SHORT-AND RESONANT-RANGE INTERACTIONS BETWEEN SCALES IN TURBULENCE AND THEIR APPLICATIONS

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence,were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.

Mesoscale Predictability of Mei-yu Heavy Rainfall

Recently reported results indicate that small amplitude and small scale initial errors grow rapidly and subsequently contaminate short-term deterministic mesoscale forecasts. This rapid error growth is dependent on not only moist convection but also the flow regime. In this study, the mesoscale predictability and error growth of mei-yu heavy rainfall is investigated by simulating a particular precipitation event along the mei-yu front on 4- 6 July 2003 in eastern China. Due to the multi-scale character of the mei-yu front and scale interactions, the error growth of mei-yu heavy rainfall forecasts is markedly different from that in middle-latitude moist baroclinic systems. The optimal growth of the errors has a relatively wide spectrum, though it gradually migrates with time from small scale to mesoscale. During the whole period of this heavy rainfall event, the error growth has three different stages, which similar to the evolution of 6-hour accumulated precipitation. Multi-step error growth manifests as an increase of the amplitude of errors, the horizontal scale of the errors, or both. The vertical profile of forecast errors in the developing convective instability and the moist physics convective system indicates two peaks, which correspond with inside the mei-yu front, and related to moist The error growth for the mei-yu heavy rainfall is concentrated convective instability and scale interaction.

Barotropic Interaction between Planetary-and Synoptic-Scale Waves during the Life Cycles of Blockings

In this paper, in an equivalent barotropic framework a new forced nonlinear Schroedinger equation is proposed to examine the interaction between the planetary-scale waves and the localized synoptic-scale eddies upstream. With the help of the perturbed inverse scattering transform method, nonlinear parameter equations can be derived to describe the evolution of the dipole soliton amplitude, frequency, group velocity and phase under the forcing of localized synoptic-scale eddies. The numerical solutions of these equations predict that in the interaction between the weak dipole soliton (weak incipient dipole anomaly) and the synoptic-scale eddies, only when the high-frequency eddies themselves have a moderate parameter match they can near resonantly enhance a quasi-stationary large-amplitude split flow. The instantaneous total streamfunction field (the sum of background westerly wind, envelope Rossby soliton and synoptic-scale waves) is found to be very similar to the observed Berggren-type blocking on the weather map(Berggren et al. 1949). The role of synoptic-scale eddies is to increase the amplitude of large-scale dipole anomaly flow, and to decrease its group velocity, phase velocity and zonal wavenumber so that the dipole anomaly system can be amplified and transferred from dispersive system to very weak dispersive one. This may explain why and how the synoptic-scale eddies can reinforce and maintain vortex pair block. Furthermore, it is clearly found that during the prevalence of the vortex pair block the synoptic-scale eddies are split into two branches around the vortex pair block due to the feedback of amplified dipole block. Key words Envelope Rossby solilon - Blocking - Synoptic-to-planetary scale interaction This research was supported jointly by the Foundation for University Key Teacher by the Ministry of Education and by the National Natural Science Foundation of China (49775266, 49905007)), the Knowledge Innovation Key Project of Chinese Academy of Sciences in the Resource Environment Field (Grant No. KZCX 2-203) and the National Key Foundation Research Project (G1998040900, Part I).

Insights into Convective-scale Predictability in East China: Error Growth Dynamics and Associated Impact on Precipitation of Warm-Season Convective Events

This study investigated the regime-dependent predictability using convective-scale ensemble forecasts initialized with different initial condition perturbations in the Yangtze and Huai River basin(YHRB)of East China.The scale-dependent error growth(ensemble variability)and associated impact on precipitation forecasts(precipitation uncertainties)were quantitatively explored for 13 warm-season convective events that were categorized in terms of strong forcing and weak forcing.The forecast error growth in the strong-forcing regime shows a stepwise increase with increasing spatial scale,while the error growth shows a larger temporal variability with an afternoon peak appearing at smaller scales under weak forcing.This leads to the dissimilarity of precipitation uncertainty and shows a strong correlation between error growth and precipitation across spatial scales.The lateral boundary condition errors exert a quasi-linear increase on error growth with time at the larger scale,suggesting that the large-scale flow could govern the magnitude of error growth and associated precipitation uncertainties,especially for the strong-forcing regime.Further comparisons between scale-based initial error sensitivity experiments show evident scale interaction including upscale transfer of small-scale errors and downscale cascade of larger-scale errors.Specifically,small-scale errors are found to be more sensitive in the weak-forcing regime than those under strong forcing.Meanwhile,larger-scale initial errors are responsible for the error growth after 4 h and produce the precipitation uncertainties at the meso-β-scale.Consequently,these results can be used to explain underdispersion issues in convective-scale ensemble forecasts and provide feedback for ensemble design over the YHRB.

