Source Of Finite Dimensions Research Articles

Separation of upslope flow over a uniform slope

Motivated by the importance of understanding mountain weather during periods of thermal convection, a laboratory study was conducted to investigate the separation of an upslope (anabatic) flow on a two-dimensional heated mountainous slope in the absence of a background mean flow. Three flow regimes were identified. In the first, at slope angles${\it\beta}$larger than a critical value${\it\beta}_{c}\approx 20^{\circ }$, the separated flow generated a rising plume completely fed by the anterior upslope flow. For this case, a simple model based on a balance between the opposing vorticities of baroclinicity and shear was proposed to predict the location of the separation point relative to the mountain base. The model also predicts the velocity and length scales at separation as well as those of the rising plume after separation. In the second regime,$10^{\circ }<{\it\beta}\leqslant {\it\beta}_{c}$, the volume flow of the separated plume was not fully supplied by the upslope flow, requiring entrainment of additional ambient fluid at the base of the plume source. The third regime occurred when${\it\beta}\leqslant 10^{\circ }$, wherein the plume almost completely engulfed the slope, similar to a buoyant plume emanating from a source of finite dimensions, thus overshadowing the upslope flow. Measurements of the separation point conducted during the MATERHORN field research program were consistent with the results of the laboratory experiments and modelling.

Mixed convection in a vertical channel with discrete heat sources at the wall

The mixed convection in a vertical plane-parallel channel with two heat sources of finite dimensions located at the wall is analyzed on the basis of a two-dimensional numerical simulation. The effect of the distance between the heat sources on the flow pattern and the temperature field is studied. Calculations are performed on the Grashof and Reynolds number ranges from 0–105 and 0–10, respectively, at a Prandtl number of 0.7. The mathematical model is based on the time-dependent Navier-Stokes equations in the Boussinesq approximation. The problem is solved by the finite element method.

Mixed Convection in a Horizontal Channel with Local Heating from Below

Mixed convection induced in the entrance region of a horizontal plane channel by a bottom heat source of finite dimensions is considered. The calculations were performed for the Prandtl number Pr = 1, Grashof numbers ranging from 4 · 103 to 3.2 · 104, and Reynolds numbers varying from 0 to 10. The dimensions of the heat source and its location were also varied. The results were obtained from a numerical solution of the 2D unsteady Navier-Stokes equations in the Boussinesq approximation, written in “vorticity – stream function – temperature ” variables. The solution was found by the Galerkin finite element method.

A proposed electron spectrometer using a concave electrostatic mirror

It is shown that a concave axially symmetric electrostatic mirror can be found with a high enough ratio of chromatic aberration to spherical aberration to allow it to be used as an electron spectrometer. The potential field is given in terms of a finite Fourier-Bessel series. Using only three nonzero Fourier coefficients, a field can be specified that allows—in the case of a point source located within the mirror field—an energy resolution of 0.003% [full width at half maximum (FWHM)] and a transmission of 0.6% of 2π steradians to be obtained. This field can be used as a starting point in an optimizing procedure reported earlier by the author, to increase the transmission or adapt the spectrometer for use with sources of finite dimensions.

Stirring the heat carrier in a heat exchanger by twisting the stream

A theoretical-experimental study was made of the effective diffusion coefficient in longitudinally streamlined helically twisted tubes with an oval profile, using as the basis a homogenized model of flow and applying the method of diffusion from linear heat sources of finite dimensions.

