Fundamentals Of Geophysical Fluid Dynamics Part 2 ppt

... D t h ∼ fV 2 /g. The geostrophic estimate for w is (2. 109). So the rigid lid approximation is accurate if w  Dh Dt V 2 H f 0 L 2  fV 2 g R 2 e  L 2 , (2. 1 12) with R e = √ gH f . (2. 113) R e is ... curl: ∂u ∂t −→ − ∂ 2 u ∂y∂t + ∂ 2 v ∂x∂t = ∂ζ ∂t ; (3.19) (u ·∇)u −→ − ∂ ∂y  u ∂u ∂x + v ∂u ∂y  + ∂ ∂x  u ∂v ∂x + v ∂v ∂y  = u  ∂ 2 v ∂x 2 − ∂ 2 u ∂y∂x  + v  ∂...

Ngày tải lên: 09/08/2014, 11:21

... relation,  ∂ 2 ∂t 2 + f 2  ∂η ∂t = gH  ∂ 3 η ∂x 2 ∂t + f ∂ 2 η ∂y∂x + ∂ 3 η ∂y 2 ∂t − f ∂ 2 η ∂y∂x  =⇒ ∂ ∂t  ∂ 2 ∂t 2 + f 2 − gH∇ 2  η = 0 . (4 .28 ) This combination thus results in a partial ... 1994.) 126 Rotating Shallow-Water and Wave Dynamics or for η 0 = 0, divide by −iη 0 to obtain ω(ω 2 − [f 2 + c 2 k 2 ]) = 0 . (4.31) The quantity c =  gH (4....

Ngày tải lên: 09/08/2014, 11:21

... imagi- nary part is when the discriminant of the quadratic dispersion relation (5. 62) is negative, i.e., P < 0 for P ≡ β 2 (2K 2 + R 2 ) 2 − 4(β 2 K 2 − U 2 K 4 (K 2 − R 2 )) (K 2 + R 2 ) = β 2 R −4 + ... gives (C − U )  K 2 Ψ 1 + 1 2R 2 (Ψ 1 − Ψ 2 )  +  β + U R 2  Ψ 1 = 0 (C + U )  K 2 Ψ 2 − 1 2R 2 (Ψ 1 − Ψ 2 )  +  β − U R 2  Ψ 2 =...

Ngày tải lên: 09/08/2014, 11:21

... z integrals of v) of the boundary-layer and Sverdrup circulations are in balance at every latitude. 25 2 Boundary-Layer and Wind-Gyre Dynamics Grouping the terms in powers of D, D −1  ∂ 2 ψ b ∂ξ 2 + ∂ψ b ∂ξ  + ... Reynolds number is not too 25 0 Boundary-Layer and Wind-Gyre Dynamics streamfunction, ψ = Ψ/H: D∇ 2 ψ + ∂ψ ∂x = A sin  2 y L y  (6. 62) for D = f 0 β  E 2...

Ngày tải lên: 09/08/2014, 11:21

... (2. 2) by ρu gives ρ ∂ ∂t  1 2 u 2  = −u · ∇∇∇p −gρw − ρu · ∇∇∇  1 2 u 2  + ρu · F , after making use of w = D t z from (2. 4). Multiplying the mass equation (2. 6) by u 2 /2 gives  1 2 u 2  ∂ρ ∂t = ... − 1 ρ 0 ∇ 2 p . (2. 55) The combination of these equations, ∂ t (2nd equation) - ∂ t (1st) - ρ 0 × (3rd), implies that ∂ 2 p ∂t 2 − C 2 s ∇ 2 p = 0 . (2. 56...

Ngày tải lên: 09/08/2014, 11:21

... linear combination of exponential functions of ky consistent with perturbation decay as |y| → ∞ and continuity of ψ  at y = ±D /2, viz., Ψ(y) = Ψ + e −k(y−D /2) , y ≥ D /2 , =  Ψ + + Ψ − 2  cosh[ky] cosh[kD /2] +  Ψ + − ... express all quantities in terms of their values at r = r o through O(δr) (cf., (2. 69)), the following equation is derived: D 2 δr Dt 2 + γ 2 δr = 0...

Ngày tải lên: 09/08/2014, 11:21

... propagation speed is U = u 2 +  gh 1 (h 1 + h 2 ) 2h 2 > u 2 , (4.90) and the velocity behind the bore is u 1 = u 2 + h 1 − h 2 h 1  gh 1 (h 1 + h 2 ) 2h 2 > u 2 and < U . (4.91) The ... B −1 ] 2 , 2 k [K 2 + B −1 ] 2  . (4. 122 ) c g can be oriented in any direction, depending upon the signs of ω, k, and . The long-wave limit (K → 0) of (4. 120 ) is...

Ngày tải lên: 09/08/2014, 11:21

... without loss of generality, been presumed to 6.1 Planetary Boundary Layer 21 5 5 10 15 20 0 1 2 3 0900 1030 120 0 1330 Virtual potential temperature, C Height AGL, km 0 5 10 15 20 25 0 1 2 3 Water ... Radiation 21 1 with (k, ) the horizontal wavenumber vector. The associated meridional phase and group speeds are c y p = ω/ = − βk (k 2 +  2 ) c y g = ∂ω ∂ = 2 k (k 2...

Ngày tải lên: 09/08/2014, 11:21

... 105, 150, 21 6, 22 2, 25 3, 25 6, 26 2 transport streamfunction, 24 7, 26 9 tripole vortex, 26 7 turbulence, 17, 21 , 24 , 65, 1 02, 107, 143, 161, 1 92, 21 3, 21 5 turbulent closure, 22 2, 22 4, 23 5 turbulent ... 183 resting state, 32, 45, 125 , 145, 168, 25 8, 26 5, 26 6 Reynolds number, 25 , 21 3, 21 8, 22 5, 23 5 Reynolds stress, 100, 164, 185, 199, 21 6, 22 2,...

Ngày tải lên: 09/08/2014, 11:21