Hamiltonian discontinuous Galerkin FEM for linear, stratified (in)compressible Euler equations: internal gravity waves

The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction

Swimming obstructed by dead-water

In nautical literature, 'dead-water' refers to the obstructive effect encountered by ships moving in stratified water due to the ship generating waves on an interface that separates different water masses. To investigate the hypothesis that open water swimming may also be obstructed by an encounter of dead-water, possibly causing drowning, we performed two experiments that assess the impact of stratified water on swimming. In the first experiment, subjects made a single front-crawl stroke while lying on a carriage that was rolling just above the water surface. The gain in kinetic energy, as a result of the stroke, was far less in stratified than in homogeneous water. In the second experiment, four subjects swam a short distance (5 m) in homogeneous and in two different settings of stratified water. At the same stroke frequency, swimming in stratified conditions was slower by 15%, implying a loss in propulsive power by 40%. Although in nature stratification will be less strong, extrapolation of the results suggests that dead-water might indeed obstruct swimming in open water as well. This effect will be most pronounced during fair weather, when stratification of a shallow surface layer is most easily established. Our findings indicate that swimmers' anecdotal evidence on 'water behaving strangely' may have to be taken more seriously than previously thought. © 2008 Springer-Verlag

Effect of bottom stress formulation on modelled flow and turbidity maxima in cross-sections of tide-dominated estuaries

A three-dimensional numerical model with a prognostic salinity field is used to investigate the effect of a partial slip bottom boundary condition on lateral flow and sediment distribution in a transect of a tidally dominated channel. The transect has a symmetrical Gaussian cross-channel bottom profile. For a deep, well-mixed, tidally dominated channel, partial slip decreases the relative importance of Coriolis deflection on the generation of cross-channel flow patterns. This has profound implications for the lateral distribution of residual salinity that drives the cross-channel residual circulation pattern. Transverse sediment transport, however, is always found to be governed by a balance between advection of residual sediment concentration by residual lateral flow on the one hand and cross-channel diffusion on the other hand. Hence, the changes in the cross-channel distribution of residual salinity modify the lateral sediment distribution. For no slip, a single turbidity maximum occurs. In contrast, partial slip gives a gradual transition to a symmetrical density distribution with a turbidity maximum near each bank. For a more shallow, partially mixed tidal channel that represents the James River, a single turbidity maximum at the left bank is found irrespective of the near-bed slip condition. In this case, semi-diurnal contributions to sediment distribution and lateral flow play an important role in cross-channel sediment transport. As vertical viscosity and diffusivity are increased, a second maximum at the right bank again exists for partial slip.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc