Fundamentals of compressible fluid mechanics
Fundamentals of Airplane Flight 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 seven variables, five 2.5 Discussion of 3DOF Equations ... the center of gravity which rotates the airplane nose-up, thereby increasing the airplane angle of attack Hence, the pilot can be thought of as controlling the angle of attack of the airplane rather...
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AA210A Fundamentals of Compressible Flow
... 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 ...
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Fundamentals Of Geophysical Fluid Dynamics Part 1 pdf
... 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 profiles of time- ... value of 10 −4 K 1 , although this varies substantially with T in the full equation of state; and ∂ρ (2.35) β = + ρ ∂S is the haline contraction coefficient for seawater, with a typical value of 10 −4...
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Fundamentals Of Geophysical Fluid Dynamics Part 2 ppt
... 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 f ∂θ ∂vg = ... scaling estimate for the relative strengths of the advective and Coriolis forces: or u· u V V /L V ∼ = , 2 × u Ω 2 V 2 L Ro = V , fL (2. 101) (2. 1 02) where f = 2 is the Coriolis frequency In the ocean...
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Fundamentals Of Geophysical Fluid Dynamics Part 3 potx
... 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 for the merger of two like-sign, ... is unstable (Sec 3. 3), indicating that the limit of vanishing separation and width is a delicate one 3. 2.2 Chaos and Limits of Predictability An important property of chaotic dynamics is the sensitive...
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Fundamentals Of Geophysical Fluid Dynamics Part 4 pptx
... (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) yields an implicit ... are independent of time and defintion of H after (4. 15), d d PE = AP E , dt dt (4. 19) dx dy η = by the (4. 20) where AP E = g dx dy η (4. 21) is the same quantity that appears in (4. 17) AP E is called...
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Fundamentals Of Geophysical Fluid Dynamics Part 5 docx
... 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 often called ... relations The layer thicknesses are h1 = hn = hN = H1 − η1 .5 Hn + ηn− .5 − ηn+ .5 , HN + ηN − .5 2≤n≤N −1 (5. 19) Hn is the resting layer depth, and ηn+ .5 is the interfacial displacement between layers n...
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Fundamentals Of Geophysical Fluid Dynamics Part 6 ppt
... ∂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 part of C) ... positive and thus reduces the magnitude of Imag [C] when P is negative Also note that in both (5 .63 ) and (5 .64 ) the instability is equally strong for either sign of U (i.e., eastward or westward vertical...
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Fundamentals Of Geophysical Fluid Dynamics Part 7 pdf
... 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 quantities of primary ... (6.6) Of course, F = ν u cannot be neglected in (6.1) since a characteristic of turbulence is that the advective cascade of variance dynamically connects the large-scale fluctuations on the scale of...
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Fundamentals Of Geophysical Fluid Dynamics Part 8 pptx
... (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 turbulence, based on 3D ... scale of the Ekman layer (Fig 6 .8) , a diagnostic eddy viscosity profile (6.23) in the log layer must have the form of u∗ z νe (z) = (6.50) K This is also a mixing-length relationship (6. 48) constructed...
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Fundamentals Of Geophysical Fluid Dynamics Part 9 pot
... 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, 258, 262 instability, ... eddy, 18, 19, 66, 164, 192 , 206, 2 59, 275 mixed layer, 214 mixing, 91 , 107, 214 mixing layer, 95 mixing length, 238, 242 mixing ratio, 25 momentum equation, 24, 66, 100, 1 19, 152, 199 Monin-Obukhov...
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