Non-Acceleration Theorem in a Primitive Equation System: I. Acceleration of Zonal Mean Flow

Non-acceleration theorem in a primitive equation system is developed to investigate the influences of waves on the mean flow variation against external forcing. Numerical results show that mechanical forcing overwhelms thermal forcing in maintaining the mean flow in which the internal mechanical forcing associated with horizontal eddy flux of momentum plays the most important roles. Both internal forcing and external forcing are shown to be active and at the first place for the mean flow variations, whereas the forcing-induced mean meridional circulation is passive and secondary. It is also shown that the effects on mean flow of external mechanical forcing are concentrated in the lower troposphere, whereas those due to wave-mean flow interaction are more important in the upper troposphere. These act together and result in the vertically easterly shear in low latitudes and westerly shear in mid-latitudes. This vertical shear of mean flow is to some extent weakened by thermal forcing.

ACOUSTIC PROPAGATION IN SHEARED MEAN FLOW USING COMPUTATIONAL AEROACOUSTICS

Acoustic propagation problems in the sheared mean flow are numerically investigated using different acoustic propagation equations , including linearized Euler equations ( LEE ) and acoustic perturbation equations ( APE ) .The resulted acoustic pressure is compared for the cases of uniform mean flow and sheared mean flow using both APE and LEE.Numerical results show that interactions between acoustics and mean flow should be properly considered to better understand noise propagation problems , and the suitable option of the different acoustic equations is indicated by the present comparisons.Moreover , the ability of APE to predict acoustic propagation is validated.APE can replace LEE when the 3-D flow-induced noise problem is solved , thus computational cost can decrease.

The Propagation of Inertia-Gravity Waves and Their Influence on Zonal Mean Flow Part Two:Wave Breaking and Critical Levels

The gravity wave breaking is crucial to the large-scale circulation of middle atmosphere. In this paper, we follow Lindzen (1981) to draw out the parameterization of two-dimensional gravity wave breaking including inertial effect. Also we present some properties of critical levels and inertial critical levels.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Quasi-40-Day Oscillation and Its Teleconnection Structure together with the Possible Dependence on Conversion of Barotropic Unstable Energy of Temporal Mean Flow

A study is made of the distribution of the diagnostic quantity vector E and the teleconnection structure of 30-50 (quasi-40) day oscillation, together with the dependence on the conversion of barotropic unstable energy of mean flow in terms of ECWMF daily 500 hPa grid data in winter, indicating that the energy transportation is closely associated with the westerly jet position, with zonal (meridional) propagation in the strong (weak) wind region, that considerable conversion of barotropic energy occurs at the jet exit region where low-frequency oscillation gains energy from the mean flow, leading to maximum kinetic energy for the oscillation observed there, which is marked by evident barotropy in striking contrast to the baroclinicity at low latitudes and that the teleconnection core is related to the center of action in the atmosphere and bound up with the pattern of the west wind.

Observed characteristics of tidal currents and mean flow in the northern Yellow Sea

Several bottom-mounted Acoustic Doppler Current Profiler (ADCP) moorings were deployed in the northern Yellow Sea (NYS) during the four seasons of 2006–2007 and also the summertime of 2009. A synthesis analysis on the time-continuous records was performed to examine the characteristics and variations of tidal currents and mean flow over the observation period at these stations. Tidal currents accounted for ~75% of the total kinetic energy, with the absolute dominance of M2 constituent. Visible vertical variations of tidal flow were found on all sites, featured by the decrease of amplitude, increase of rotation rate as well as a decreasing trend of the phase for M2 component with depth. A notable exception was in the central NYS, where the maximum tidal currents occurred in the upper or middle layers (~20–40 m) instead of near the surface (<10 m). The observed mean flow was relatively weak, smaller than 15 cm/s. Velocity on the northern end of Yellow Sea Trough (YST) was characterized by low magnitude and an obvious layered structure vertically. In the Bohai Strait (BS) and the northern slope area, the currents weakened and the flow direction presented a major trend to deflect counterclockwise with depth in most observations. Summertime cyclonic circulation around the Yellow Sea Cold Water Mass (YSCWM), its intensification on the frontal zone and the Yellow Sea Warm Current (YSWC) for the winter season were all evident by our direct current measurements. However, the details of water exchange through the BS appeared partly diff erent from the traditionally-accepted pattern. The vertical diff erences of tidal and mean flow were larger in summer than that in winter, implying the influence of thermal structure to the local currents. Aff ected by the water stratification, mean flow usually reached its maximum near the thermocline in spring and summer, while showing a nearly uniform vertical distribution during winter.

