A dimensional analysis of supersaturated total dissolved gas dissipation

Elevated levels of total dissolved gas (TDG) may occur downstream of dam discharges, leading to increased incidence of gas bubble disease in fish. Accelerating the dissipation of supersaturated TDG in the downstream river can mitigate this negative problem. However, developing effective mitigation techniques is hampered by limitations in present models of TDG dissipation processes. Furthermore, data useful for modelling the dissipation of supersaturated TDG through the free surface in natural rivers are limited. Past studies indicated that the TDG dissipation process is quantitatively different from the reaeration process, and TDG behavior is quantitatively different from dissolved oxygen. However, a correct parameterization of the TDG dissipation process is still missing. The paper presents a novel dimensional analysis of the dissipation of supersaturated TDG. This approach can provide a relationship between the TDG dissipation coefficient and some classical fluid mechanics index-numbers. This dimensional analysis considers some key parameters for the dissipation process both water and TDG properties as well as flow characteristics, including turbulence. These parameters are water kinematic viscosity, TDG molecular diffusivity and vertical turbulent diffusivity, and channel width. The application of dimensional analysis pointed out that the TDG dissipation coefficient is a function of the Schmidt number, the aspect ratio of the channel, and the shear Reynolds number. The dimensional analysis was then verified using both field data collected in some large natural rivers and reservoirs in Sichuan and experimental data in laboratory flume at State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University. The analysis revealed the key role of turbulence in controlling the TDG dissipation while the importance of gas/water characteristics remains still unclear and needs further investigations

Scaling properties in the production range of shear dominated flows

Recent developments in turbulence are focused on the effect of large scale anisotropy on the small scale statistics of velocity increments. According to Kolmogorov, isotropy is recovered in the large Reynolds number limit as the scale is reduced and, in the so-called inertial range, universal features -namely the scaling exponents of structure functions - emerge clearly. However this picture is violated in a number of cases, typically in the high shear region of wall bounded flows. The common opinion ascribes this effect to the contamination of the inertial range by the larger anisotropic scales, i.e. the residual anisotropy is assumed as a weak perturbation of an otherwise isotropic dynamics. In this case, given the rotational invariance of the Navier-Stokes equations, the isotropic component of the structure functions keeps the same exponents of isotropic turbulence. This kind of reasoning fails when the anisotropic effects are strong as in the production range of shear dominated flows. This regime is analyzed here by means of both numerical and experimental data for a homogeneous shear flow. A well defined scaling behavior is found to exist, with exponents which differ substantially from those of classical isotropic turbulence. Contrary to what predicted by the perturbation approach, such a deep alteration concerns the isotropic sector itself. The general validity of these results is discussed in the context of turbulence near solid walls, where more appropriate closure models for the coarse grained Navier-Stokes equations would be advisable.Comment: 4 pages, 4 figure

Goto's generalized Kaehler stability theorem

In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small deformations of J_1 can be coupled with small deformations of J_2 so that the pair remains a generalized Kaehler structure.Comment: 9 pages, 5 figure

Engineering Electron Superpositions Using a Magnetic Field

A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects