Analysis of field measurements of ocean surface wave activity in the marginal ice zone, from campaigns in the Arctic and Antarctic and over a range of different ice conditions, shows the wave attenuation rate with respect to distance has a power law dependence on the frequency with order between two and four. With this backdrop, the attenuation‐frequency power law dependencies given by three dispersion relation models are obtained under the assumptions of weak attenuation, negligible deviation of the wave number from the open water wave number, and thin ice. It is found that two of the models (both implemented in WAVEWATCH III®), predict attenuation rates that are far more sensitive to frequency than indicated by the measurements. An alternative method is proposed to derive dispersion relation models, based on energy loss mechanisms. The method is used to generate example models that predict power law dependencies that are comparable with the field measurements.
Carbonation caused by atmospheric carbon dioxide is one of the major physicochemical processes which can compromise the service life of reinforced concrete structures. While the bulk of the carbonation reaction is that of calcium hydroxide, other constituents of the porous matrix can also carbonate and compete with calcium hydroxide for carbon dioxide. Particularly the carbonation of calcium-silicate hydrates and unhydrated constituents are neglected by most authors in carbonation prediction models. In this paper, a mathematical model of carbonation is extended to include additional carbonation and hydration reactions. The competition of the several reactions and their effect on the carbonation depth is investigated by dimensional analysis and numerical simulations. A parameter study emphasises that multiple internal reaction layers appear. Their position and speed essentially depend on the strength of the different reactions. It is also observed that, for a wide range of parameters, the effect of some of the additional reactions on the carbonation depth is small. In particular, a comparison with data from laboratory experiments justifies the neglect of the carbonation of the unhydrated constituents in prediction models. (M. A. Peter), a.muntean@tue.nl (A. Muntean), sebam@math.uni-bremen.de (S. A. Meier), mbohm@math.unibremen.de (M. Böhm).
We present a solution to the water-wave interaction with a submerged elastic plate of negligible thickness by the eigenfunction-matching method. The eigenfunction expansion depends on the solution of a special dispersion equation for a submerged elastic plate and this is discussed in detail. We show how the solution can be calculated for the case of normal incidence on a semi-infinite plate in two spatial dimensions and then extend this solution to obliquely incident waves, to a plate of finite length and to a circular finite plate in three dimensions. Numerical calculations showing various properties of the solutions are presented and a near-orthogonality relation for the eigenfunctions is used to derive an energy-balance relation.
Carbonation is the reaction of environmental carbon dioxide with alkaline species in concrete. It is one of the major degradation mechanisms affecting the durability of reinforced concrete structures. In this paper, a mathematical model of the carbonation process is formulated and simulated using the finite-element method. Nonlinear reaction rates, Robin boundary conditions and a decrease of the concrete porosity in time are taken into account. A dimensional analysis based on a nondimensionalisation of the entire model is introduced to identify the key parameters and the different characteristic time and length scales of the whole process. Numerical simulations show the occurrence of an internal reaction layer travelling through the material. The speed and the width of the layer are rigorously defined via dimensionless quantities. A parameter study shows that the speed and the width are strongly related to the size of the Thiele modulus which is typically large. The relevance of other parameters is also investigated. The model is validated for accelerated and natural carbonation settings.
A structure capable of substantially amplifying water waves over a broad range of frequencies at selected locations is proposed. The structure consists of a small number of C-shaped cylinders arranged in a line array, with the cylinder properties graded along the array. Using linear potential-flow theory, it is shown that the energy carried by a plane incident wave is amplified within specified cylinders, for wavelengths comparable to the array length, and for a range of incident directions. Transfer matrix analysis is used to attribute the large amplifications to excitation of Rayleigh-Bloch waves and gradual slowing down of their group velocity along the array. arXiv:1806.05404v1 [physics.flu-dyn]
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