Effect of carbon, silicon, and manganese content on mean flow stress at elevated temperature

Ten studied steels including different carbon content, silicon content, and manganese content were deformed in compression over a temperature range of 600 ?C to 1 000 ?C at the strain rate of 1 s-1. The curves of the mean flow stressdeformation temperature were drawn up. The mean flow stresses of higher carbon content steels decreased continuously as the applied deformation temperature increased in the whole temperature range, while the mean flow stress of lowest carbon steel displayed an abrupt drop near the two phases region. The reason for the abrupt drop phenomena was explained as the result of phase transformation. The mean flow stresses of steels with high silicon content and low manganese content also have this phenomena.

基于K-means与GRNN的高原山区高速公路短时交通流预测

为了研究可适用于高原山区高速公路短时交通流的预测方法,以及预测方法思路对绩效的影响,提出基于广义回归神经网络(General Regression Neural Network,GRNN),构建K均值聚类算法(K-means clustering algorithm,K-means)与GRNN混合预测方法思路,即通过K-means和绩效指标判断GRNN模型参数最佳值,进而建立最佳预测模型。与传统上通过经验或一定指标判断模型参数值的思路相比,采用K-means和GRNN混合预测思路得出的模型参数值更佳,且模型RMSE、MAE最高可分别改善45.92%、45.05%,则构建的混合预测方法思路是科学有效的,可为高原山区交通流预测方法优化提供借鉴。

CFD analysis of a transfer matrix of exhaust muffler with mean flow and prediction of exhaust noise

A multi-dimensional computational fluid dynamics(CFD) approach was proposed in this study aiming to calculate the transfer matrix of an engine exhaust muffler in the conditions with and without mean flow.The CFD model of the muffler with absorptive material defined as porous zone was calibrated with the measured noise reduction without mean flow,and was further employed to study the effect of the mean flow on the acoustic performance of the muffler.Furthermore,the exhaust acoustical source was derived from the calculated transfer matrices of six different additional acoustic loads obtained by the proposed CFD approach as well as the measured tail noise based on a multiload least squares method.Finally,the exhaust noise was predicted based on Thevenin's theorem.The proposed CFD approach was suggested to be able to predict the acoustic performance of a complex muffler considering mean flow(without and with mean flow) and heat transfer,and provide reasonable results of the exhaust noise.

Sound Transmission Comparisons of Active Elastic Wave Metamaterial Immersed in External Mean Flow

Using the active feedback control system on the elastic wave metamaterial,this research concentrates on the sound transmission with the dynamic effective model.The metamaterial is subjected to an incident pressure and immersed in the external mean flow.The elastic wave metamaterial consists of double plates and the upper and lower four-link mechanisms are attached inside.The vertical resonator is attached by the active feedback control system and connected with two four-link mechanisms.Based on the dynamic equivalent method,the metamaterial is equivalent as a single-layer plate by the dynamic effective parameter.With the coupling between the fluid and structure,the expression of the sound transmission loss(STL)is derived.This research shows the influence of effective mass density on sound transmission properties,and the STL in both modes can be tuned by the acceleration and displacement feedback constants.In addition,the dynamic response and the STL are also changed obviously by different values of structural damping,incident angle(i.e.,the elevation and azimuth angles)and Mach number of the external fluid with the mean flow property.The results for sound transmission by two methods are compared,i.e.,the virtual work principle for double plates and the dynamic equivalent method corresponding to a single one.This paper is expected to be helpful for understanding the sound transmission properties of both pure single-and double-plate models.

Principal Modes of Summertime Zonal-Mean Flow and Their Connections with the AO and ENSO

The NCEP/NCAR reanalysis data have been employed to diagnose variations of the zonal mean flow in boreal summer. Two leading EOF modes are found to dominate the spatial and temporal changes of the summertime zonal mean winds in the troposphere. EOF1 shows the distribution of zonal-mean flow anomalies with higher variance in the North Polar Region, whereas the EOF2 shows the distribution of zonal-mean flow anomalies with higher variance in tropical and extra-tropical regions. The EOF1 and EOF2 have respectively the periodicities similar to those of AO and ENSO. Significant lag correlations have been found between EOF1 and ENSO, and between EOF2 and AO, in the seasons including spring, autumn, and winter. However, no significant correlations have been found between EOF1 in summer and ENSO in any other seasons, and between EOF2 in summer and AO in other seasons, no matter how big the lag that represents number of seasons has been set. These results suggest that the principal modes of summertime zonal mean flow could be statistically separated from each other. Hence, EOF1 and EOF2 are physically related to the AO and ENSO respectively. A theory called quasi-geostrophic non-acceleration theorem has been used to partly explain the possible mechanisms of the maintenance of the two principal modes. The composite differences of the divergence of Eliassen-Palm flux （E-P flux） between positive and negative years as obtained from the time series of EOF1 and EOF2 display the distributions that contribute to the zonal mean wind anomalies represented by EOF1 and EOF2, respectively. The planetary other than the synoptic waves dominate the behaviors of the E-P fluxes, suggesting the crucial role of the planetary waves in the maintenance of the zonal mean flow anomalies. The residual circulation as well as the friction, which cancel the divergence of the E-P flux, also play an important role in some places. These results are very helpful for our better understanding how the anomalous zonal mean flows maintain and how the ENSO and AO influence the global climate variations.

