Fully nonlinear Boussinesq equations for long wave propagation and run-up in sloping channels with parabolic cross sections

A general framework for derivation of long wave equations in narrow channels, and their transformation to Lagrangian coordinates is briefly established. Then, fully nonlinear Boussinesq equations are derived for channels of parabolic cross sections. The simplified version with normal nonlinearity is compared with corresponding models from the literature, and propagation properties are discussed. A Lagrangian run-up model is adapted to the fully nonlinear set. This model is tested by means of controlled residues and by a well-controlled comparison to exact analytic solutions from the literature. Then, run-up of solitary waves in simple geometries is simulated and compared to a semi-analytic solution that is derived for propagation and run-up in a composite channel. The dispersive model retains the higher run-up height in a parabolic channels, as reported in the recent literature for NLSW solutions, as compared to a rectangular channel.     

Modelling of run up of steep non-breaking waves

A Navier–Stokes solver is used to examine steep waves as they run up a steep beach (10.54°). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results shows reasonable overall agreement in the prediction of the free-surface, velocities and accelerations within the flow. A spurious feature at the free-surface was found which does reduce the quality of the results. For a steep wave we see the transition from a steep wave front to a smooth run-up tongue at the beach that is in qualitative agreement with experiment.     

Microzooplankton and mesozooplankton in an upwelling filament off Galicia: modelling and sensitivity analysis of the linkages and their impact on the carbon dynamics

This paper reports estimates of trophic flows of carbon off the Galician coast from a 1D ecological model, which are compared with field data from a two week Lagrangian drift experiment. The model consists of 9 biological components: nitrate, ammonium, >5μm phytoplankton, <5μm phytoplankton, heterotrophic nanoflagellates/dinoflagellates (5–20 μm), heterotrophic dinoflagellates (>20 μm), ciliates, fast sinking detritus and slow sinking detritus. Calculations were made for the fluxes of carbon between biological components within the upper 45m of the water column. The temporal development of primary production during the simulation period of two weeks was in good agreement with field estimates, which varied between 248 and 436mgC.m⁻².d⁻¹. Heterotrophic nanoflagellates had the greatest impact on carbon flux, with a grazing rate of 168mgC.m⁻².d⁻¹. Herbivorous grazing by microzooplankton amounted to 215mgC.m⁻².d⁻¹, whereas grazing by copepods on phytoplankton was 35mgC.m⁻² d⁻¹. Copepods grazing on microzooplankton was minor (0.47mgC.m⁻².d⁻¹) and the export flux from the upper 45m was 302mgC.m⁻².d⁻¹. Sensitivity analyses, in which the grazing parameters (i.e the functional relationship between ingestion and food concentration) were changed, were carried out on the heterotrophic dinoflagellate, ciliate and heterotrophic nanoflagellates/dinoflagellate components of the model. These changes did not alter the temporal development of heterotrophic nanoflagellates/dinoflagellates biomass significantly, but ciliates and heterotrophic dinoflagellates were more sensitive to variations in the grazing parameters. The overall conclusion from this modelling study is that the coupling between small phytoplankton and heterotrophic nanoflagellates was the quantitatively most important process controlling carbon flow in this region.     

Elastic behaviour of North Sea chalk: A well-log study

We present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk. We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate. The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.     

Total and opportunistic algal cover in relation to environmental variables

Based on a large data set from the national Danish monitoring program, spatial and temporal variability in total algal cover and in the fraction of opportunistic macroalgae was analysed in relation to environmental variables. Variations in water clarity and salinity combined with information on geographical location of sampling areas were found to explain almost 80% of the large-scale variation in algal cover between areas. As water clarity was largely regulated by concentrations of total-nitrogen (TN), and TN-concentrations by TN-input from land, total algal cover at given water depths was partly related to TN-input from land. The fraction of opportunistic algae responded predominantly to differences in salinity, the highest fractions being found in the most brackish areas. Temporal variability in algal cover and fraction of opportunists over the 14-year investigation period was much smaller than the variability between areas and could not be predicted from variations in environmental variables. In order for macroalgal cover to become a more sensitive indicator of water quality it would be necessary to either increase the sensitivity of the method or identify and include supplementary regulating factors in the model.     

Development of crystallographic preferred orientations by nucleation and growth of new grains in experimentally deformed quartz single crystals

Deformation experiments have been carried out to investigate the effect of dynamic recrystallisation on crystallographic preferred orientation (CPO) development. Cylindrical samples of natural single crystals of quartz were axially deformed together with 1 vol.% of added water and 20 mg of Mn₂O₃ powder in a Griggs solid medium deformation apparatus in different crystallographic orientations with compression direction: (i) parallel to <c>, (ii) at 45° to <c> and 45° to <a> and (iii) parallel to <a>. The experiments were performed at a temperature of 800 °C, a confining pressure of 1.2 GPa, a strain rate of  10^− 6 s^− 1, to bulk finite strains of  14–36%. The deformed samples were analysed in detail using optical microscopy, electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). Two different microstructural domains were distinguished in the deformed samples: (i) domains with undulatory extinction and deformation lamellae, and (ii) domains with new recrystallised grains. Within the domains of undulatory extinction, crystal-plastic deformation caused gradual rotations of the crystal lattice up to  30° away from the host orientation. New recrystallised grains show a strong CPO with c-axis maxima at  45° to the compression direction. This is the case in all experiments, irrespective of the initial crystallographic orientation. The results show that c-axes are not continuously rotated towards the new maxima. The new grains thus developed through a mechanism different from subgrain rotation recrystallisation. New grains have a subeuhedral shape and numerous microcavities, voids, fluid channels and fluid inclusions at their grain boundaries. No host control is recorded in misorientation axes across their large angle grain boundaries. New grains might have been created by nucleation from solution in the μm-scale voids and microfractures. The CPO most likely developed due to preferred growth of the freshly precipitated grains with orientations suitable for intracrystalline deformation at the imposed experimental conditions.