The authors study strongly nonlinear and time-dependent regimes of Rossby adjustment in a channel generated when the initial depth difference is large. Using the semigeostrophic approximation and the method of characteristics, semi-analytical solutions are obtained in the limiting case when the fluid depth downstream of the barrier goes to zero. These solutions are explored and compared with numerical calculations of the full shallow water equations with a good agreement. For the numerical solution, the authors use a finite volume method combined with the cell-centred flux-corrected transport method. Finally, the authors discuss the applicability of the semigeostrophic model.