scholarly journals Slowly Vibrating Axially Symmetric Bodies-Transverse Flow

2021 ◽  
Vol 26 (1) ◽  
pp. 226-250
Author(s):  
D.K. Srivastava

AbstractStokes drag on axially symmetric bodies vibrating slowly along the axis of symmetry placed under a uniform transverse flow of the Newtonian fluid is calculated. The axially symmetric bodies of revolution are considered with the condition of continuously turning tangent. The results of drag on sphere, spheroid, deformed sphere, egg-shaped body, cycloidal body, Cassini oval, and hypocycloidal body are found to be new. The numerical values of frictional drag on a slowly vibrating needle shaped body and flat circular disk are calculated as particular cases of deformed sphere.

2014 ◽  
Vol 41 (3) ◽  
pp. 177-212
Author(s):  
Deepak Srivastava ◽  
Nirmal Srivastava

In this paper, Oseen?s correction to Stokes drag experienced by axially symmetric particle placed in a uniform stream perpendicular to axis of symmetry(i.e. transverse flow) is obtained. For this, the linear relationship between axial and transverse Stokes drag is utilized to extend the Brenner?s formula for axial flow to transverse flow. General expression of Oseen?s correction to Stokes drag on axially symmetric particle placed in transverse flow is found to be new. This general expression is applied to some known axially symmetric bodies and obtained values of Oseen?s drag, up to first order terms in Reynolds number ?R?, are also claimed to be new and never exist in the literature. Numerical values of Oseen drag are also evaluated and their variations with respect to Reynolds number, eccentricity and deformation parameter are depicted in figures and compared with some known values. Some important applications are also highlighted.


Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.


1967 ◽  
Vol 29 (3) ◽  
pp. 485-494 ◽  
Author(s):  
M. I. G. Bloor

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.


1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.


1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.


The general solution in closed form, including all the static axisymmetric solutions of Weyl, is presented in the canonical coordinates ρ and z of his line element. This general solution is constructed from an arbitrary function f ( z ), which coincides with his potential function along the axis of symmetry. To illustrate how the solution may be used, a particular function f , one resulting from a Newtonian solution, is used to find both the potential function and its associated function in the line element.


1961 ◽  
Vol 10 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. P. Kanwal

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.


2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
H. Vargas-Rodríguez ◽  
A. Gallegos ◽  
M. A. Muñiz-Torres ◽  
H. C. Rosu ◽  
P. J. Domínguez

In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole.


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