19
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

On solutions of the burns condition (which determines the speed of propagation of linear long waves on a shear flow with or without a critical layer)

Pages 115-133 | Received 10 Sep 1990, Published online: 19 Aug 2006

References

  • Benney , D. J. and Bergeron , R. F. 1969 . A new class of nonlinear waves in parallel flows . Stud. Appl. Maths. , 48 : 181 – 204 .
  • Brotherton-Ratcliffe , R. V. and Smith , F. T. 1989 . Viscous effects can destabilize linear and nonlinear water waves . Theoret. Comput. Fluid Dynamics , 1 : 21 – 39 .
  • Burns , J. C. 1953 . Long waves on running water . Proc. Camb. Phil. SOC. , 49 : 695 – 706 .
  • Freeman , N. C. and Johnson , R. S. 1970 . Shallow water waves on shear flows . J. Fluid Mech. , 42 : 401409
  • Johnson , R. S. 1986 . On the nonlinear critical layer below a nonlinear unsteady surface wave . J. Fluid Mech. , 167 : 327 – 351 .
  • Johnson , R. S. 1990 . Ring waves on the surface of shear flows: a linear and nonlinear theory . J. Fluid Mech. , 215 : 145 – 160 .
  • Thompson , P. D. 1949 . The propagation of small surface disturbances through rotational flow . Ann. NY Acad. Sci. , 51 : 463 – 474 .
  • Tutty , O. R. and Cowley , S. J. 1986 . On the stability and the numerical solution of the unsteady interactive boundary-layer equation . J. Ffuid Mech. , 168 : 431456
  • Velthuizen , H. G. M. and van Wijngaarden , L. 1969 . Gravity waves over a non-uniform flow . J. Fluid Mech. , 39 : 817 – 829 .
  • Yih , C.-S. 1972 . Surface waves in flowing water . J. Fluid Mech. , 51 : 209 – 220 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.