Propagation problems connected with special source structures

In my preceding talk I treated phenomena the main characteristics of which were already apparent from effects produced by an infinitesimal point source. Let me now [Walker‐Ames Lecture at the University of Washington, June 25, 1979] consider cases in which, on the contrary, the structure of an extended source is essential for the problem in question. Having some experience in problems dealing with rather different applications, such as radio waves, optical and electron‐optical imagings, and plasma physics problems, it struck me that fundamental phenomena occurring in any of them are often discussed while overlooking results that have been obtained in one of the related fields. Today I would like to emphasize the existence of some common features in all of these problems, all having to do with sources of finite dimensions. This may be illustrated by considering a special parameter with the dimension of a length and connected with the size of the source, which plays a role in all of them. As a matter of fact, it is just the finiteness of the source which implies that some length (however, not necessarily just the size itself of the source) becomes most essential. This is at once clear in the case of the three‐dimensional source representing a transmitting antenna system. In the immediate vicinity of the latter the field depends mainly on the nearest parts of the system, but at larger distances the effects of all parts interfere, and we arrive in the so‐called ‘wave zone.’ The transition occurs at distances D at which the various parts of the source, with separations L perpendicular to the propagation direction, can reach the point of observation along path lengths differing by not more than about the operating wavelength. According to the relation we find the expression for this critical distance. Of course, this transition distance is rather vague, since the dominating scale length L of the antenna, here introduced, is not well defined. However, it is well known that the approximations needed in order to determine radiation diagrams are only applicable in the wave zone which is just fixed, apart from the almost trivial conditions D ≫ λ and D ≫ L by the property D > Dcr = L2/λ.

Experimental investigation of the hydrodynamic boundary layer and heat transfer on a stationary disk with radial-slit air injection

This paper gives the main results of an experimental investigation of the laws of flow and heat transfer for the case of a turbulent jet emerging from a radial source of finite dimensions and spreading along a wall in the Rex range 104-2 · 105.

Disturbances produced in a visco-elastic medium by transient torsional body forces

The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.

Discussion of preceding paper

No mention has been made in the preceding article by Hoffman and Horton concerning two limiting aspects of the magnetotelluric method. So that the reader is not misled about the significance of the analyses presented, the following remarks are added. First, as Price [1962] and Wait [1962] have noted, the Cagniard method of interpretation of magnetotelluric data assumes a uniform plane wave source. The magnetotelluric soundings made at Tikhaya Bay, U.S.S.R., unquestionably involve magnetic and electric field perturbations which arise in modulation of the auroral electrojet; these are sources of finite dimensions and demand a modified magnetotelluric interpretation. The idea that pi 2 micropulsations (as well as bay disturbances) originate in modulations of the auroral electrojet is due to Campbell [1964] and has been developed by O'Brien [1965], Other geomagnetic disturbances observed near the auroral zone may have originated deep in the exosphere but were propagated in the Alfven mode over only a limited region of space. Thus it is probable, in our opinion, that a substantial part of the geomagnetic spectrum observed at Tikhaya Bay and chosen for analysis by Hoffman and Horton has arisen in sources of finite dimensions. The question therefore arises, ‘Is the plane wave approximation valid?” To answer this question we follow an approach used by Wait [1962] and by Madden and Nelson [1964] to define a critical horizontal scale length Lc below which the fields change by an amount sufficient to cause the apparent resistivity to depart by more than 10% from the plane wave value. This critical length must be computed for each earth model studied; for the data of Horton and Hoffman (a layer 30 km thick with a resistivity of 10 ohm m underlain by an infinite half-space of resistivity 0.1 ohm m) the critical length is shown in Figure 1. For this particular model the relationship is very nearly linear over the period range considered. It is evident that at the longer periods, √T over 30, the fields must be ‘uniform’ over distances greater than 40 km, which may be questionable for the assumed sources in this region. It is also quite probable that the very low values of apparent resistivity at the longer periods are caused by the nonuniformity of the fields and are not necessarily related to the true resistivity distribution.

Diffraction of Light from Sources of Finite Dimensions

The distribution of light intensity in the diffraction pattern of continuous light sources is treated analytically for Fraunhofer diffraction phenomena. Sources and diffracting apertures of any dimensions are first discussed, and a result of general application is derived which relates the illumination and dimensions of the diffraction pattern to the dimensions of the source and aperture. A source consisting of a luminous strip is considered in more detail, the form of the pattern is derived for such a source, and tables are supplied to facilitate numerical evaluation. Consideration is given to the maxima and minima of intensity in the image, and the conditions under which these are observable are indicated. In particular, attention is drawn to certain diffraction effects which do not seem to have been previously recorded and which are in agreement with the theory. These effects consist of faint but visually discernible fringes associated with the image of a strip when viewed through a narrow slit. Applications to the optics of the telescope and spectroscope are discussed.