Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

Growth response of Heterobranchus longifilis (Valenciennes, 1840) fingerlings fed raw and boiled Mucuna cochinchinensis seed meal

Feeding trial was conducted in static water to assess the growth of H. longifilis fingerlings fed different I inclusion levels of mucuna seed meal (MSM). Raw and boiled MSM were used in the diets at 10%, 20%, 30% and 40% inclusion levels and the performance of fish fed these diets was compared with fish fed a fishmeal-based diet which contained 40% protein. All diets were prepared to be isonitrogenous and isocaloric A two by five factorial experiment with three replicates using ten fish of average initial weight 1 .46g was carried out. Daily fish ration of five percent body weight was administered two times for eight weeks. The specific growth rate in diets 1 (control) and 6(10% boiled MSM) were similar and significantly (P<0.05) higher than the other dietary groups. The significantly lower growth performance of fish fed diets containing higher inclusion levels of both raw and boiled MSM might be due to incomplete elimination of the antinutritional factors present in MSM by boiling. Other methods of processing MSM to improve its nutritive value should be investigated. (7 page document)