Mechanics of floating bodies

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes, allows bodies with vertices and edges, we assume the bodies to be convex and take care not to assume more regularity than that implied by convexity. One main result is the (Lyapunov) stability of equilibria satisfying a condition equivalent to the standard ‘metacentric’ criterion.

Hydrodynamic Analysis of Twin-Hull Structures Supporting Floating PV Systems in Offshore and Coastal Regions

In this paper, a novel model based on the boundary element method (BEM) is presented for the hydrodynamic analysis of floating twin-hull structures carrying photovoltaic panels, supporting the study of wave responses and their effects on power performance in variable bathymetry regions. The analysis is restricted to two spatial dimensions for simplicity. The method is free of any mild-slope assumptions. A boundary integral representation is applied for the near field in the vicinity of the floating body, which involved simple (Rankine) sources, while the far field is modeled using complete (normal-mode) series expansions that are derived using separation of variables in the constant depth half-strips on either side of the middle, non-uniform domain, where the depth exhibited a general variation, overcoming a mild bottom-slope assumption. The numerical solution is obtained by means of a low-order panel method. Numerical results are presented concerning twin-hull floating bodies of simple geometry lying over uniform and sloping seabeds. With the aid of systematic comparisons, the effects of the bottom slope and curvature on the hydrodynamic characteristics (hydrodynamic coefficients and responses) of the floating bodies are illustrated and discussed. Finally, the effects of waves on the floating PV performance are presented, indicating significant variations of the performance index ranging from 0 to 15% depending on the sea state.

A novel p-harmonic descent approach applied to fluid dynamic shape optimization

We introduce a novel method for the implementation of shape optimization for non-parameterized shapes in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $$p-$$ p - Laplacian for $$p > 2$$ p > 2 . This approach is closely related to the computation of steepest descent directions of the shape functional in the $$W^{1,\infty }-$$ W 1 , ∞ - topology and refers to the recent publication Deckelnick et al. (A novel $$W^{1,\infty}$$ W 1 , ∞ approach to shape optimisation with Lipschitz domains, 2021), where this idea is proposed. Our approach is demonstrated for shape optimization related to drag-minimal free floating bodies. The method is validated against existing approaches with respect to convergence of the optimization algorithm, the obtained shape, and regarding the quality of the computational grid after large deformations. Our numerical results strongly indicate that shape optimization related to the $$W^{1,\infty }$$ W 1 , ∞ -topology—though numerically more demanding—seems to be superior over the classical approaches invoking Hilbert space methods, concerning the convergence, the obtained shapes and the mesh quality after large deformations, in particular when the optimal shape features sharp corners.

The complex basal morphology and ice dynamics of Nansen Ice Shelf, East Antarctica

Ice shelf dynamics and morphology play an important role in the stability of floating bodies of ice, in turn impacting their ability to buttress upstream grounded ice. We use a combination of satellite-derived data, airborne and ground-based radar data, and oceanographic data collected at the Nansen Ice Shelf in East Antarctica to examine the spatial variations in ice shelf draft, the cause and effects of ice shelf strain rates, and the role of a suture zone driving channelization of ocean water and resulting sub-ice shelf melt and freeze-on. We also use the datasets to assess limitations that may arise from examining only a sub-set of the data, in particular the reliance on hydrostatic balance equations applied to surface digital elevation models to determine ice draft morphology. We find that the Nansen Ice Shelf has highly variable basal morphology driven primarily by the formation of basal crevasses near the onset of floating ice convergence in the suture zone. This complex morphology is reflected in the ice shelf strain rates but not in the calculated hydrostatic balance thickness, which underestimates the scale of vertical and horizontal variability at the ice shelf base. The combination of thinner ice in the channelized suture zone, enhanced melt rates near the ice shelf edge, and complex strain rates driven by ice dynamics and morphology have led to the formation of fractures within the suture zone that have resulted in large-scale calving events. Other Antarctic ice shelves may also have complex morphology, which is not reflected in the satellite data, yet may influence their stability.

Effect of Geometric Parameters of New Semisubmersible Platform on Stability and Hydrodynamic Performance

The JCSM concept (short for Jackup Combined Semisubmersible Multifunction Platform) is a new type of semisubmersible platform presented by the first author, which overcomes the shortcomings of the available semisubmersible platforms, and combines the advantages of the traditional semisubmersible platform, the Jackup platform and the new FPSO concept - IQFP. Due to the complicated interaction between stability and hydrodynamic performance, it is necessary to explore the effect of geometrical parameters of the main body on the stability and hydrodynamic performance in order to obtain the optimal design plan of a JCSM platform. Firstly, the structure components and innovations of the JCSM were briefly reviewed in order to facilitate readers to understand its full picture. Then, six independent geometric parameters were selected by carefully studying the shape characteristics of the initial design plan of a JCSM study case. Furthermore, the stability heights and motion responses of various floating bodies of the JCSM case with different geometric parameters in wave were calculated using boundary element method based on potential flow theory. Lastly, effect of the shape parameters on stability and hydrodynamic performance of the JCSM was qualitatively evaluated. The research would shed lights on the shape design of the JCSM main body.