Vortex model

Figure 7.5. Tangential velocity and pressure distributions based on Rankine s combined vortex model.

The spin-vortex model assumes the existence of spin-vortices with their centers at small polarons. It is also assumed that the system response to the incident... 

In Fig. 15, magnetic excitation spectra calculated by the spin-vortex model are depicted. Results obtained by the Holstein-Primakoff method are also depicted. The dispersions exhibit hourglass-shapes. As the number of spin-vortices are increased, the peaks of the dispersion become blur. The neck energy increases with the increase of the number of holes in agreement with experiment. 

Vortex models which describe file drop heating by considering the internal flow, i.e., the Hill vortex... 

Anemometric investigations of Bakewell and Lumley (11) and Blackwelder and Eckelmann (20) as well as visual investigations carried out recently by Smith and Schwartz (10) give evidence for the existence of counter-rotating stream-wise vortex pairs. It is generally assumed that the vortex pairs are responsible for the lift up of fluid from the wall. Fig. 3 shows the vortex model proposed by Blackwelder and Eckelmann. The sense of rotation of the two vortices is such that they pump low speed fluid away from the wall and simultaneously... 

These events have been modeled by a variety of different flow structures. In this paper we make use of a model proposed by PERRY CHONG (1982). The reasons why this -vortex model is prefered are given in chapter I. 

The authors postulate that a 1-vortex consists of viscous sublayer material and that it formed from a sheet of such material which rolls up at the edges into rods. This model is close to the wall combined with the model of a viscous tornado. Using such a A-vortex model GYR SCHMID (1984) show that the onset of the drag reducing effect can be explained by events just able to stretch the molecules. The local rheology in these events is changed by the stretched molecules and it is therefore of interest in which way the internal flow in these events is altered. Of main interest is the interaction of the vorticity stretching and the diffusion under these new material conditions. 

We know that PERRY CHONG s /I-vortex model is based on a wrapping process as shown in fig. 2.2... 

Fig. 2.2 Schematic of the/i-vortex formation and definition scotch Initially the vorticity is organized spanwise at it is uniformly distributed in flow direction. By an instability process, the vorticity starts to wrap up into a vortex which by stretching takes the idealized form of a A composed mainly of two side-vortex-rods with an internal flow behaviour as described by eq.(2.2). This process ends when the vorticity cannot be concentrated anymore and viscous diffusion processes start to dominate the flow field in the event, which starts from thereon to decay. Since this model also has to account for the non-slip condition, the wall near flow can be described by a viscous tornado. Therefore the question arises whether by incorporating the model of the viscous tornado into the 1-vortex model it would be possible to describe the flow field completely.

In the outer flow with respect to the wall, the l-vortex model will be dominant. Since in this region the vorticity equation is tractable in the form of eq. (2.3) we approximate the outer flow field of the event by this model. The tornado like wall-near flow then represents a boundary condition for the i1-vortices. 

This approximation is also supported by the very successful calculation of the momentum transfer made by PERRY CHONG, which are based on thevl-vortex model and on a similarity assumption according to which the relevant vorticity processes close to the wall scale with its inner parameter (v,u ). This assumption was made by KLINE et al. (1967) based on their famous observations. The main profit of such a model is the conservation of the circulation. The level at which the vorticity is wrapped completely into the rods can be estimated from the visual study by PERRY et al. (1981). We find from this very... 

Electromagnetism (Faraday-Maxwell historical episode) Maxwell s magnetic vortex model of electromagnetic interaction [did not feature in the classroom talk] e.g. the role of analogies in the development of Maxwell s theory of electromagnetism... 

Daniel s Electromagnetism lesson provides a similar episode. Students have been discussing the Faraday-Maxwell historical episode in small groups. Daniel begins the whole class review by stating explicitly to the class his reactions to what he has heard of their discussions. In particular, he recognises that some students have been struggling with the conceptual basis of Maxwell s vortex model ... 

Figure 17.4. Rankine vortex model For the Rankine model, we deduce ...

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