地震活动的随机标度和非线性标度律

把地震作为一个复杂系统，研究了地震活动的随机性质．当不考虑震级范围时，全球地震活动、人震的余震和区域震群均有以幂次律为特征的长尾现象．地震的强度由震级确定，具有一特定震级的地震可形成一个地震活动系列，很多这样的地震活动系列就形成具有各种震级的地震的集合．不同地震系列间的统计特征由随机标度来表征，随机标度表明了由地震震级分类的不同地震系列间统计时刻的标度关系．为了统一地方、区域和全球地震活动性的统计特性，引入了非线性标度率．     

STOCHASTIC THEORY OF THE DISTRIBUTION OF SEDIMENT PARTICLES SUSPENDED IN A TURBULENT FLOW

The random motion of sediment particles suspended in a turbulent flow is studied by means of stochastic process. Results of analysis of particle's frequency response to the random force exerted on the particle due to fluid turbulence suggest that only the lower part of the whole frequency range of the eddy motion will govern the motion of the particle. The mean values of particle velocity and displacement in the vertical direc- tion are calculated and it is found that particle velocity vp- can be decomposed into a mean motion and a velocity fluctuation vp- , where is equal to the fall velocity in tranquil fluid. An Ito^ random differential equation for particle dis- placement Yp is developed, from which a Fokker-Planck equation for the probability density function p(y,t) is derived on the basis of the theory of Markov process, where y denotes the vertical coordinate. The vertical distribution of the particle is thus interrelated to the random motion of the particle. The an effect that a particle will be subject to in the neighborhood or the bottom boundary is taken into consideration and a corresponding Fokker-Planck equation is developed. Analytical solution of the Fok- ker-Planck equation including the lift force effect shows that probability density p(y,t) for the particle displacement has a maximum value at y = H where the perpen- dicular component of the lift force balances the particle gravity. This theoretical result agrees with experimental observations as reported in literature.     

Parameter identification in tidal models with uncertain boundary conditions

In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.     

Stochastic analysis of multiphase flow in porous media: 1. Spectral/perturbation approach

Stochastic analysis of steady-state multiphase (water, oil, and air) flow in heterogeneous porous media was performed using the perturbation theory and spectral representation techniques. The gas phase is assumed to have constant pressure. The governing equations describing the flow of oil and water are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil grain size distribution index, . Three different stochastic combinations of these two input parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the derivation of the mean flow equations and estimation of the effective flow properties. The impact of the spatial variability ofk and on the effective conductivities and the variances of pressures and specific discharges was examined.     

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, . These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter . The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.     

Nonlinear aspects of sea surface temperature in Monterey Bay

Nonlinear aspects of sea surface temperature (SST) in Monterey Bay are examined, based on an 85-year record of daily observations from Pacific Grove, California. Oceanic processes that affect the waters of Monterey Bay are described, processes that could contribute to nonlinearity in the record. Exploratory data analysis reveals that the record at Pacific Grove is non-Gaussian and, most likely, nonstationary. A more recent test for stationarity based on a power law approximation to the slope of the power spectrum indicates that the record is stationary for frequencies up to ∼8 cycles per year (∼45 days), but nonstationary at higher frequencies. To examine the record at Pacific Grove for nonlinear behavior, third-order statistics, including the skewness, statistical measures of asymmetry, the bicorrelation, and the bispectrum, were employed. The bicorrelation revealed maxima located approximately 365 days apart, reflecting a nonlinear contribution to the annual cycle. Based on a 365-day moving window, the running skewness is positive almost 80% of the time, reflecting the overall impact of warming influences. The asymmetry is positive approximately 75% of the time, consistent with the asymmetric shape of the mean annual cycle. Based on the skewness and asymmetry, nonlinearities in the record, when they occur, appear to be event-driven with time scales possibly as short as several days, to several years. In many cases, these events are related to warm water intrusions into the bay, and El Niño warming episodes.The power spectrum indicates that the annual cycle is a dominant source of variability in the record and that there is a relatively strong semiannual component as well. To determine whether or not the annual and semiannual cycles are harmonically related, the bispectrum and bicoherence were calculated. The bispectrum is nonzero, providing a strong indication of nonlinearity in the record. The bicoherence indicates that the annual cycle is a major source of nonlinearity and further implies that the annual and semiannual cycles are harmonically related. Based on the wavelet power spectrum (WPS), the appearance of the semiannual cycle is transitory; however, pathways between the annual and semiannual cycles appear at certain times when nonlinear interaction between them could occur. Comparisons between the WPS and the running skewness suggest that there is a tendency for periods when pathways exist, to coincide with increased positive skewness, and, often, with El Niño warming episodes. The Hilbert-Huang transform, a relatively new tool for nonstationary and nonlinear spectral analysis, was used to further examine the origin of the semiannual cycle. The time-dependent Hilbert spectrum reveals large and erratic variations in frequency associated with semiannual cycle but far greater stability associated with the annual cycle. As a result, the time-integrated Hilbert spectrum does not indicate the presence of a semiannual cycle. The method of surrogates from the field of nonlinear dynamics was also employed to test the Hopkins record for nonlinearity. Differences between the data and the surrogates were found that were statistically significant, implying the existence of nonlinearity in the record. Using the method of surrogates together with a one-year moving window, El Niño warming episodes appear to be a likely source of nonlinearity, consistent with the other analyses that were performed. Finally, the influence of stochastic variability due to serial correlation in the data was examined by comparing standardized statistics for the observations and for simulations based on an autoregressive model whose properties were obtained from the observations. The magnitude of the variability for the simulations was found to be far less than that associated with the original data, and thus stochastic variability does not appear to be a factor that significantly affects the interpretation of our results.     

