| Автор | Shepherd, Theodore G. |
| Дата выпуска | 1988 |
| dc.description | A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnolʼd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions. |
| Издатель | Cambridge University Press |
| Название | Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flowsWith an appendix by P. H. Haynes. |
| DOI | 10.1017/S002211208800271X |
| Electronic ISSN | 1469-7645 |
| Print ISSN | 0022-1120 |
| Журнал | Journal of Fluid Mechanics |
| Том | 196 |
| Первая страница | 291 |
| Последняя страница | 322 |
| Аффилиация | Shepherd Theodore G.; University of Cambridge; |
