostrophic and thermal wind
Reminder Geostrophic wind in pressure coordinates In the free atmosphere, wind is usually close to geostrophic. The departure from geostrophy is the ageostrophic wind Thermal Wind:
Worked Example 10 July 2006 Jet Stream, wind up to 60 m/s 300 mb Same direction, but 20 m/s 700 mb
Weather charts, 10 July 2006 300 mb Consider the geopotential gradient across the solid red line. Δz = 952 – 912 Dm = 400 m, ΔΦ = 4000 m 2 s-2 Δx = 5. 5 deg lat = 616 km (1 deg = 111 km) pΦ = 4000 / 616000 = 0. 0065 m s-2 Ug = f-1 k x pΦ = 54. 5 ms-1 (f = 1. 19 x 10 -4 s-1) Ug = 106 kt compared with 100 -110 kt measured (1 knot = I nautical mile hr-1= 1852 m hr-1 = 0. 514 ms-1)
700 mb Consider the geopotential gradient across the solid red line. Δz = 316 – 300 Dm = 160 m, ΔΦ = 1600 m 2 s-2 Δx = 5. 5 deg lat = 616 km (1 deg = 111 km) pΦ = 1600 / 616000 = 0. 0026 m s-2 Ug = f-1 k x pΦ = 22 ms-1 (f = 1. 19 x 10 -4 s-1) Ug = 43 kt compared with 40 -45 kt measured (1 knot = 1 nautical mile hr-1= 1852 m hr-1 = 0. 514 ms-1)
Thermal wind 700 mb 300 mb Consider T between Camborne and Valentia Camborne temperature at 700 mb = 5° Valentia temperature at 700 mb = -1° ΔT = 6° at 700 mb, Δx = 3. 7 degrees latitude = 411 km T = 1. 46 x 10 -5 K m-1 Increase of wind speed from 700 to 300 mb = ∂Ug/∂lnp. Δlnp ΔUg = - (r/f) T Δln p (f now 1. 13 x 10 -4 s-1 at 51°) = (286/1. 13 x 10 -4) x 1. 13 x 10 -5 x ln(7/3) = 31 ms-1 Actual value is 34 ms-1 but the result is within the errors of this crude calculation.
Surface chart Temperature gradient coincides with a front
