Studies in Applied Mathematics

Levinson, Norman; McCalla, Clement

doi: 10.1002/sapm19745311pmid: N/A

Saffman, P. G.

doi: 10.1002/sapm197453117pmid: N/A

A set of model equations for the calculation of turbulent shear flows is presented. It is shown how the equations can be modified to allow for the inclusion of viscosity, compressibility and density variations. Some results of numerical computations are given. The constant in the law of the wall is predicted to within 10% for flow over a perfectly smooth wall, and a dependence on wall roughness is obtained. The empirical law of the wall for compressible flow is also shown to be a consequence of the equations.

Greenspan, H. P.

doi: 10.1002/sapm197453135pmid: N/A

The function α that describes the generation of large scale magnetic fields from small scale motions is assumed to be non‐zero only in a thin boundary layer. As a consequence, the problems for the poloidal and meridional fields in a symmetric rotating configuration decouple and may be solved sequentially. Analysis of the boundary layer yields equivalent boundary conditions on interior and exterior field components. The general eigenvalue problem is formulated but only the case of neutral stability is examined.

Miura, Robert M.

doi: 10.1002/sapm197453145pmid: N/A

The fully nonlinear long wave equations describe the motion over a flat bottom of a two‐dimensional inviscid fluid with a free surface in a gravitational field in the long wave approximation. These equations are shown to possess an infinite number of conservation laws (in two space dimensions) in the form The conserved densities T and the fluxes −X and −Y are polynomials in the height h and the horizontal and vertical components of velocity, u and v, and also in integrals of powers of u. The method of proof is a modification of the method recently devised by D. J. Benney to prove that these same equations possess an infinite number of conservation laws (in one space dimension) in the form where T and X are polynomials in the height h and integrals of powers of u. Conservation laws which explicitly contain x and t are also given.

Greene, Curtis; Kleitman, Daniel J.; Magnantit, T. L.

doi: 10.1002/sapm197453157pmid: N/A

Hellinger, Steven J.

doi: 10.1002/sapm197453165pmid: N/A

A lane of traffic approaches an intersection where a traffic signal mediates between two possibilities: continued travel on that lane, or a turn onto a one‐way street. Movement stops temporarily whenever a vehicle arrives at the intersection during a period permitting the alternative that is not the driver's intention. A simple model is presented which mathematically verifies the intuition that this type of signal cannot allow traffic to move efficiently during the rush‐hour.

Seaman, W. J.; Wan, F. Y. M.

doi: 10.1002/sapm197453173pmid: N/A