ALBERT

Notes: Abstract Convection into regions with open, or partially-open, lateral boundaries is considered. The products of convectively-driven mixing can flow out from under the source generating a compensating inflow as they do so. The effects of rotation, ambient stratification and the geometry of the region on these flow quantities are considered, since all affect the density and velocity distributions that result. Three typical geometries are considered: convection into a channel or sea with an exit constriction; convection from a patch or strip into stratified and/or rotating surroundings and, finally, into a rotating coastal environment. In each case the simplest possible models are considered in the hope that they can offer some insight into the dynamical processes that affect the overall behaviour of each system. These are supplemented by reference to numerical and laboratory experiments as well as field observations. Finally suggestions for future work in the former two cases are presented in the hope that they will stimulate the reader's interest.

Notes: We have studied experimentally the dynamics of freely decaying turbulence in a stratified fluid. At low Froude number this flow has a quasi-2-D behavior1 that modifies the mixing (Fr=0.004, Re=1000; based on the integral scales). We characterize the vorticity evolution in the range scales where the enstrophy cascade is taking place. The quasi-2-D period of this turbulence is studied by photographic analysis of the velocity field V, which is interpolated on a regular grid (128×128). We are able to decompose it into its internal wave and turbulent component, and to compute its derivative fields up to the vector η=curlHΩV (related to the enstrophy cascade; where ΩV is the vertical vorticity). An enstrophy transfer model is developed by generalizing the model of Weiss to slightly divergent flows: the tensor F=∇HVH−DivH VHI2 (where H denotes the horizontal component, and I2 is the identity tensor of order 2) enters the equation of evolution for η as dtη=ηF+ΩV curlH (DivHVH). (1) An elongation of η corresponds to an increase of the local vorticity gradient, which is the mechanism of the enstrophy cascade to small scales.We neglect the second term of (1) since it occurs at the measurement noise scale. Thus eigenvalues λi and eigenvectors of F characterize Eq. (1) and we present maps of these functions. The analysis of these eigenvalues of F gives us the "coherent'' zones of the flow where λ is complex, i.e., where the local effect of rotation counteracts the local strain induced by the whole vorticity field. In the remaining zones the λi are generally of opposite sign. Under this condition, the histogram of the angle α between the elongating (V+) and the contracting (V−) eigenvectors shows broad peaks centered on ±π/2, Where the separating curve of ΩV=0 on an Ω map corresponds to α=±π/2. In these regions the strain provokes a deformation of the vorticity field, which corresponds to the enstrophy cascade phenomenon. Statistics on the angles β±=(angle)(η,V±) reveals a mean alignment of η with V+ (elongation) and a mean right angle with V−. Thus, the relations between F and η are clearly shown in our experimental case.The main effect of vertical compression or expansion at every point of the field, due for instance to a weak internal wave, is to modify the eigenvalues of F, thus inhibiting or favoring the local enstrophy cascade. In some cases, it is able to impose its sign onto the two eigenvalues: this is observed at the border of the coherent zone.

Notes: The addition of a polymer to a fluid has been observed to delay the transition to turbulence. The question then arises: Can the polymer delay the appearance of a hydrodynamic instability, such as the one that leads to Goertler vortices? The experimental technique was the same as that used in Maxworthy [Turbulence Measurements in Liquids (Univ. of Missouri—Rolla, Rolla, MO, 1971), pp. 32–38], where a cylindrical container of fluid in solid body rotation was suddenly brought to rest. The diffusing boundary layer on the curved side wall became unstable to a Goertler vortex pattern after a time that could be related to the initial rotation rate and the critical Goertler number (Gc). For small concentrations of polymer, the increase in Gc was linear in concentration for both Separan AP30 and polyethylene oxide. This number seemed to asymptote to a value of 9.5 for the Separan AP30 above a concentration of 0.10% by weight and to a value of 7.5 for the polyethylene oxide above a concentration of 0.07%. The wavelength of the instabilities increased due to the presence of the polymer; for a 0.1% concentration, the increase was 50% to 90%, depending on the initial rotation speed.

Notes: Flow visualization studies and laser-Doppler anemometry (LDA) measurements have been performed on the flow field generated at a sudden expansion in a cylindrical pipe during the intake stroke of a piston. The range of piston Reynolds numbers investigated, based on piston diameter and velocity, was 18–125 and covered a laminar and a transition-to-turbulence regime. A detailed study of the parameters influencing the structure of the flow, i.e., the clearance volume and the piston velocity, was carried out and is presented, and the mechanism for the creation of flow instabilities at low Reynolds numbers is outlined. One of the striking features of the flow relates to the formation of vortex structures during the intake flow. It is found that under some circumstances these structures become unstable, despite the relatively low Reynolds number of the flow.