Multi-scale Equations for Incompressible Turbulent Flows

The short-range property of interactions between scales in incompressible turbulent flow was examined. Some formulae for the short-range eddy stress were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress were also derived. Multi-scale equations for the incompressible turbulent flows were proposed. Key words turbulence - incompressible flow - interactions between scales - multi-scale equations MSC 2000 76F70

Multi-scale Equations for Compressible Turbulent Flows

The short-range property of interactions between scales in the compressible turbulent flow was examined. An estimation of the short-range scale scope and some formulae for the short-range eddy stress and heat transfer etc. were given. A concept of resonant-range interactions between extremely contiguous scales was introduced and some formulae for the resonant-range eddy stress and heat transfer etc. were also given. Multi-scale equations for the compressible turbulent flows were presented. The multi-scale equations are approximately closed and do not contain any empirical constants. The compressibility effects on turbulence are determined by the Farve averaged variables and the nonlinear relationships between the Farve- and physical-averaged variables.

Energy Paths that Sustain the Warm-Sector Torrential Rainfall over South China and Their Contrasts to the Frontal Rainfall: A Case Study

Predicting warm-sector torrential rainfall over South China,which is famous for its destructive power,is one of the most challenging issues of the current numerical forecast field.Insufficient understanding of the key mechanisms underlying this type of event is the root cause.Since understanding the energetics is crucial to understanding the evolutions of various types of weather systems,a general methodology for investigating energetics of torrential rainfall is provided in this study.By applying this methodology to a persistent torrential rainfall event which had concurrent frontal and warm-sector precipitation,the first physical image on the energetics of the warm-sector torrential rainfall is established.This clarifies the energy sources for producing the warm-sector rainfall during this event.For the first time,fundamental similarities and differences between the warm-sector and frontal torrential rainfall are shown in terms of energetics.It is found that these two types of rainfall mainly differed from each other in the lower-tropospheric dynamical features,and their key differences lay in energy sources.Scale interactions(mainly through downscale energy cascade and transport)were a dominant factor for the warm-sector torrential rainfall during this event,whereas,for the frontal torrential rainfall,they were only of secondary importance.Three typical signals in the background environment are found to have supplied energy to the warm-sector torrential rainfall,with the quasi-biweekly oscillation having contributed the most.

On the Variation of Divergent Flow： An Eddy-flux Form Equation Based on the Quasi-geostrophic Balance and Its Application

Based on basic equations in isobaric coordinates and the quasi-geostrophic balance,an eddy-flux form budget equation of the divergent wind has been derived. This newly derived budget equation has evident physical significance. It can show the intensity of a weather system,the variation of its flow pattern,and the feedback effects from smaller-scale systems(eddy flows). The usefulness of this new budget equation is examined by calculating budgets for the strong divergent-wind centers associated with the South Asian high,and the strong divergence centers over the Tibetan Plateau,during summer(June–August) 2010. The results indicate that the South Asian high significantly interacts with eddy flows. Compared with effects from the mean flow(background circulation),the eddy flows’ feedback influences are of greater importance in determining the flow pattern of the South Asian high. Although the positive divergence centers over the Tibetan Plateau intensify through different mechanisms,certain similarities are also obvious. First,the effects from mean flow are dominant in the rapid intensification process of the positive divergence center. Second,an intense offsetting mechanism exists between the effects associated with the eddy flows’ horizontal component and the effects related to the eddy flows’ convection activities,which weakens the total effects of the eddy flows significantly. Finally,compared with the effects associated with the convection activities of the mean flow,the accumulated effects of the eddy flows’ convection activities may be more favorable for the enhancement of the positive-divergence centers.

Measurement and assessment of water resources carrying capacity in Henan Province, China

As demands on limited water resources intensify, concerns are being raised about water resources carrying capacity（WRCC）, which is defined as the maximum sustainable socioeconomic scale that can be supported by available water resources and while maintaining defined environmental conditions. This paper proposes a distributed quantitative model for WRCC, based on the principles of optimization, and considering hydro-economic interaction, water supply, water quality, and socioeconomic development constraints. With the model, the WRCCs of 60 subregions in Henan Province were determined for different development periods. The results showed that the water resources carrying level of Henan Province was suitably loaded in 2010, but that the province would be mildly overloaded in 2030 with respect to the socioeconomic development planning goals. The restricting factors for WRCC included the available water resources, the increasing rate of GDP, the urbanization ratio, the irrigation water utilization coefficient, the industrial water recycling rate, and the wastewater reuse rate, of which the available water resources was the most crucial factor. Because these factors varied temporally and spatially, the trends in predicted WRCC were inconsistent across different subregions and periods.

