On upstream blocking in a viscous diffusive stratified flow

The effect of diffusion of specie upon the flow about a transverse flat plate moving horizontally in a viscous stratified medium is considered. Asymptotic expansions are used to define a parameter regime where a viscous-diffusive-buoyancy balance is dominant. The solution, expressed in terms of an inverse Fourier transform, is numerically integrated. The results show that, as in the non-diffusive problem, a region of closed streamlines exists ahead of the body. However, unlike the case where diffusion is neglected, the density field within this recirculating region is uniquely determined and found to be statically stable. It is also found that varying the relative amount of diffusion affects not only the density distribution, but the velocity profile as well, indicating a strong coupling between the vorticity and specie equation

Models for strongly-nonlinear evolution of long internal waves in a two-layer stratification

International audienceModels describing the evolution of long internal waves are proposed that are based on different polynomial approximations of the exact expression for the phase speed of uni-directional, fully-nonlinear, infinitely-long waves in the two-layer model of a density stratified environment. It is argued that a quartic KdV model, one that employs a cubic polynomial fit of the separately-derived, nonlinear relation for the phase speed, is capable of describing the evolution of strongly-nonlinear waves with a high degree of fidelity. The marginal gains obtained by generating higher-order, weakly-nonlinear extensions to describe strongly-nonlinear evolution are clearly demonstrated, and the limitations of the quite widely-used quadratic-cubic KdV evolution model obtained via a second-order, weakly-nonlinear analysis are assessed. Data are presented allowing a discriminating comparison of evolution characteristics as a function of wave amplitude and environmental parameters for several evolution models

A weakly nonlinear model for multi-modal evolution of wind-generated long internal waves in a closed basin

A weakly nonlinear evolution model that accounts for multi-modal interaction in a small, continuously stratified lake of variable depth is derived. In particular, an evolution model for the first two vertical modes in a lake that is subject to wind stress forcing is numerically simulated. Defining modal energies, energy transfer between the first and the second vertical modes is calculated for several different forms of the density stratification. Modal energy transfer mainly occurs during reflection of mode-one waves at the vertical end walls, and it is shown that the amount of energy transfer from the first to the second mode is greatly dependent on the shape of the stratification profile. Also, the initial modal energy partition at the wind setup is shown to depend significantly on the penetration depth of the internal shear stress induced by the wind stress, especially if the stress distribution extends into the upper levels of the metalimnion

A numerical study of bifurcations in a barotropic shear flow

In the last few years, more and more evidence has emerged suggesting that transition to turbulence may be viewed as a succession of bifurcations to deterministic chaos. Most experimental and numerical observations have been restricted to Rayleigh-Benard convection and Taylor-Couette flow between concentric cylinders. An attempt is made to accurately describe the bifurcation sequence leading to chaos in a 2-D temporal free shear layer on the beta-plane. The beta-plane is a locally Cartesian reduction of the equations describing the dynamicss of a shallow layer of fluid on a rotating spherical planet. It is a valid model for large scale flows of interest in meteorology and oceanography

Internal solitary waves in the Coastal Mixing and Optics 1996 experiment : multimodal structure and resuspension

Observations of internal solitary waves (ISWs) and of their role in sediment resuspension during the Coastal Mixing and Optics 1996 (CMO 96) experiment are reported. The largest resuspension events observed in the experiment can be related to retarded flow under the wave footprint. Two distinctly different periods of resuspension events could be distinguished based on the prevailing atmospheric conditions: a calm period, which we consider characteristic of nominal conditions, and an energetic period, during which two major storms occurred. ISWs arrived at the mooring site from a variety of sources, though a common intermodal dynamics seemed to occur repeatedly. Both mode 1 and mode 2 ISWs have been observed. The present analysis of the month-long portion of the CMO 96 data set constitutes the first reported observations, insofar as we are aware, of mode 2 waves on the continental shelf. Both mode 1 and mode 2 ISWs were found to stimulate resuspension. The mode 2 waves seem to be generated locally by resonant or topographic interactions with mode 1 ISWs. Internal wave fields of the type described here are expected to exist in a variety of other shallow seas as well

Lagrangian transport in a circular lake: effect of nonlinearity and the second vertical mode

Effects of the second vertical mode and nonlinearity of the background flow field on the Lagrangian transport of particle clouds are studied by employing a wind-forced linear hydrostatic model and a weakly-nonlinear, weakly-nonhydrostatic evolution model. It is confirmed that Kelvin waves primarily advect particles near the basin perimeter in a cyclonic direction, and Poincaré waves primarily advect particles in off-shore (radial) directions in a manner that is oscillatory in time with frequencies near the inertial period. The internal current associated with the second vertical mode is usually far smaller than that associated with the energetically dominant, lowest vertical mode. However, because of the disparately slow eigenspeed of the vertical mode-two Kelvin wave, the resultant particle transport associated with the vertical mode-two flow near the basin perimeter can drive transport that is comparable with that associated with the Kelvin wave of the lowest vertical mode. It is discovered that nonlinear interaction between the Kelvin-Poincaré wave pair can give birth to a solitary-like wave of large amplitude in an off-shore region. This new type of wave generates a large current and co-propagates with the Kelvin wave in a cyclonic direction and, eventually, can cause a burst of particle transport in an off-shore direction