Small Perturbation Assumption Research Articles

Subsonic Potential Aerodynamics for Complex Configurations : A General Theory

A general theory of subsonic potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. Under the small perturbation assumption, the potential at any point in the field depends only upon the values of the potential and its normal derivative on the surface of the body. On the surface of the body, this representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The theory is applied to finite-thickness wings in subsonic steady and oscillatory flows.

Über die Äquivalenz von Wärme-, Kraft- und Massenquellen

The steady, nonviscous flow in fields with sources of energy, force and mass is investigated under the assumption of small perturbations. The different sources are equivalent in such a way that it is possible to change the sources without changing certain values of the flow field if one does not change certain combinations of the sources. In the same way it is possible to obtain an unchanged drag-coefficient by changing the sources.

Über die Äquivalenz von Wärme‐, Kraft‐ und Massenquellen

The steady, nonviscous flow in fields with sources of energy, force and mass is investigated under the assumption of small perturbations. The different sources are equivalent in such a way that it is possible to change the sources without changing certain values of the flow field if one does not change certain combinations of the sources. In the same way it is possible to obtain an unchanged drag-coefficient by changing the sources.

Simple Models of Thermally Driven Mesopheric Circulation

Possible thermally driven symmetric circulations of the mesosphere and upper stratosphere are considered, subject to the following major assumptions: the motions are in hydrostatic and geostrophic balance; the motions are small perturbations about a state of rest which is defined by the horizontal average of the radiative equilibrium temperature; the eddy fluxes of momentum and heat act only as Rayleigh friction and Newtonian conductivity, or as vertical eddy viscosity and conductivity. The assumption of small perturbations is justified by consideration of photochemical and radiative processes. The derived meridional circulations have a principal flow branch from summer pole to winter pole with maximum amplitude less than 1 m sec−1. There is good agreement with the observed amplitude, distribution, and seasonal phase of the mean zonal winds if eddy viscosity and eddy conductivity parameters are assumed to be about 500 m2 sec−1. Radiative and photochemical processes are found to have an important damping effect on motions of this type; a radiative-photochemical damping parameter can be derived having the order of magnitude 10−6 sec−1.

Coupling of Modes between a Slow-Wave Plasma Mode and a Helix

Propagation of waves in a transmission system consisting of a plasma column and a coaxial helix is investigated. The propagating characteristics of the structure are analyzed by a straightforward field analysis. It is demonstrated that the field solution can be reduced to a simple circuit equation describing two coupled tuned circuits. This analytical result shows that the propagation of waves in the plasma-helix structure can be described by a purely capacitive coupling of modes between the space-charge modes of plasma column and the helix mode. The result of this study is compared with the earlier Russian work by Bulgakov et al. The limitation of the perturbation techniques is discussed and the condition for the validity of the small perturbation assumption is given. The experimental method of separating and measuring the two coupled modes of propagation by means of mode-selecting techniques is described.

On the Hodograph Method in Magnetogasdynamics

R Yur'ev 1 discussed the Chaplygin-type equations in magnetogasdynamics. Mathematically speaking, the hodograph method tacitly has been introduced in magnetogasdynamics. The object of this paper is to obtain such an equation in the form of a function ^ representing the streamlines for the plane motion of an electrically conducting, compressible, steady flow with infinite conductivity in the presence of a magnetic field, co-linear with linear momentum of the flow. I t is shown that the flow is essentially similar to the ordinary perfect flow in gasdynamics with an appropriate pressure-density relation. Taniuti has independently found the basic equation for plane flows without making the assumption of small perturbations, showing that a discontinuity surface can occur in slow subsonic flow if the magnetic field is of adequate strength. Taniuti's equation is extended to the general case of threedimensional flow by Imai. Moreover, in Refs. 3 and 4 the hodograph method has not been explicitly introduced. In communications between the present author and Prof. W. R. Sears, there have been more explicit introductions of the hodograph method in magnetogasdynamics, but these are as yet unpublished. However, the work in this paper was developed by the author independently at the same time.