A Simulation Study of the Mesoscale Convective Systems Associated with a Meiyu Frontal Heavy Rain Event

In this study, evolution of the mesoscale convective systems （MCSs） within a Meiyu front during a particularly heavy rainfall event on 22 June 1999 in East China was simulated by using a nonhydrostatic numerical model ARPS （Advanced Regional Prediction System）. Investigations were conducted with emphasis on the impact of the interaction among multi-scale weather systems （MWSs） on the development of MCSs in the Meiyu frontal environment. For this case, the development of MCSs experienced three different stages. （1） The convections associated with MCSs were firstly triggered by the eastward-moving Southwest Vortex （SWV） from the Sichuan Basin, accompanying the intensification of the upper-level jet （ULJ） and the low-level jet （LLJ） that were approaching the Meiyu front. （2） Next, a low-level shear line （LSL） formed, which strengthened and organized the MCSs after the SWV decayed. Meanwhile, the ULJ and LLJ enhanced and produced favorable conditions for the MCSs development. （3） Finally, as the MCSs got intensified, a mesoscale convective vortex （MCV）, a mesoscale LLJ and a mesoscale ULJ were established. Then a coupled-development of MWSs was achieved through the vertical frontal circulations, which further enhanced the MCV and resulted in the heavy rainfall. This is a new physical mechanism for the formation of Meiyu heavy rainfall related to the SWV during the warm season in East China. In the three stages of the heavy rainfall, the vertical frontal circulations exhibited distinguished structures and played a dynamic role, and they enhanced the interaction among the MWSs. A further examination on the formation and evolution of the MCV showed that the MCV was mainly caused by the latent heat release of the MCSs, and the positive feedback between the MCSs and MCV was a key characteristic of the scale interaction in this case.

Energy Budgets on the Interactions between the Mean and Eddy Flows during a Persistent Heavy Rainfall Event over the Yangtze River Valley in Summer 2010

In this study,a persistent heavy rainfall event（PHRE） that lasted for around 9 days（from 0000 UTC 17 to0000 UTC 26 June 2010） and caused accumulated precipitation above 600 mm over the Yangtze River valley,was reasonably reproduced by the advanced research WRF model.Based on the simulation,a set of energy budget equations that divided the real meteorological field into the mean and eddy flows were calculated so as to understand the interactions between the precipitation-related eddy flows and their background circulations（BCs）.The results indicated that the precipitation-related eddy flows interacted with their BCs intensely during the PHRE.At different layers,the energy cycles showed distinct characteristics.In the upper troposphere,downscaled energy cascade processes appeared,which favored the maintenance of upper-level eddy flows;whereas,a baroclinic energy conversion,which reduced the upper-level jet,also occurred.In the middle troposphere,significant upscaled energy cascade processes,which reflect the eddy flows＇ reactionary effects on their BCs,appeared.These effects cannot be ignored with respect to the BCs＇ evolution,and the reactionary effects were stronger in the dynamical field than in the thermodynamical field.In the lower troposphere,a long-lived quasi-stationary lower-level shear line was the direct trigger for the PHRE.The corresponding eddy flows were sustained mainly through the baroclinic energy conversion associated with convection activities.Alongside this,the downscaled energy cascade processes of kinetic energy,which reflect the direct influences of BCs on the precipitation-related eddy flows,were also favorable.A downscaled energy cascade of exergy also appeared in the lower troposphere,which favored the precipitation-related eddy flow indirectly via the baroclinic energy conversion.

Molecular simulation of oligomer inhibitors for calcite scale

Molecular simulation was performed to study the interaction between CaCO3 crystal and several oligomer inhibitors, by using the equilibrium morphology method to calculate the growth morphology of CaCO3 without inhibitors. The calculated morphology agreed well with SEM photographs. Then, a double-layer model was built to investigate the interaction between calcite crystal and oligomer inhibitors containing maleic anhydride （MA） and acrylic acid （AA）. Interaction energy per gram of an oligomer inhibitor was introduced as a scale of inhibition efficiency of different monomers. The results indicated that, for calcite scale inhibition, acrylamide （AM） and vinyl phosphonic acid （VPA） were the most efficient monomers, while allylsulfonic acid （AS） was the poorest. Increasing proportion of AM in dimer inhibitor molecule would improve the inhibition efficiency of MA, though, for a trimer, such as MA-AA-AM, certain sequence of monomers in the inhibitor molecule was necessary besides higher proportion of AM.

