Identifying Nonstationarity in Turbulence Series

Because of rapid forcing by varying cloud and sky conditions, turbulence time series collected in the atmospheric surface layer over land may often be nonstationary. The meteorological community, however, has no consensus definition of what nonstationarity is and, thus, no consensus method for how to identify it. This study, therefore, adopts definitions for first-order and second-order stationarity taken from the time series analysis literature and implements new analysis techniques and probabilistic tests to quantify first-order and second-order nonstationarity. First-order nonstationarity manifests as a change in the series mean; second-order nonstationarity, as a change in the variance. The analysis identifies nonstationarity in surface-level turbulent temperature and water vapour series collected during two sample days with solar forcing influenced by cirrus and cirrostratus clouds, but that nonstationarity is not as severe as expected despite the rapid thermal forcing by these clouds. On the other hand, even with negligible cloud forcing, both sample days exhibited severe nonstationarity at night.     

Photometric Solution of the O-type Eclipsing Binary V1007 Sco

A Cosmological model with a viscous fluid in Kaluza-Klein metric is obtained assuming a time-dependent equation of state. The solution is in fact a generalization of an earlier work by Hajj and Boutros for a perfect fluid. It is also found that dimensional reduction of the extra space takes place such that the five-dimensional universe naturally evolves into an effective four-dimensional one. The dynamical behavior of the model is examined and it is also found that with a decrease in extra space the observable 3D space entropy increases thus accounting for the large value of entropy observable at present.     

Cosmological models with viscous fluid and time- dependent equation of state in Wesson’s theory

Assuming the time-dependent equation of state p=λ(t)ρ, five dimensional cosmological models with viscous fluid for an open universe (k=−1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys. 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this theory, i.e. the mass scale factor A(t) which characterizes the rest mass of a typical particle is evolving with cosmic time just as the spatial scale factor R(t). It is further found that rest mass is approximately constant in the present universe.     

A creep–rupture model of synthetic fiber ropes for deepwater moorings based on thermodynamics

The synthetic fiber ropes such as polyester, aramid and high modulus polyethylene (HMPE) are increasing applied to deepwater mooring systems for oil and gas exploitation. Due to that mooring ropes generally bear tensions for a long period, synthetic fiber ropes that are composed of the viscoelastic material would present creep behaviors and even the creep rupture, which is the failure mode of greatest concern especially for HMPE ropes and on which still less study can be found. A creep damage analysis of synthetic fiber ropes is of necessity to ensure the safe and economic operation of mooring systems. Therefore further investigation on the creep–rupture behavior is beneficial to fully establishing confidence in the viability of synthetic fiber ropes for deepwater moorings. In the present study, a creep–rupture model is proposed within the framework of thermodynamics to investigate the creep and damage behaviors of synthetic fiber ropes. Methods for identifying the model parameters are also proposed in detail, which apply to any component of fiber ropes such as the fiber, yarn, strand and rope. Experimental data of aramid yarns available from the literature are utilized to validate the constitutive model. Creep and creep–rupture tests of HMPE strands at different loading levels are specially performed to further examine the present model. The present work demonstrates that the proposed model can effectively describe the viscoelastic property and damage evolution of synthetic fiber ropes at different loading levels.     

On the modeling of wave propagation on non-uniform currents and depth

By transforming two different time-dependent hyperbolic mild slope equations with dissipation term for wave propagation on non-uniform currents into wave-action conservation equation and eikonal equation, respectively, shown are the different effects of dissipation term on the eikonal equation in the two different mild slope equations. The performances of intrinsic frequency and wave number are also discussed. Thus the suitable mathematical model is chosen in which the wave number vector and intrinsic frequency are expressed both more rigorously and completely. By using the perturbation method, an extended evolution equation, which is of time-dependent parabolic type, is developed from the time-dependent hyperbolic mild slope equation which exists in the suitable mathematical model, and solved by using the alternating direction implicit (ADI) method. Presented is the numerical model for wave propagation and transformation on non-uniform currents in water of slowly varying topography. From the comparisons of the numerical solutions with the theoretical solutions of two examples of wave propagation, respectively, the results show that the numerical solutions are in good agreement with the exact ones. Calculating the interactions between incident wave and current on a sloping beach [Arthur, R.S., 1950. Refraction of shallow water waves. The combined effects of currents and underwater topography. EOS Transactions, August 31, 549–552], the differences of wave number vector between refraction and combined refraction–diffraction of waves are discussed quantitatively, while the effects of different methods of calculating wave number vector on numerical results are shown.     

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.     

Time-dependent tunnel deformations in homogeneous and heterogeneous weak rock formations

To investigate long-term, time-dependent tunnel deformations, this study employs a non-linear rheological model capable of considering the tertiary creep behaviour of the rock mass (Okubo and Fukui, 2006). A model parametric study is undertaken with a 3D numerical model encompassing a tunnel. The results show that the tunnel walls start to deform at an accelerating rate after a lapse of ten years. The results offer an explanation to previously reported tunnel instability cases. A 3D numerical model encompassing weak rock formation obliquely intersecting with the tunnel is then constructed. The analysis yields asymmetric wall deformation pattern, suggesting the need for optimizing rock supports.     

Integration of creep into a modified hardening soil model for time-dependent analysis of a high rockfill dam

This paper proposes an approach to extend a modified hardening soil model into the time-dependent analysis of high rockfill dams. The key feature of the extended model is the integration of a creep model and the double yield surface elasto-plastic model, via modifying the hardening functions. The integrated model is validated by a laboratory multistage creep test. Results from three-dimensional analyses including the without creep and with creep considerations of the Nam Ngum 2 dam have been compared with the in-situ measurements. The prediction of dam deformation can be significantly enhanced by the proposed model.     

Analytic solutions to transient groundwater flow under time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage

Analytical solutions for the water table and lateral discharge in a heterogeneous unconfined aquifer with time-dependent source and fluctuating river stage were derived and compared with those in an equivalent homogeneous aquifer. The heterogeneous aquifer considered consists of a number of sections of different hydraulic conductivity values. The source term and river stage were assumed to be time-dependent but spatially uniform. The solutions derived is useful in studying various groundwater flow problems in a horizontally heterogeneous aquifer since the spatially piecewise-constant hydraulic conductivity and temporally piecewise-constant recharge and lateral discharge can be used to quantify variations in these processes commonly observed in reality. Applying the solutions derived to an aquifer of three sections of different hydraulic conductivity values shown that (1) the aquifer heterogeneity significantly increases the spatial variation of the water table and thus its gradient but it has little effect on lateral discharge in the case of temporally and spatially uniform recharge, (2) the time-dependent but spatially uniform recharge increases the temporal variation of groundwater table over the entire aquifer but its effect on lateral discharge is limited in the zone near the river, and (3) the effect of river stage fluctuation on the water table and lateral discharge is limited in the zone near the river and the effect of the heterogeneity is to increase lateral discharge to or recharge from the river.     

Several effects of baroclinic currents on the three‐dimensional propagation of inertial‐internal waves†

A ray theory is applied to the problem of three‐dimensional propagation of inertial‐internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate. As time increases, the Doppler‐shifted wave frequency, or intrinsic frequency, tends to a limiting value determined by the horizontal and vertical variations of the mean current and density fields. The limiting value of the intrinsic frequency determines critical surfaces where energy is transferred to the mean motion. Also, the group velocity tends to the mean current velocity, and the phase velocity tends to be oriented towards or away from the core of the mean current, depending upon whether the wave is either initially propagating with a wave number component antiparallel or parallel to the mean current.