Yulu Liu

An amplitude-frequency study of turbulent scaling intermittency using Empirical Mode Decomposition and Hilbert Spectral Analysis

Hilbert-Huang transform is a method that has been introduced recently to decompose nonlinear, nonstationary time series into a sum of different modes, each one having a characteristic frequency. Here we show the first successful application of this approach to homogeneous turbulence time series. We associate each mode to dissipation, inertial range and integral scales. We then generalize this approach in order to characterize the scaling intermittency of turbulence in the inertial range, in an amplitude-frequency space. The new method is first validated using fractional Brownian motion simulations. We then obtain a 2D amplitude-frequency representation of the pdf of turbulent fluctuations with a scaling trend, and we show how multifractal exponents can be retrieved using this approach. We also find that the log-Poisson distribution fits the velocity amplitude pdf better than the lognormal distribution.

Analysis of temperature time series based on Hilbert-Huang Transform

In this paper, with consideration of the nonlinear and non-stationary properties of the temperature time series, we employ the Hilbert-Huang Transform, based on the empirical mode decomposition (EMD), to analyze the temperature time series from 1959 to 2012 in the Fengxian district of Shanghai, obtained from a certain monitoring station. The oscillating mode is drawn from the data, and its characteristics of the time series are investigated. The results show that the intrinsic modes of 1, 2 and 6 represent the periodic properties of 1 year, 2.5 years, and 27 years. The mean temperature shows periodic variations, but the main trend of this fluctuation is the rising of the temperature in the recent 50 years. The analysis of the reconstructed modes with the wave pattern shows that the variations are quite large from 1963 to 1964, from 1977 to 1982 and from 2003 to 2006, which indicates that the temperature rises and falls dramatically in these periods. The volatility from 1993 to 1994 is far more dramatic than in other periods. And the volatility is the most remarkable in recent 50 years. The log-linear plots of the mean time scales T and M show that each mode associated with a time scale almost twice as large as the time scale of the preceding mode. The Hilbert spectrum shows that the energy is concentra- ted in the range of low frequency from 0.05 to 0.1 Hz, and a very small amount of energy is distributed in the range of higher frequency over 0.1 Hz. In conclusion, the HHT is better than other traditional signal analysis methods in processing the nonlinear signals to obtain the periodic variation and volatility’s properties of different time scales.

Analysis of Nonlinear Biophysical Time Series in Aquatic Environments: Scaling Properties and Empirical Mode Decomposition

Aquatic environmental time series often display large fluctuations at many time scales, possessing stochastic properties, as well as deterministic forcing coming from seasonal or annual meteorological and climatic cycles. In this work we are interested in the characterization of these properties, using different statistical tools, borrowed from the field of turbulence, or of nonlinear time series analysis. We first present the analysis of a long (30 years) time series of daily river flow data, recorded in the Seine River (France). We consider the scale dependence and scale invariance of river flow data, using structure function analysis; we also apply a decomposition method called Empirical Mode Decomposition (EMD). We then consider the statistical properties, and the nonlinear dynamics behaviour of a long-term copepod (small crustaceans) time series sampled every week in the Meditarranean sea from 1967 to 1992. We first consider its high variability and characterize its properties, including extreme evens obeying power law tail pdf. We then consider their scale dependence, using Fourier power spectra together with an EMD approach.

Vortex shedding in the flow around two side-by-side circular cylinders of different diameters

In this paper, the 3-D turbulent flow around two side-by-side circular cylinders of different diameters, at sub-critical Reynolds number (Re = 3 900), is numerically simulated by the large eddy simulation (LES). The spacing ratios (T /D) between the two cylinders are considered in four cases (T /D = 1.2, 1.5, 1.8 and 2.7) to study the vortex shedding and turbulent properties in the flow field. The main results are focused on the drag and lift coefficients, the vortex shedding frequency, the coherent structure, and the scale properties. It is shown that when T /D is equal to 1.2, the vortex shedding of the main cylinder is strongly suppressed by the small cylinder, the drag and lift coefficients of the main cylinder are smaller than those in other three cases. While T /D is equal to 1.5, the vortex shedding of the main cylinder can be improved, the drag and lift coefficients of the main cylinder are larger than those in other three cases. The empirical mode decomposition (EMD) method is applied to decompose the velocity signals traced by the LES. It is shown that there is a linear relationship between the mean period and the mode in the semi-log coordinates. The vortex shedding period of the main cylinder is consistent with the period of the restructured coherent structures quantitatively.