An Investigation into Effect of Randomly Distributed Small Scale Vortices on Vortex Self-Organization

Previous studies concerning the interaction of dual vortices have been made generally in the deterministic framework. In this paper, by using an advection equation model, eight numerical experiments whose integration times are 30 h are performed in order to analyze the interaction of dual vortices and the vortex self-organization in a coexisting system of deterministic and stochastic components. The stochastic components are introduced into the model by the way that the Iwayama scheme is used to produce the randomly distributed small-scale vortices which are then added into the initial field. The different intensity of the small-scale vortices is described by parameter K being 0.0, 0.4, 0.6, 0.8, and 1.0, respectively. When there is no small-scale vortex （K=0.0）, two initially separated meso-beta vortices rotate counterclockwise mutually, and their quasi-final flow pattern is still two separated vortices; after initially incorporating small-scale vortices （K=0.8, 1.0）, the two separated meso-beta vortices of initially same intensity gradually evolve into a major and a secondary vortex in time integration. The major vortex pulls the secondary one, which gradually evolves into the spiral band of the major vortex. The quasi-final flow pattern is a self-organized vortex with typhoon-like circulation, and the relative vorticity at its center increases with increasing in K value, suggesting that small-scale vortices feed the self-organized vortex with vorticity. This may be a possible mechanism responsible for changes in the strength of the self-organized vortex. Results also show that the quasi-final pattern not only relates with the initial intensity of the small-scale vortices, but also with their initial distribution. In addition, three experiments are also performed in the case of various boundary conditions. Firstly, the periodic condition is used on the E-W boundary, but the fixed condition on the S-N boundary; secondly, the fixed condition is set on all the boundaries; and thirdly, the periodic condition is chosen on all the boundaries. Their quasi-final flow patterns in the three experiments are the same with each other, exhibiting a larger scale typhoon-like circulation. Based on these results mentioned above, authors think that the transition of vortex self-organization study from the deterministic system to the coexisting system of deterministic and stochastic components is worth exploring.

Impacts of Randomly Distributed Small-Scale Vortices on Typhoon Tracks

Impacts of small-scale vortices on typhoon or tropical cyclone（TC） tracks in a system of three components （an idealized subtropical high ridge,a TC,and small-scale vortices） were examined numerically using a barotropic primitive equation model and idealized initial fields.Two small-scale vorticity fields were generated stochastically,where the number of initial small-scale vortices is 100.In the two fields,the number, size,structure as well as the total kinetic energy of the small-scale vortices were all the same,but their center coordinates were randomly distributed.Two experiments,named EXA and EXB,with the integration time of 56 h,were performed. Comparison of the integration outputs from the two experiments indicates that various small-scale vorticity fields involved could produce both various horizontal winds in the TC outer area and various intensities of the environmental steering for TC.The values of the environmental flow speed along the east-west direction are 7.8,8.2,and 8.7 m s^（-1） in EXA and 8.3,9.5,and 9.7 m s^（-1） in EXB at t = 24,36,and 48 h,respectively. The values along the south-north direction are 0.9,1.8,and 2.5 m s^（-1） in EXA and 2.3,2.3,and 5.9 m s^（-1） in EXB,respectively.The various intensities of the environmental steering could lead to various TC center positions.For example,the difference between the coordinates of TC centers in EXA and EXB reaches 120 km at t = 48 h,which is about 56%of the prediction error of TC tracks in the northwestern Pacific region derived from eight operational models. Dynamics of the interplays between a subtropical high ridge and a TC in previous works has shown that when the TC was located equatorwards of the subtropical ridge,the relationship between the propagation of TC and the local absolute vorticity gradient was characterized by points scattered around their mean values.After introducing the stochastic vorticity field into the model,the interplays among the subtropical high ridge,the TC,and small-scale vortices might make this relationship more complex,that is,besides the scattered points,there also exists a high correlation between the propagation of TC and the local absolute vorticity gradient.

Recent Advance in Understanding the Dynamics of the Madden-Julian Oscillation

The Madden-Julian oscillation （MJO） is a dominant atmospheric low-frequency mode in the tropics. In this review article, recent progress in understanding the MJO dynamics is described. Firstly, the fundamental physical processes responsible for MJO eastward phase propagation are discussed. Next, a recent modeling result to address why MJO prefers a planetary zonal scale is presented. The effect of the seasonal mean state on distinctive propagation characteristics between northern winter and summer is discussed in a theoretical framework. Then, the observed precursor signals and the physical mechanism of MJO initiation in the western equatorial Indian Ocean are further discussed. Finally, scale interactions between MJO and higher- frequency eddies are delineated.