Studying dynamic stability of a vertically suspended, fully submerged pipe conveying fluid upwards, researchers have found a contradiction between theoretical predictions and experiments. Experiments did not show any instability, while theory predicts instability at infinitesimally low fluid velocities for a pipe without dissipation mechanisms. To explain this contradiction, in 2005 Païdoussis and co-workers postulated a new description of the boundary condition at the free end of the pipe. Subject to this boundary condition the pipe is predicted to become unstable by divergence (stable node to saddle bifurcation) at a velocity higher than yet achieved in experiments. In this paper, it is shown that a realistic description of hydrodynamic drag in combination with conventional boundary conditions might result in even higher critical velocity, and hence, this could also be an explanation of the contradiction. The description of the hydrodynamic drag is based on experimental data available in literature. This data has been obtained by experimenting with submerged rigid cylinders. To make it applicable to flexible pipes, a key step is undertaken in this paper to translate the data from the frequency domain to the time domain. Using the time-domain description of the hydrodynamic drag in combination with the conventional boundary conditions at the free end, it is shown that the pipe becomes unstable by flutter (stable focus to unstable focus bifurcation) at a critical velocity, which is much higher than that attainable in small-scale experiments. For fluid velocities exceeding the critical one, the pipe motion reaches a steady oscillation of finite amplitude, i.e. a stable limit cycle.

A frequency-domain Boussinesq model with good linear shoaling, improved linear dispersion characteristics and a dissipation formulation to account for wave breaking is extended to include the computation of the vertical structure of the horizontal velocity. The extended model is used to predict bottom velocities and resulting velocity variance and skewness in (partially) breaking irregular waves. The comparison of measured and computed velocity moments indicates that for moderately long waves the spectral Boussinesq model can be successfully used for sediment transport purposes. For shorter waves the crest velocity values of the higher waves are significantly underestimated, and as a result the velocity skewness as well.

Existing Boussinesq models are extended to include the computation of the vertical structure of the horizontal velocity. A time-domain model is tested against laboratory measurements of the vertical profile of the horizontal velocity in regular waves; good results are obtained, especially in the near-bed zone. A spectral model, which includes a dissipation formulation to account for wave breaking, is tested against laboratory measurements of bottom velocities in (partially) breaking irregular waves. For moderately long waves, the comparison on velocity variance and skewness, which are relevant to sediment transport, yields good results.