Abstract
Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the farfield, and their stability. Using the forced Kortewegde Vries (fKdV) equation the weaklynonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Nonuniqueness is established and a seemingly infinite set of steady solutions is uncovered. Nonuniqueness is also demonstrated for the fully nonlinear problem via boundaryintegral calculations. It is shown analytically that critical flow solutions have algebraic decay in the farfield both for the fKdV equation and for the fully nonlinear problem and, moreover, that the leadingorder form of the decay is the same in both cases. The linear stability of the steady fKdV solutions is examined via eigenvalue computations and by a numerical study of the initial value fKdV problem. It is shown that there exists a linearly stable steady solution in which the deflection from the otherwise uniform surface level is everywhere negative.
Original language  English 

Pages (fromto)  7396 
Number of pages  24 
Journal  Journal of Fluid Mechanics 
Volume  832 
Early online date  26 Oct 2017 
DOIs  
Publication status  Published  10 Dec 2017 
Profiles

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