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An experiment which discussed the appearance of an internal wave attractor in a uniformly stratified, free-surface fluid [Maas, L.R.M., Benielli, D., Sommeria, J., Lam, F.-P.A., 1997. Observation of an internal wave attractor in a confined, stably stratified fluid. Nature 388(6642), 557–561] is revisited. This is done in order to give a more detailed and more accurate description of the underlying focusing process. Evolution of the attractor can now be quantified. For the tank with one sloping sidewall, and for the parameter regime (density stratification, forcing frequency) studied, the inverse exponential growth rate determined at several locations in the fluid turns out to be 122 s always. Only the start and duration of the growth differed: away from the attractor region it appeared later and of shorter duration. Here, these features are interpreted by employing a new theoretical basis that incorporates an external forcing via a surface boundary condition (an infinitesimal barotropic seiche) and that describes the solution in terms of propagating waves.

In this paper, the geometrical properties of the resolved vorticity vector derived from large-eddy simulation are investigated using a statistical method. Numerical tests have been performed based on a turbulent Couette channel flow using three different dynamic linear and nonlinear subgrid-scale stress models. The geometrical properties of have a significant impact on various physical quantities and processes of the flow. To demonstrate, we examined helicity and helical structure, the attitude of with respect to the eigenframes of the resolved strain rate tensor _ij and negative subgrid-scale stress tensor -τ_ij, enstrophy generation, and local vortex stretching and compression. It is observed that the presence of the wall has a strong anisotropic influence on the alignment patterns between and the eigenvectors of _ij, and between and the resolved vortex stretching vector. Some interesting wall-limiting geometrical alignment patterns and probability density distributions in the form of Dirac delta functions associated with these alignment patterns are reported. To quantify the subgrid-scale modelling effects, the attitude of with respect to the eigenframe of -τ_ij is studied, and the geometrical alignment between and the Euler axis is also investigated. The Euler axis and angle for describing the relative rotation between the eigenframes of -τ_ij and _ij are natural invariants of the rotation matrix, and are found to be effective for characterizing a subgrid-scale stress model and for quantifying the associated subgrid-scale modelling effects on the geometrical properties of .

We use a formal asymptotic analysis to study the effects of weak viscosity on interfacial Stokes waves, which are nonlinear, periodic and steady progressive motions between two incompressible fluids. Our results provide a natural representation of viscous contribution to the motion of Stokes waves.