Double-averaging analysis of turbulent kinetic energy fluxes and budget based on large-eddy simulation

The turbulent flow over a channel bed roughened by three layers of closely packed spheres with a Reynolds number of Re= 15 000 is investigated using the large eddy simulation（LES） and the double-averaging（DA） method. The DA velocity is compared with the results of the corresponding laboratory experiments to validate the LES results. The existence of the types of vortex structures is demonstrated by the Q-criterion above the permeable bed. The turbulent kinetic energy（TKE） fluxes and budget are quantified and discussed. The results show that the TKE fluxes are directed downward and downstream near the virtual bed level. In the TKE budget, the form-induced diffusion rate is significant in the vicinity of the crest bed level, and the TKE production rate and the dissipation rate attain their peaks at the crest bed level and decrease sharply below it.

Numerical investigation of flow through vegetated multi-stage compound channel

This paper addresses the problem of the renormalization group k turbulence modeling of a vegetated multi-stage compound channel. Results from Micro acoustic Doppler velocimeter（ADV） tests are used with time and spatial averaging（doubleaveraging method） in the analysis of the flow field and the characterization. Comparisons of the mean velocity, the Reynolds stress, and the turbulent energy distribution show the validity of the computational method. The mean velocity profile sees an obvious deceleration in the terraces because of vegetation. Secondary flow exists mainly at the junction of the main channel and the vegetation region on the first terrace. The bed shear stress in the main channel is much greater than that in the terraces. The difference of the bed shear stress between two terraces is insignificant, and the presence of vegetation can effectively reduce the bed shear stress.

Dynamical models for secular evolution of navigation satellites

In this work,two dynamical models are formulated to describe the secular dynamics of navigation satellites moving in the medium Earth orbit(MEO)and geosynchronous orbit(GSO)regions.In the dynamical models,the leading terms of the Earth’s oblateness and the luni-solar gravitational perturbations are considered.For convenience,the orbits of the Sun and the Moon are described in the geocentric ecliptic reference frame,where the regression of nodal line and precession of apsidal line of the lunar orbit can be approximated as linear functions of time.The disturbing function acting on navigation satellites is analytically averaged over the mean motions of both the satellite and the third body(the Sun or the Moon).Explicit expressions of the averaged disturbing function are provided in the geocentric ecliptic and equatorial reference frames,corresponding to averaged model 1 and averaged model 2,respectively.It is found that there are seven resonant arguments in averaged model 1,while there are thirty-two resonant arguments in averaged model 2.The associated resonance curves corresponding to these resonant arguments in each model form the dynamical backbone in the phase space,organizing secular behavior of navigation satellites.At last,the averaged models are numerically compared to the associated non-averaged model,and simulation results indicate that(a)the averaged models formulated in the geocentric ecliptic and equatorial reference frames are identical,and(b)both of these two averaged models are applicable in predicting secular behavior of navigation satellites.