Understanding mixing efficiency in the oceans: Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids, both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy (APE); 2) the turbulent rate of change Wr,turbulent of background potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to D(APE)=Wr,turbulent holding exactly for a Boussinesq fluid with a linear equation of state. It was recently pointed out, however, that this equality no longer holds for a thermally-stratified compressible fluid, the ratio \xi=Wr,turbulent/D(APE) being then lower than unity and sometimes even negative for water/seawater. In this paper, the behavior of the ratio \xi is examined for different stratifications having the same buoyancy frequency N(z), but different vertical profiles of the parameter \Upsilon = \alpha P/(\rho C_p), where \alpha is the thermal expansion, P the hydrostatic pressure, \rho the density, and C_p the isobaric specific heat capacity, the equation of state considered being that for seawater for different particular constant values of salinity. It is found that \xi and Wr,turbulent depend critically on the sign and magnitude of d\Upsilon/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured.Comment: 17 pages, 5 figures, 1 Table, accepted in Ocean Science (special issue on seawater) on July 10th 200

Remarks on nonlinear Schroedinger equations with harmonic potential

Bose-Einstein condensation is usually modeled by nonlinear Schroedinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schroedinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the blow up time.Comment: 16 pages, no figur

Heat Kernel Measure on Central Extension of Current Groups in any Dimension

We define measures on central extension of current groups in any dimension by using infinite dimensional Brownian motion.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Perceptual Abstraction for Robotic Cognitive Development

We are concerned with the design of a developmental robot that learns from scratch simple models about itself and its surroundings. A particular attention is given to perceptual abstraction from high-dimensional sensors