Scour below pipelines and around vertical piles in random waves

An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsøe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsøe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested.     

Optimisation of an idealised ocean model,stochastic parameterisation of sub-grid eddies

An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30 km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5 km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model.The system considered is an idealised barotropic double gyre that is chaotic at both resolutions. Using the optimisation scheme, we find and apply the constant in time, but spatially varying, forcing term that is equal to the time integrated forcing of the sub-grid scale eddies. A linear stochastic term, independent of the large-scale flow, with no spatial correlation but a spatially varying amplitude and time scale is used to represent the transient eddies. The climatological mean, variance and 5 day lag-covariance of the velocity from a single high resolution integration is used to provide an optimisation target. No other high resolution statistics are required. Additional programming effort, for example to build a tangent linear or adjoint model, is not required either.The focus of this paper is on the optimisation scheme and the accuracy of the optimised flow. However the forcing can provide insights in the design of deterministic and stochastic parameterisations. In the present study, we found that the stochastic parameterisation correcting the model variance is associated with the spatial pattern of eddy-decorrelation timescales rather than the spatial pattern of the amplitude of the variance. The method can be applied in future investigations into the physical processes that govern barotropic turbulence and it can perhaps be applied to help understand and correct biases in the mean and variance of a more realistic coarse or eddy-permitting ocean model. The method is complementary to current parameterisations and can be applied at the same time without modification.     

Influence of yaw-roll coupling on the behavior of a FPSO: An experimental and numerical investigation

An inconvenience in the experimental set-up of a FPSO in regular waves highlighted occurrence of parametric-roll events promoted by yaw-roll coupling and motivated a combined physical and numerical analysis on the relevance of this phenomenon on the roll resonance, as well as on the water shipping. The model tests examine the ship in head- and bow-sea waves in the zone of the first parametric resonance. Numerically, it is adopted a 3D Domain-Decomposition (DD) strategy combining a weakly-nonlinear potential-flow solver based on the weak-scatterer theory with a shallow-water approximation for the shipped liquid and with a bottom-slamming solution. Detailed comparisons against these and other seakeeping experiments validated the numerical method in its different aspects with global success.At first, a 2-dof equivalent linearized yaw-roll coupled system is examined and the measurements are used to estimate hydrodynamic coefficients required to complete the mathematical model of the problem. Then the DD method is applied to verify the instability occurrence and compared against the experiments. From the analysis, the parametric-roll instability does not occur if all nonlinearities in the roll restoring load are not accounted for. However the amplitude of the resonant roll is affected by the coupling with the other degrees of freedom. Especially the coupling with yaw tends to increase the steady-state roll amplitude. It also affects the water shipping with the trend in reducing its severity for the vessel, this is opposite to the influence of the parametric roll in head-sea waves on the water on deck, as documented in Greco et al. (2014) [4].