Hyperbolic layer line

In terms of the measurements of Table IV the basis for a 20 A. pseudoperiod may be stated as follows The two strong meridional arcs are not hyperbolic intersections of the flat film with widely extended reciprocal disks (21), but their circular arc shape indicates clearly that their expression is caused by disorientation. That layer lines exist at these levels is indicated by the fainter diffuse lines with approximately the same axial spacing components. In addition, there is evidence for another layer line at about 5.0 A. These, along with the distinct ones, can be assigned indices 0, 2, 4, 5, and 7 to very nearly account for their relationships. 

Bradshaw et al. (B3) use Eqs. (40) to derive a differential equation for the turbulent shear stress t. The transport velocity Qa is taken as (Tmei/p), where Tm x is the maximum value of riy) in the boundary layer. G and I are prescribed as functions of the position across the boundary layer, and o is essentially taken as constant. Together with Eqs. (10a,b), Eq. (36) gives a closed set of equations for U, V, and t this system is of hyperbolic type, with three real characteristic lines. Bradshaw et al. construct a numerical solution using the method of characteristics it can also be done using small streamwise steps with an explicit difference scheme (Nl A. J. Wheeler and J. P. Johnston, private communications). There is a great physical appeal to the characteristics, especially since it is found that the solutions along the outward-going characteristic dominates the total solution. This... 

A certain minimum consolidation percentage is frequently prescribed in Specifications. Analysis of the consolidation process in the field is, however, not always that simple, especially if very soft and/or non-homogene-ous layers are present. In such cases use could be made of observational methods like the hyperbolic method which assumes that the settlement (s) versus time (t) behaviour approaches a straight line after some time in a t/s versus t diagram. This straight line describes a hyperbolic relation, hence the term hyperbolic method. The inverse of the slope of this line would then yield the ultimate settlement. Thus, once sufficient data are available for the settlement to reach the hyperbolic line, the subsequent consohdation can be predicted (Thiam Soon Tan et al., 1991). 

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