Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

A comparison of seafloor habitats and associated benthic fauna in areas open and closed to bottom trawling along the central California Continental Shelf

Executive Summary: A number of studies have shown that mobile, bottom-contact fishing gear (such as otter trawls) can alter seafloor habitats and associated biota. Considerably less is known about the recovery of these resources following such disturbances, though this information is critical for successful management. In part, this paucity of information can be attributed to the lack of access to adequate control sites – areas of the seafloor that are closed to fishing activity. Recent closures along the coast of central California provide an excellent opportunity to track the recovery of historically trawled areas and to compare recovery rates to adjacent areas that continue to be trawled. In June 2006 we initiated a multi-year study of the recovery of seafloor microhabitats and associated benthic fauna inside and outside two new Essential Fish Habitat (EFH) closures within the Cordell Bank and Gulf of the Farallones National Marine Sanctuaries. Study sites inside the EFH closure at Cordell Bank were located in historically active areas of fishing effort, which had not been trawled since 2003. Sites outside the EFH closure in the Gulf of Farallones were located in an area that continues to be actively trawled. All sites were located in unconsolidated sands at equivalent water depths. Video and still photographic data collected via a remotely operated vehicle (ROV) were used to quantify the abundance, richness, and diversity of microhabitats and epifaunal macro-invertebrates at recovering and actively trawled sites, while bottom grabs and conductivity/temperature/depth (CTD) casts were used to quantify infaunal diversity and to characterize local environmental conditions. Analysis of still photos found differences in common seafloor microhabitats between the recovering and actively trawled areas, while analysis of videographic data indicated that biogenic mound and biogenic depression microhabitats were significantly less abundant at trawled sites. Each of these features provides structure with which demersal fishes, across a wide range of size classes, have been observed to associate. Epifaunal macro-invertebrates were sparsely distributed and occurred in low numbers in both treatments. However, their total abundance was significantly different between treatments, which was attributable to lower densities at trawled sites. In addition, the dominant taxa were different between the two sites. Patchily-distributed buried brittle stars dominated the recovering site, and sea whips (Halipteris cf. willemoesi) were most numerous at the trawled site though they occurred in only five of ten transects. Numerical classification (cluster analysis) of the infaunal samples also revealed a clear difference between benthic assemblages in the recovering vs. trawled areas due to differences in the relative abundances of component species. There were no major differences in infaunal species richness, H′ diversity, or J′ evenness between recovering vs. trawled site groups. However, total infaunal abundance showed a significant difference attributable to much lower densities at trawled sites. This pattern was driven largely by the small oweniid polychaete Myriochele gracilis, which was the most abundant species in the overall study region though significantly less abundant at trawled sites. Other taxa that were significantly less abundant at trawled sites included the polychaete M. olgae and the polychaete family Terebellidae. In contrast, the thyasirid bivalve Axinopsida serricata and the polychaetes Spiophanes spp. (mostly S. duplex), Prionospio spp., and Scoloplos armiger all had significantly to near significantly higher abundances at trawled sites. As a result of such contrasting species patterns, there also was a significant difference in the overall dominance structure of infaunal assemblages between the two treatments. It is suggested that the observed biological patterns were the result of trawling impacts and varying levels of recovery due to the difference in trawling status between the two areas. The EFH closure was established in June 2006, within a month of when sampling was conducted for the present study, however, the stations within this closure area are at sites that actually have experienced little trawling since 2003, based on National Marine Fishery Service trawl records. Thus, the three-year period would be sufficient time for some post-trawling changes to have occurred. Other results from this study (e.g., similarly moderate numbers of infaunal species in both areas that are lower than values recorded elsewhere in comparable habitats along the California continental shelf) also indicate that recovery within the closure area is not yet complete. Additional sampling is needed to evaluate subsequent recovery trends and persistence of effects. Furthermore, to date, the study has been limited to unconsolidated substrates. Ultimately, the goal of this project is to characterize the recovery trajectories of a wide spectrum of seafloor habitats and communities and to link that recovery to the dynamics of exploited marine fishes. (PDF has 48 pages.)

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Researches on essential mechanics issues for submerged floating tunnel

Since 2001, a research group in the Institute of Mechanics, Chinese Academy of Sciences, has been devoted to the research of essential mechanics issues for submerged floating tunnel (SFT). In addition to the structural design of the SFT prototype in Qiandao Lake, the relevant researches cover a number of topics. This paper briefly describes the research procedure and results, including dynamic response of SFT due to surface wave, vortex-induced vibration of anchoring system, structural analysis of curved SFT, temperature effects of curved SFT, structural dynamic response due to accidental load, and effects of structural parameters (buoyancy-weight ratio, tunnel length，tether stiffness，etc.) on dynamic response.