stability of and Waves in Stratified Flows 



DISCUSSION 



L. van Wijngaarden 



Twente Institute of Technology 

 Ensohede, The Netherlands 



The flow with a free surface of a fluid, homogeneous In density, 

 but with Inhomogeneous velocity distribution. Is a special case of your 

 class of stratified fluids. Burns [ 1953] considered this case and I 

 guess his results are comprised In yours. When viscosity Is allowed 

 for, the problem becomes much more complicated. It may be of 

 Interest to note that Velthulzen and I [ 1969a, 1969b] studied this prob- 

 lem taking viscosity Into account. We obtained results essentially 

 different from Burn's results, which Is due to viscous effects. 



At large Reynolds number the flow can be divided In an Invlscld 

 region and viscous regions at the critical layer and at the bottom. At 

 the outer edge of the viscous layer at the wall the Reynolds stress 

 cannot be put equal to zero a priori because a stress may build up in 

 the wall layer. 



REFERENCES 



Bums, J. C, , "Long Waves In Running Waters," Proc, Camb. Phil, 

 Soc. 49, 695, 1953. 



Velthulzen, H.G.M, and L. v, Wijngaarden, J. Fluid Mech, 39, 4, 

 817, 1969a, 



Velthulzen, H.G.M, and L. v, Wijngaarden, lUTAM Symposium on 

 Instability of Continuous Systems, Herrenalb, Sept. 1969. 



235 



