University:
Widener University
Course:
PHYS-121 | Fundamentals of Physics I
Academic year:

2023
Views:

186

Pages:

27
Author:

zgotovi6tm

The Walker Circulation Two-Box Model: Weak circulation: Deep convection in both boxes Strong circulation: Deep convection only in warm box Sub-cloud layer QE: ⎡ ε p Fs Q& cool ⎤ − ⎢ ⎥, S ⎦ ⎣ sb − sm γ Q& cool ⎤ 1 ⎡ Fs − Mu = ⎢ ⎥ S ⎦ 1 − γε p ⎣ sb − sm 1 w = 1 − γε p Mass Continuity: ww = − wc For convenience: CD | V |= constant Q& cool ≡ R = constant S sb − sm ≡ ∆s = constant Scale variables: R w→ w, 1 − γε p Rγ Mu → M, 1 − γε p R∆s s→ s, CD | V | ε p α≡ 1 γε p Nondimensional equations: w = s0 − s − 1, M = α ( s0 − s ) − 1 Requirement that ww = − wc : 1 s = ( s0 w + s0 c ) − 1, 2 1 ww = − wc = ( s0 w − s0 c ) , 2 M w = α −1+ M c = α −1− α 2 α 2 ( s0 w − s0c ) , ( s0 w − s0c ) . Convection ceases when s0 w − s0 c > Balance in cold box when (Dimensional): Mc < 0 : 2 (α − 1) α Mc = 0 : wc = − R CD | V | −γ wc = ( s0c − sc ) ∆s (free atmosphere) (boundary layer) Nondimensional solutions for cold box: α −1 wc (= − ww ) = − , α sc = s0 c − 1 . α Nondimensional solutions for warm box: ww = s0 w − sw − 1 = 1 − 1 α → sw = s0 w + 1 α −2 M w = α ( s0 w − sw ) − 1 = 2 (α − 1) . Simulations with 2-D model using 20 columns spanning 100 degrees of longitude ∆SST = 2 C o ∆SST = 5 C o