Abstract
We consider the classical problem of a free surface flowing past one or more disturbances in a channel. The fluid is assumed to be inviscid and incompressible, and the flow, irrotational. Both the effects of gravity and surface tension are considered. The stability of critical flow steady solutions, which have subcritical flow upstream of the disturbance and supercritical flow downstream, is investigated. We compute the initial steady solution using boundary integral equation techniques based on Cauchy integral formula and advance the solution forward in time using a mixed EulerLagrange method along with AdamsBashforthMoulton scheme. Both gravity and gravitycapillary critical flow solutions are found to be stable. The stability of solutions with a train of waves trapped between two disturbances is also investigated in the pure gravity and gravitycapillary cases.
Original language  English 

Article number  126604 
Journal  Physics of Fluids 
Volume  26 
Issue number  12 
DOIs  
Publication status  Published  Dec 2014 
Keywords
 free surface flows
 hydraulic falls
 gravitycapillary waves
Profiles

Emilian Parau
 School of Mathematics  Professor of Applied Mathematics
 Fluid and Solid Mechanics  Member
Person: Research Group Member, Academic, Teaching & Research