A General Approach for Kinematic Waves.
Interim rept. 1 Oct 76-15 Dec 77,
MASSACHUSETTS INST OF TECH CAMBRIDGE FLUID DYNAMICS RESEARCH LAB
Pagination or Media Count:
Whithams results for slowly varying wavetrains are generalized to include 1 explicitly the effect of modal dependence, 2 the effect of low-order linear or nonlinear nonconservative terms and their role in modifying the basic competition between frequency and amplitude dispersion, 3 the effects of moving media, rotational or irrotational, and space-time inhomogeneities, and 4 the effect of high-order dispersive or diffusive modifications to the low-order amplitude and phase equations. A modal law is also derived which, when integrated over the cross-space, leads to a generalized Whitham action law modified by a source term that is introducted by nonconservative effects the use of complex frequencies here is avoided, thus enabling linear and nonlinear problems to be treated on an equal basis. A self-consistent perturbation method is presented that leads to generalizations and extensions of those ideas due to Whitham, Hayes, Davey, Stewartson, Bretherton and Garrett, Taylor, Landahl, and others, and shows how each of these generalized subsets appears as a specific limit of a broader theory. A number of examples illustrating the basic ideas are presented and which lead to simple formulas that can be used in many direct applications of the general theory.
- Numerical Mathematics