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Register a new userMathematical investigation of the Boltzmann collisional operator
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Problems associated with the Boltzmann collisional operator are unveiled and discussed. By careful investigation it is shown that collective effects of molecular collisions in the six-dimensional position and velocity space are more sophisticated than they appear to be.
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High-spatial-resolution (HSR) two-component, two-dimensional particle-image-velocimetry (2C-2D PIV) measurements of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) and an adverse-pressure-gradient (APG)-TBL were taken in the LMFL High Reynolds number Boundary Layer Wind Tunnel. The ZPG-TBL has a momentum-thickness based Reynolds number $Re_{delta_2} = delta_2 U_e/ u = 7,750$ while the APG-TBL has a $Re_{delta_2} = 16,240$ and a Clausers pressure gradient parameter $beta = delta_1 P_x/tau_w = 2.27$ After analysing the single-exposed PIV image data using a multigrid/multipass digital PIV (Soria, 1996) with in-house software, proper orthogonal decomposition (POD) was performed on the data to separate flow-fields into large- and small-scale motions (LSMs and SSMs), with the LSMs further categorized into high- and low-momentum events. Profiles of the conditionally averaged Reynolds stresses show that the high-momentum events contribute more to the Reynolds stresses than the low-momentum between wall to the end of the log-layer and the opposite is the case in the wake region. The cross-over point of the profiles of the Reynolds stresses from the high- and low-momentum LSMs always has a higher value than the corresponding Reynolds stress from the original ensemble at the same wall-normal location. Furthermore, the cross-over point in the APG-TBL moves further from the wall than in the ZPG-TBL. By removing the velocity fields with LSMs, the estimate of the Reynolds streamwise stress and Reynolds shear stress from the remaining velocity fields is reduced by up to $42 %$ in the ZPG-TBL. The reduction effect is observed to be even larger (up to $50%$) in the APG-TBL. However, the removal of these LSMs has a minimal effect on the Reynolds wall-normal stress in both the ZPG- and APG-TBL.
A lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of nonlinear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound.
The impact of boat traffic on the health of coastal ecosystems is a multi-scale process: from minutes (individual wakes) to days (tidal modulation of sediment transport), to seasons and years (traffic is seasonal). A considerable numerical effort, notwithstanding the value of a boat-by-boat numerical modeling approach, is questionable, because of the practical impossibility of specifying the exact type and navigation characteristics for every boat comprising the traffic at any given time. Here, we propose a statistical-mechanics description of the traffic using a joint probability density of the wake population in some characteristic parameter space. We attempt to answer two basic questions: (1) what is the relevant parameter space and (2) how should a numerical model be tested for a wake population? We describe the linear and nonlinear characteristics of wakes observed in the Florida Intracoastal Waters. Adopting provisionally a two-dimensional parameter space (depth- and length-based Froude numbers) we conduct numerical simulations using the open-source FUNWAVE-TVD Boussinesq model. The model performance is excellent for weakly-dispersive, completely specified wakes (e.g., the analytical linear wakes), and also for the range of Froude numbers observed in the field, or for large container ships generating relatively long waves. The model is challenged by the short waves generated by small, slow boats. However, simulations suggest that the problem is confined to the deeper water domain and linear evolution. Nonlinear wake shoaling, essential for modeling wake-induced sediment transport and wake impact on the environment, is described well.
We apply a new threshold detection method based on the extreme value theory to the von Karman sodium (VKS) experiment data. The VKS experiment is a successful attempt to get a dynamo magnetic field in a laboratory liquid-metal experiment. We first show that the dynamo threshold is associated to a change of the probability density function of the extreme values of the magnetic field. This method does not require the measurement of response functions from applied external perturbations, and thus provides a simple threshold estimate. We apply our method to different configurations in the VKS experiment showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors. Moreover, for the experimental configurations in which a dynamo transition is not observed, the method provides a way to extrapolate an interval of possible threshold values.
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.
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