Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding lines and subglacial cavities. In this work, we propose a novel numerical method for solving viscous contact problems based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equations. The advection equation for evolving the geometry of the domain occupied by the fluid is then solved via a specially-built upwinding scheme, leading to a robust and accurate algorithm for viscous contact problems. We first verify the method by comparing the numerical results to analytical results obtained by a linearised method. Then we use this numerical scheme to reconstruct friction laws for glacial sliding with cavitation. Finally, we compute the evolution of cavities from a steady state under oscillating water pressures. The results depend strongly on the location of the initial steady state along the friction law. In particular, we find that if the steady state is located on the downsloping or rate-weakening part of the friction law, then the cavity evolves towards the upsloping section, indicating that the downsloping part is unstable.

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Helicopters are one of the most important tactical elements in maritime operations. The necessity to improve the conditions in which the landing and takeoff operations are carried out leads to the study of the flow that separates from the ship's superstructure over the flight deck. To investigate this flow a series of wind tunnel experiments have been performed by testing a sub-scale model of a frigate. Measurements of the flow velocity have been taken by means of laser Doppler anemometry in five points that simulate the last path of the landing trajectory. The data obtained in these experiments is analyzed in the frequency domain where the corresponding spectra are calculated. Onboard measurements from an actual full-scale frigate are analyzed and compared with the wind tunnel results. Conclusions obtained consist of a series of illustrative values of turbulent energy frequency ranges, which are valuable for any study in this field. The comparison shows a similarity between both experiments, reasserting the role of the wind tunnel measurements in these kind of studies.

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates for this interpolation operator and show that optimal convergence to the solution can be obtained in SBFEM. These theoretical results are backed by a numerical example.