HYPERBOLIC MEAN CURVATURE FLOW:EVOLUTION OF PLANE CURVES

In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the following evolution equation δ^2F /δt^2 （u, t） = k（u, t）N（u, t）-▽ρ（u, t）, ∨（u, t） ∈ S^1 × [0, T ） with the initial data F （u, 0） = F0（u） and δF/δt （u, 0） = f（u）N0, where k is the mean curvature and N is the unit inner normal vector of the plane curve F （u, t）, f（u） and N0 are the initial velocity and the unit inner normal vector of the initial convex closed curve F0, respectively, and ▽ρ is given by ▽ρ Δ=（δ^2F /δsδt ,δF/δt） T , in which T stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F , it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere equation. Based on this, we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at a finite time interval [0, Tmax） and when t goes to Tmax, either the solution convergesto a point or shocks and other propagating discontinuities are generated. Furthermore, we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support functions and the curvature of the curve. In the end, we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time R^1,1.

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature.

SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Given a family of smooth immersions of closed hypersurfaces in a locally symmetric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case

Wave-mean flow interaction and its relationship with the atmospheric energy cycle with diabatic heating

Based on the traditional theory of wave mean flow interaction, an improved quasi-geostrophic Eliassen-Palm flux with diabatic heating included is deduced. It is shown that there exists an intrinsic relation between the atmospheric energy cycle derived by Lorenz and the wave energy transfer derived by Eliassen and Palm. From this relation it becomes clear that the energy propagation process of large-scale stationary wave is indeed a part of Lorenz energy cycle, and the energy transform from mean flow to wave equals the global mass integral of the divergence of local wave energy flux or the global integral of local wave energy. The diagnostic results by using NCEP/NCAR reanalysis data suggest that the classical adiabatic Eliassen-Palm flux relation can present only the wintertime wave energy transformation. For other seasons, however, the diabatic effect must be taken into account.

The Propagation of Inertia-Gravity Waves and Their Influence on Mean Zonal Flow, Part One: the Propagation of Inertia-Gravity Waves

Inertia-gravity waves play an increasingly important role in the middle atmosphere dynamics. As a result, more attention has been paid to the study of inertia-gravity waves, especially to the middle atmosphere gravity waves. This paper presents some aspects of inertia-gravity waves with emphasis on the propagation. Two methods are used here, namely, geometric optical method and physical optical method. We can see from the study that inertia-gravity waves are similar to planetary waves in some respects and they are different from planetary waves in others.

Generalized Mean-Flow Theory of Wave-Current-BottomInteractions

The interaction between waves, currents and bottoms in estuarine and coastal regions is ubiquitious, in particular the dynamic mechanism of waves on large-scale slowly varying currents. The wave action concept may be extended and applicated to the study of the mechanism. Considering the effects of moving bottoms and starting from the Navier-Stokes equation of motion of a vinous fluid including the Coriolis force, a generalized mean-flow medel theory for the nearshore region, that is, a set of mean-flow equations and their generalized wave action equation involving the three new kinds of actions termed respectively as the current wave action, the bottom wave action and the dissipative wave action which can be applied to arbitrary depth over moving bottoms and ambient currents with a typical vertical structure, is developed by vertical integration and time-averaglng over a wave peried, thus extending the classical concept, wave action, from the ideal averaged flow conservative system to the real averaged flow dissipative dynamical system, and having a large range of application.

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi(FIK) identity(FUKAGATA, K., IWAMOTO, K., and KASAGI, N.Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows.Physics of Fluids, 14(11), L73–L76(2002)) and the Renard-Deck(RD) identity(DECK,S., RENARD, N., LARAUFIE, R., and WEISS, P.′E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650.Journal of Fluid Mechanics, 743, 202–248(2014)). The direct numerical simulation(DNS) data provided by Lee and Moser(LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics,774, 395–415(2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers.The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.