Section: New Results

Modelling of free surface flows

• Participants: Umberto Bosi, Mathieu Colin, Maria Kazolea, and Mario Ricchiuto

• Corresponding member: Mario Ricchiuto

  This year we have continued our work on Boussinesq-type models. We have focused on the enhanced equations of Nwogu [101], and on a frequency enhanced version of the Green-Naghdi system as proposed in [55], [77]. These models allow to account for weak dispersive effects which become relevant in the near shore region. Two papers on the topic are published. The first one [9] compares two popular wave breaking closures. We perform a study of the behaviour of the two closures for different mesh sizes, with attention to the possibility of obtaining grid independent results. Based on a classical shallow water theory, we also suggest some monitors to quantify the different contributions to the dissipation mechanism, differentiating those associated to the scheme from those of the partial differential equation. Our main results show that numerical dissipation contributes very little to the the results obtained when using eddy viscosity method. This closure shows little sensitivity to the grid, and may lend itself to the development and use of non-dissipative/energy conserving numerical methods. The opposite is observed for the hybrid approach, for which numerical dissipation plays a key role, and unfortunately is sensitive to the size of the mesh. The second paper [8] presents the application and validation, with respect to the transformation, breaking and run-up of irregular waves, of an unstructured high-resolution finite volume (FV) numerical solver for the 2D extended BT equations of [101].

  The extension of these techniques to also account for the presence of floating structures is ongoing [34].

  The methods and models developed have also led to physical studies and applications. In particular, in collaboration with the EPOC laboratory in Bordeaux, we are conducting a parametric study of bore propagation in estuaries. In particular, Three types of bores are observed in nature long wavelength undulating, short wavelength undulating, and breaking. The first kind is invisible to the eye, but measurable. The other two can be seen during mascarets. Understanding the mechanisms ruling the transition from one to the other has tremendous impact on human activities in estuarine areas. We introduced a new set of dimensionless parameters to characterize the transition to breaking bores. We have shown that they allow to determine if the transition is dominated by friction or nonlinearity (wave amplitude). The work discussed in [7] somewhat represents an accomplishment of our activity, combining simulations using fully non-linear unstructured grid dispersive models, an exploration of parameter space based on adaptive sampling, locally enriched using a smoothness indicator related to the onset of wave breaking. Further extensions of this work are ongoing, and aim at proposing some mechanism for the first transition (see the preprint [35]).