By S. V. Alekseenko
ISBN-10: 3540733752
ISBN-13: 9783540733751
ISBN-10: 3540733760
ISBN-13: 9783540733768
This publication provides entire and authoritative insurance of the large box of centred vortices saw in nature and procedure. The equipment for examine in their kinematics and dynamics are thought of. specific cognizance is paid to the flows with helical symmetry. The authors have defined types of vortex constructions used for interpretation of experimental info which function a floor for improvement of theoretical and numerical methods to vortex research. Achievements within the fields of balance research, waves on vortices and vortex breakdown also are awarded.
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Example text
It is oriented normally to direction of the body or flow motion as it is shown in Fig. 11, and determined only by circulation around the body. Correspondingly, the module of this force is F = ρ U∞ |Γ|. 7 Vortex forces and invariants of vortex motion 53 To determine the direction of the equivalent force action, the following rule may be used: the direction of the resultant force affecting the body is obtained by rotation of the body velocity vector by the angle of 90° relative to the fluid towards the velocity circulation.
On the definition of forces in the ideal fluid Let us apply the theorem of momentum to a fluid volume between the body boundary A and circumference s of a large radius R (in 2-D statement). Normal vectors n are directed outward from the body surface A and inward from the circumference s. 98) where u is the velocity of fluid in the absolute coordinate system. In fact, u is the perturbation of fluid velocity caused by a solid body. , |u| = O(1/R) at R lution to the problem on circulation flow around a cylinder (circle) with the radius of a (see Loitsyanskii (1966)): u = U a2 Γ − ∞2 → at 2πiz z R → ∞, where z = x + iy.
37), which in helical variables r and χ reduces to one scalar equation where ∆ = ∂2 ∂ωz ∂ωz ∂ωz ∂u r ⎛ ⎞ ∂u + ur + uχ = ωr z + ⎜ ωθ − ωz ⎟ z . 71) equals zero. This means that the axial vorticity component does not vary along the trajectory of the fluid particle, and in steady state conditions ωz is an arbitrary function depending only on stream function ψ and not depending explicitly on spatial coordinates. Moreover, because of Eq. 69) the latter claim is valid also for the ratio ωθ /r. 66), which can be obtained, if considering flow in the coordinate system, uniformly moving with u0 velocity along the z axis.
Theory of concentrated vortices: an introduction by S. V. Alekseenko
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