Numerical study of high-order Lagrangian structure functions in a turbulent channel flow with low Reynolds number

The scaling exponents of Lagrangian velocity structure functions from orders 1 to 10 in a low Reynolds number turbulent channel flow are investigated by using direct numerical simulation. The Reynolds number Reτ is 80 (based on friction velocity on the wall). The Lagrangian velocity structure functions are shown to obey the scaling relations ∼τζL(q). The scaling exponents are normalized by ζL(2) (so-called ESS procedure). The coincidence between the theoretical predictions and numerical calculations is very good for the longitudinal scaling exponent in the channel center. It is also found that the high-order longitudinal scaling exponents agree with theoretical values better than those for the transverse direction.

Large eddy simulation of turbulent statistical and transport properties in stably stratified flows

Three dimensional large eddy simulation (LES) is performed in the investigation of stably stratified turbulence with a sharp thermal interface. Main results are focused on the turbulent characteristic scale, statistical properties, transport properties, and temporal and spatial evolution of the scalar field. Results show that the buoyancy scale increases first, and then goes to a certain constant value. The stronger the mean shear, the larger the buoyancy scale. The overturning scale increases with the flow, and the mean shear improves the overturning scale. The flatness factor of temperature departs from the Gaussian distribution in a fairly large region, and its statistical properties are clearly different from those of the velocity fluctuations in strong stratified cases. Turbulent mixing starts from small scale motions, and then extends to large scale motions.

Eulerian and Lagrangian Structure Function's Scaling Exponents in Turbulent Channel Flow

The relation between Eulerian structure function’s scaling exponents and Lagrangian ones in turbulent channel flows is explored both theoretically and numerically. A nonlinear parametric transformation between Eulerian structure function’s scaling exponents and Lagrangian ones is derived, following Landau and Novikov’s frame work. This relation is then compared to some known experimental and numerical results, but mainly to our DNS (direct numerical simulation) results of a fully developed channel flow with Reτ = 100. The scaling exponents are evaluated in terms of the ESS (extended self-similarity) method, since the Reynolds number is too low to make the standard scaling laws applicable. The agreement between theory and simulation is satisfactory

Scaling and variability of biophysical time series in aquatic environments

Preface.- Introducing Networks in Climate Studies.- Two Paradigms in Landscape Dynamics: Self-Similar Processes and Emergence.- Effects of Systematic and Random Errors on the Spatial Scaling Properties in Radar-Estimated Rainfall.- Nonlinear Dynamics in the Earths Magnetosphere.- Microseism Activity and Equilibrium Fluctuations.- An Exponential Langevin-type Model for Rainfall Exhibiting Spatial and Temporal Scaling.- Storm Tracking and Ensemble Prediction .- Towards a Nonlinear Geophysical Theory of Floods in River Networks: An Overview of 20 Years of Progress.- Investigations of Wave-induced Nonlinear Response of Minor Species with the KBM Averaging Method.- ENSO Signal Propagation Detected by Wavelet Coherence and Mean Phase Coherence Methods.- Twenty-Five Years of Nonlinearity in Oceanography from the Lagrangian Perspective.- Self-Scaling of the Statistical Properties of a Minimal Model of the Atmospheric Circulation .- Hindcast AGCM Experiments on the Predictability of Stratospheric Sudden Warming.- Self Organized Criticality and/or Low Dimensional Chaos in Second Earthquake Processes: Theory and Practice in Hellenic Region.- Analysis of Nonlinear Biophysical Time Series in Aquatic Environments: Scaling Properties and Empirical Mode Decomposition.- The Arctic Ocean as a Coupled Oscillating System to the Forced 18.6 Year Lunar Gravity Cycle.- Dynamical Synchronization of Truth and Model as an Approach to Data Assimilation, Parameter Estimation, and Model Learning.- Scale, Scaling and Multifractals in Geosciences: Twenty Years On.- Statistics of Return Intervals and Extreme Events in Long-Term Correlated Time Series.- Statistical Properties of Mid-Latitude Atmospheric Variability.- On the Spatiotemporal Variability of the Temperature Anomaly Field.- Time Evolution of the Fractal Dimension of Electric Self-Potential Time Series.- Diffusion Entropy Analysis in Seismicity.- Snow Avalanches as a Non-Critical, Punctuated Equilibrium System.- Evidence fromWavelet Lag Coherence for Negligible Solar Forcing of Climate at Multi-year and Decadal Periods .- From Diversity to Volatility: Probability of Daily Precipitation Extremes.- Stochastic Linear Models of Nonlinear Geosystems.- Reducing Forecast Uncertainty to Understand Atmospheric Flow Transitions.- The Role of El Nino-Southern Oscillation in Regulating its Background State.- Nonlinear Dynamics of Natural Hazards .- Predicting the Multifractal Geomagnetic Field.- Index.