Fundamentals of compressible fluid mechanics

... Introduction to Airplane Flight Mechanics These equations are referred to as the six degree of freedom (6DOF) equations of motion The use of these equations depends on the particular area of flight mechanics ... degrees of freedom of a system of equations is the number of variables minus the number of equations The system of equations of motion (2.24) involves sev...

Ngày tải lên: 20/06/2014, 13:07

... University Department of Aeronautics and Astronautics Problem - Relate the drag of a 2-D airfoil in steady flow to its wake flow field Control Volume Stanford University Department of Aeronautics and ... Volume Stanford University Department of Aeronautics and Astronautics Stanford University Department of Aeronautics and Astronautics

Ngày tải lên: 20/06/2014, 16:18

... 2.2 .1) The spatial gradient of velocity, u, can be partitioned into several components with distinctively different roles in fluid dynamics 2 .1 Fluid Dynamics (a) 31 (b) n n S d area V d area ... consequence of the decreases in pressure and density Also, p = p0 1/ κ T θ0 ⇒ p = p0 − gz cp θ0 1/ κ (2. 61) and ρ = p0 Rθ0 p p0 1/ γ (2.62) 46 Fundamental Dynamics Fig 2.6 Vertical...

Ngày tải lên: 09/08/2014, 11:21

... in (2. 118), the associated northward velocity is v = −u0 sin[f t + λ0 ] (2. 121 ) 64 Fundamental Dynamics The solution (2. 120 )- (2. 121 ) is called an inertial oscillation, with a period P = 2 /f ... −g(1 − αθ) , = −g ∂z ρo (2. 104) expressed here as a notational hybrid of (2. 33), (2. 58) and (2. 80) with the simple equation of state, ρ/ρo = − αθ Combining (2. 103)- (2. 104) yields...

Ngày tải lên: 09/08/2014, 11:21

... 100 Barotropic and Vortex Dynamics Again consider the particular situation of a parallel zonal flow (as in Sec 3. 3 .3) with ˆ u = U (y, t) x (3. 96) In the absence of fluctuations or forcing, this ... substantially control the dynamics of 2D turbulent evolution 3. 7 Two-Dimensional Turbulence 1 13 ζ (x,y) t=0 t = 1.25 t = 38 t=4 t = 63 t=8 y x Fig 3. 18 Computational solution...

Ngày tải lên: 09/08/2014, 11:21

... (4. 44) using the relations following (4. 26), the modal form (4. 29), and the dispersion relation (4. 37) A linearized approximation of q from (4. 24) is q− f +ζ f ζ fη f = − ≈ − H H +η H H H (4. 45) ... a∞ = a0 + ξ(a∞ ) (4. 69) From (4. 54) and (4. 59), f X(∞) + v(X(∞)) = =⇒ f x + v =⇒ ξ f X(0) f (x − ξ) v = − f = (4. 70) Inserting (4. 65)- (4. 67) into (4. 70) and evaluating (4. 69) yiel...

Ngày tải lên: 09/08/2014, 11:21

... gn+ .5 ηn+ .5 = φn+1 − φn , n = 1, , N − , (5. 20) and gn+ .5 = g ρn+1 − ρn ρ0 (5. 21) is the reduced gravity for the interface n + The vertical velocity at the interfaces is wn+ .5 = Dηn+ .5 , Dt ... N − (5. 22) And the buoyancy field is bn+ .5 = − 2gn+ .5 ηn+ .5 , Hn + Hn+1 n = 1, , N − (5. 23) Because of the evident similarity among the governing equations, this N -layer model is...

Ngày tải lên: 09/08/2014, 11:21

... ∂K (5 .65 ) or K = 21/4 R (5 .66 ) At this K value, the value for P is P = β R−4 − U R−8 (5 .67 ) 5.2 Baroclinic Instability 183 Therefore, a necessary condition for instability is U > βR2 (5 .68 ) ... influence of β When P < 0, the solution to (5 .62 ) is √ β(2K + R−2 ) i −P C = − ± (5 .69 ) 2K (K + R−2 ) 2K (K + R−2 ) Thus the zonal phase propagation for unstable modes (i.e., the real par...

Ngày tải lên: 09/08/2014, 11:21

... perspective of the slowly varying (x, y, t) values) as determined from the interior dynamics independent of the details of the boundary-layer flow, and the planetary boundary-layer dynamics resolves ... yet another geophysically important example of eddy– mean interaction Often, especially from a large-scale perspective, the mean boundarylayer flow and tracer profiles are the quantit...

Ngày tải lên: 09/08/2014, 11:21

... (Coleman, 1999.) product of an eddy speed, V , and an eddy length scale, L An eddy viscosity relation of this form, with νe ∼ V L , (6. 48) 2 38 Boundary-Layer and Wind-Gyre Dynamics β [deg.] 40 20 ... [deg.] 40 20 Re 0 500 1000 Fig 6.7 Sketch of clockwise rotated angle, β, of the surface velocity relative to ui as a function of Re within the regime of fully developed turbulenc...

Ngày tải lên: 09/08/2014, 11:21

... boundary layer, J Atmos Sci 56, 891 90 0 Cushman-Roisin, B ( 199 4) Introduction to Geophysical Fluid Dynamics (Prentice-Hall, Englewood Cliffs) Drazin, P.G and Reid, W.H ( 198 1) Hydrodynamic Stability ... 164, 214, 258 instability growth rate, 49 instability, baroclinic, 18, 97 , 164, 178, 182, 188, 199 , 258, 262, 271, 272 instability, barotropic, 87, 93 , 94 , 99 , 102, 164, 187...

Ngày tải lên: 09/08/2014, 11:21