Applying a Random Time Mapping to Mann modelled turbulence for the generation of intermittent wind fields

A new approach to derive a synthetic wind field model which combines spatial correlations from the Mann model and intermittency is introduced. The term intermittency describes the transition from Gaussian to non-Gaussian velocity increment statistics at small scales, where non-Gaussian velocity increment statistics imply a higher probability for extreme values than a Gaussian distribution. The presented new model is named the Time-mapped Mann model. The intermittency is introduced by applying a special random time-mapping procedure to the regular Mann model. The Time-mapping procedure is based on the so-called Continuous-time random walk model. As will be shown, the new Time-mapped Mann field reflects spatial correlations from the Mann model in the plane perpendicular to flow direction and temporal intermittency. In a first wind turbine study, the new Time-mapped Mann field and a regular Mann field are used as inflow to a wind turbine in a Blade Element Momentum simulation. It is shown that the wind field intermittency carries over to the loads of the wind turbine, and, thus, shows the importance of carefully modeling synthetic wind fields.

Design Optimization and Parameter Analysis of a Hybrid Rocket Motor-Powered Small LEO Launch Vehicle

In this paper, the effects of different grain shapes of a hybrid rocket motor (HRM) and different payload mass/orbit heights on the design of small launch vehicles (SLVs) are systematically discussed. An integrated overall design model for the hybrid rocket motor-powered small launch vehicle (HPSLV) is established, and two groups of three-stage SLVs capable of sending small payloads to the low earth orbit (LEO) are designed and optimized. In the first group, the SLVs with different grain shapes and different numbers of chambers in HRMs at the 1st and the 2nd stages are optimized and analyzed. In the second group, the SLVs capable of sending different payload mass to different orbit heights are optimized and analyzed. Pareto graphs of the design results show that the design of HRM at the 1st stage has the greatest impact on the take-off mass, total velocity increment, and maximum axial overload of the SLV. Self-organizing maps show that the take-off mass, maximum diameter, overall length, and velocity increment of the SLVs have the same variation tendency. For the 1-chamber HRM at the 1st stage, the wheel-shaped grain is better than circle-shaped and star-shaped grains in terms of reducing the total mass and length of the SLV, and the 4-chamber parallel HRM has more advantages over all 1-chamber designs for the same reason. The theoretical velocity increments are calculated by the Tsiolkovsky formula, and the actual velocity increments are obtained based on the trajectory simulation data. The results indicate that the HPSLV has a regular distribution in terms of the ratio of theoretical (actual) velocity increments at three different stages, and the estimated distribution ratio is around 1 : 1.55 : 1.69 (1 : 1.9 : 2.39), which can provide some reference for future development of HPSLV.

Generalized Description of Intermittency in Turbulence via Stochastic Methods

We present a generalized picture of intermittency in turbulence that is based on the theory of stochastic processes. To this end, we rely on the experimentally and numerically verified finding by R. Friedrich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)] that allows for an interpretation of the turbulent energy cascade as a Markov process of velocity increments in scale. It is explicitly shown that phenomenological models of turbulence, which are characterized by scaling exponents ζn of velocity increment structure functions, can be reproduced by the Kramers–Moyal expansion of the velocity increment probability density function that is associated with a Markov process. We compare the different sets of Kramers–Moyal coefficients of each phenomenology and deduce that an accurate description of intermittency should take into account an infinite number of coefficients. This is demonstrated in more detail for the case of Burgers turbulence that exhibits pronounced intermittency effects. Moreover, the influence of nonlocality on Kramers–Moyal coefficients is investigated by direct numerical simulations of a generalized Burgers equation. Depending on the balance between nonlinearity and nonlocality, we encounter different intermittency behavior that ranges from self-similarity (purely nonlocal case) to intermittent behavior (intermediate case that agrees with Yakhot’s mean field theory [Phys. Rev. E 63 026307 (2001)]) to shock-like behavior (purely nonlinear Burgers case).

P-wave velocity structures of the upper mantle and mantle transition zone beneath the northern South China Sea based on triplication fitting

<p>The South China Sea (hereafter as SCS) located in the southeastern Asia has been affected by the subduction of the western Pacific, Indo-Australian and Eurasian plates (Sun et al., 2018). Broadband P waveforms from the China Digital Seismograph Network (Zheng et al., 2010) for three intermediate-depth earthquakes that occurred closely in Mindoro, Philippine are used to detect velocity structures of the lowermost upper mantle and mantle transition zone (MTZ) beneath the northern SCS. The study area is divided into five profiles distributed from southwest to northeast azimuthally to reduce the computational costs and concern possible lateral variations (Li et al., 2018), and the corresponding 1-D best-fit velocity models are obtained from the observed and synthetic triplicated waveform fitting based on the iterative grid-search procedure. The searching grid can be described as below, three parameters for the low-velocity layer (LVL) atop the 410 km discontinuity (hereafter as the 410), five parameters for the high-velocity anomaly (HVA) atop the 660 km discontinuity (hereafter as the 660) and one parameter for the velocity perturbation below the 660. After the sensitivity tests of the synthetic waveforms with different parameters, the grid steps of the depth and velocity perturbation are set as 5 km and 0.5%, respectively.</p><p>Relative to the reference model IASP91 (Kennett and Engdahl, 1991), our results reveal that there are ubiquitous HVAs in five profiles at the bottom of the MTZ with a velocity increment of 1.5~3.5% and a thickness of 209~219 km, which show no apparent progressive velocity increment or decrement along the southwest-northeast direction. We prefer that the weak and abnormal thick HVAs are induced by the proto-SCS north slab remnants. We also observe an uplift 410 and depressed 660 with the depth change of 5 km and 5~15 km, respectively, which further support the low-temperature anomaly related to the stagnant slab. In addition, our results show there is an LVL atop the MTZ with a velocity decrement of 2.0~2.5% and a thickness of 60~75 km, and can be interpreted by the partial melting induced by upwelling materials from the MTZ, which are hydrated by water released from the stagnant slab. We infer that the LVL with little lateral variations may result from the percolation of the partial melts atop the MTZ under vertical pressure.</p><p> </p><p>Kennett B L N, Engdahl E R. 1991. Traveltimes for global earthquake location and phase identification. Geophys. J. Int. 105(2): 429-465, doi:10.1111/j.1365-246X.1991.tb06724.x.</p><p>Li W, Wei R, Cui Q, et al. 2018. Velocity structure around the 410 km discontinuity beneath the East China Sea area based on the waveform fitting method. Chinese J. Geophys. 61(1): 150-160, doi:10.6038/cjg2018L0370.</p><p>Sun W, Lin C, Zhang L, et al. 2018. The formation of the South China Sea resulted from the closure of the Neo-Tethys: A perspective from regional geology. Acta Petrol. Sin. 34(12): 3467-3478, doi:1000-0569/2018/034(12)-3467-78.</p><p>Zheng X, Jiao W, Zhang C, et al. 2010. Short-Period Rayleigh-Wave Group Velocity Tomography through Ambient Noise Cross-Correlation in Xinjiang, Northwest China. Bull. Seismol. Soc. Am. 100(3): 1350-1355, doi:10.1785/0120090225.</p><p> </p>