@article{oai:soar-ir.repo.nii.ac.jp:00012967,
author = {大路, 通雄},
journal = {信州大学工学部紀要},
month = {Dec},
note = {The expansion in powers of Reynolds number R for weak homogeneous turbulence of Burgers' model fluid is extended to the fourth approximation. The solution is composed of the quasi-normal cotribution and the fourth-cumulant contribution. The quasi-normal approximation retains the former only, while Deissler's approximation is solely concerned with the latter. Mathematical procedures are straightforward in principle but exceedingly tedious in practice because of the generation of very many terms representing a complicated structure of higher order interactions. As an accessible example, the case of a line spectrum model (Dirac's δprofile) is worked out. It is thus found that both of the quasi-normal and fourth-cumulant contributions are comparable in magnitude and that they remain essentially positive except in an early stage of decay. This result is in favor of delaying the appearance of negative energy spectra to improve the lower approximations partly, yet may produce a negative decay when the value of R is a little too large. Incidentally, the first-order effect of nonnormality in the initial probability distribution is discussed in some detail. To conclude the paper, a new difficulty associated with the present perturbation scheme is pointed out. All the solutions obtained in this and the preceding reports indicate that the expansion series does not converge at large values of the wave number k. Neither the final period solution is approached as the decay time t tends to infinity. These findings are proved to be inherent in the essential character of the problem, and the need of further studies is suggested., Article, 信州大学工学部紀要 33: 37-54 (1972)},
pages = {37--54},
title = {弱い一様な乱れの理論III},
volume = {33},
year = {1972}
}