NON-EQUILIBRIUM,NONLINEAR CRITICAL LAYERS IN LAMINAR-TURBULENT TRANSITION

We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows.The classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas,which continue to underlie much of current theoretical thinking,as well as its difficulty in dealing with unbounded flows.We show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption,which leads to a nonlinear critical-layer theory.Major recent results are reviewed with emphasis on the non-equilibrium effect.Future directions of investigation are indicated.

Critical layer in liquid-solid system influencing the remediation of chromium using zeolite-supported sulfide nano zero-valent iron

Sulfidated nano zero-valent iron particles were immobilized on ZSM-5 zeolite(Z/S-nZⅥ)and used for hexavalent chromium(Cr(Ⅵ))remediation.The performance of Z/S-nZⅥimproved with the increase in Cr(Ⅵ)concentration(<60 mg/L),while the performance significantly decreased for a Cr(Ⅵ)concentration of more than 60 mg/L.The adsorption behavior for Cr(Ⅵ)was different from that reported in previous studies.The improved performance can be tailored for increasing efficiency of nano zero-valent iron(nZⅥ)corrosion,while the degree of corrosion of nZⅥwas affected by the concentration of the pollutant as discussed by kinetics,X-ray diffraction(XRD)and X-ray photoelectron spectrometer(XPS)analyses.The experiments for the dissolution of ferrous ions and the dosage of adsorbent demonstrated that the critical layer in the liquid-solid system changed with the increase in the concentration of Cr(Ⅵ)(Cr(Ⅵ):Z/S-nZⅥ>0.6).Moreover,the removal mechanisms of Cr(Ⅵ)were elucidated through XRD,transmission electron microscopy(TEM)and XPS techniques.This results demonstrate that the species of chromium in the critical layer changed from Cr(Ⅲ)to Cr(Ⅵ)as the concentration of chromium increased from low to high.Furthermore,the critical layer was composed of Cr(Ⅵ),Fe(Ⅱ),O and H elements.Additionally,the experiments of coexisting ions and aging time confirmed that Z/S-nZⅥpossessed high selectivity and stability to ensure efficiency and cost-effectiveness in practical applications.

A MODEL FOR THE VARIATIONS OF THE CRITICAL FREQUENCY OF F_2 LAYER DURING THE NEGATIVE PHASES OF IONOSPHERIC STORMS

A model for the negative phase of ionospheric storms in middle latitudes is presented. It is assumed that there will be molecule enriched air in the thermosphere above the auroral oval during the period of the main phase of a magnetic storm. The molecule enriched air is carried to the middle latitudes by thermospheric neutral wind, and at the same time it diffuses away. When the molecule enriched air arrives at the F2 layer above a station, the electron loss rate in the F2 layer increases, the electron density decreases and then the negative phase at the station begins. We have calculated the variations of the fo F2 following magnetic storms for Manzhouli （29.5°N, 117.5°E）, Freiburg （48°N, 07°E） and Billerica （43°N, 71°W） respectively. The results agree very well with typical events observed at the three stations and can be used to explain some average features of negative phase ionospheric storms in middle latitudes.

STOCHASTIC LAYER OF DUFFING'S EQUATION NEAR ITS SUBHARMONIC RESONANT ORBIT

In this Paper,the stochastic layer of Duffing's equation hosed on the chosen resonance is investigated.A general method is provided for studying the stochastic layer near the assigned resonant orbit. Several approximate critical conditions are given for the theoretical predictions of that stochastic layer. For non-dissipative Duffing's equation, two critical conditions are obtained when its global stochastic layer occurs and vanishes for the given resonance. In addition, a limit critical condition has been presented when all Possible resonances exist risible in the stochastic layer.Our results are compared with the critical conditions resulting from both Chirikov overlap method and renormalization techniques. Finally, using the cirtical conditions, numerical simulations are Performed to check our theoretical predictions of the stochastic layer based on the given resonance.

SOUTHERN BOUNDARY FORCING RELATIVE TO GENESIS,MAINTENANCE AND OSCILLATION OF A SUBTROPICAL HIGH

A nonlinear critical layer and a Kelvin cat's eye excited thereupon are simulated through four schemes in the context of a nonlinear quasi-geostrophic barotropic vorticity equation model with forced stationary wave acting along the southern boundary to investigate effects of tropical steady forcing on the genesis,maintenance and oscillation of a subtropical high(STH).Evidence suggests that the southern forcing is responsible for the planetary quasi-steady anticyclonic Kelvin cat's eye- form flow field inside the nonlinear critical layer,with the eye shifting,vigor and shape changing quite similar to the behaviors of a summer STH,in striking contrast to the northern stationary forcing.As such,the southern boundary-caused cat's eye is likely to be an even more important mechanism for STH genesis and evolution.In addition,a physical mechanism is introduced for quasi-steady planetary wave moving through the critical layer at subtropical latitudes.