Estimation of Turbulent Triplet Covariances for Bora Flows

Bora is a strong or severe, relatively cold, gusty wind that usually blows from the northastern quadrant at the east coast of the Adriatic Sea. In this study bora’s turbulence triplet covariances were analysed, for the first time, for bora flows. The measurements used were obtained from the measuring tower on Pometeno brdo (“Swept-Away Hill”), in the hinterland of the city of Split, Croatia. From April 2010 until June 2011 three components of wind speed and sonic temperature were measured. The measurements were performed on three heights, 10, 22 and 40 m above the ground with the sampling frequency of 5 Hz. During the observed period, total of 60 bora episodes were isolated. We analyse the terms in prognostic equations for turbulence variances. In that respect, the viscous dissipation term was calculated using two approaches: (i) inertial dissipation method (εIDM) and (ii) direct approach from the prognostic equations for variances of turbulence (εEQ). We determine that the direct approach can successfully reproduce the shape of the curve, but the values are for several orders of magnitudes smaller compared to the real data. Further, linear relationship between εIDM and εEQ was obtained. Using the results for εEQ, viscous dissipation rate in longitudinal, transversal and vertical direction was determined. It is shown that viscous dissipation has the greatest impact on bora’s longitudinal direction. The focus is on the turbulence transport term, i.e., the triplet covariance term. For the first time, it is found that turbulence transport is very significant for the intensity of near−surface bora flows. Furthermore, turbulence transport can be both positive and negative, yet intensive. It is mostly negative at the upper levels and positive at the lower levels. Therefore, turbulence transport, in most cases, takes away turbulence variance from the upper levels and brings it down to the lower ones. This is one of the main findings of this study; it adds to the understanding of peculiarities of bora wind, and perhaps some other severe winds.

Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard [Formula: see text]–[Formula: see text] PANS model is also used. The results demonstrate that compared to [Formula: see text]–[Formula: see text] PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at [Formula: see text] and [Formula: see text], it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

Nucleation and Growth of Lattice Crystals

A variational lattice model is proposed to define an evolution of sets from a single point (nucleation) following a criterion of “maximization” of the perimeter. At a discrete level, the evolution has a “checkerboard” structure and its shape is affected by the choice of the norm defining the dissipation term. For every choice of the scales, the convergence of the discrete scheme to a family of expanding sets with constant velocity is proved.

Discrete Schemes for a Class of Semilinear Hyperbolic Eqution

This paper focuses on the numerical algorithm of a class of semilinear hyperbolic equation. The dissipation term and external force source term existing in the equation enhance the nonlinearity of the model and make the nonlinear effect complicated. However, this nonlinear effect has a great influence on the discrete scheme, which cannot be neglected. Discretizing the nonlinear terms to ensure the validity of the scheme is the core issue in this paper. An effective scheme based on linearization techniques and iteration theory is proposed. It is based on the finite difference method. The efficiency of the proposed schemes was verified via some numerical examples showing that they compare well with existing methods.

Modeling viscoacoustic wave propagation using a new spatial variable-order fractional Laplacian wave equation

We propose a new time-domain viscoacoustic wave equation for simulating wave propagation in anelastic media. The new wave equation is derived by inserting the complex-valued phase velocity described by the Kjartansson attenuation model into the frequency-wavenumber domain acoustic wave equation. Our wave equation includes one second-order temporal derivative and two spatial variable-order fractional Laplacian operators. The two fractional Laplacian operators describe the phase dispersion and amplitude attenuation effects, respectively. To facilitate the numerical solution for the proposed wave equation, we use the arbitrary-order Taylor series expansion (TSE) to approximate the mixed domain fractional Laplacians and achieve the decoupling of the wavenumber and the fractional order. Then the proposed viscoacoustic wave equation can be directly solved using the pseudospectral method (PSM). We adopt a hybrid pseudospectral/finite-difference method (HPSFDM) to stably simulate wave propagation in arbitrarily complex media. We validate the high accuracy of the proposed approximate dispersion term and approximate dissipation term in comparison with the accurate dispersion term and accurate dissipation term. The accuracy of numerical solutions is evaluated by comparison with the analytical solutions in homogeneous media. Theory analysis and simulation results show that our viscoacoustic wave equation has higher precision than the traditional fractional viscoacoustic wave equation in describing constant- Q attenuation. For a model with Q < 10, the calculation cost for solving the new wave equation with TSE HPSFDM is lower than that for solving the traditional fractional-order wave equation with TSE HPSFDM under the high numerical simulation precision. Furthermore, we demonstrate the accuracy of HPSFDM in heterogeneous media by several numerical examples.

Linear-model-based estimation in wall turbulence: improved stochastic forcing and eddy viscosity terms

We use Navier–Stokes-based linear models for wall-bounded turbulent flows to estimate large-scale fluctuations at different wall-normal locations from their measurements at a single wall-normal location. In these models, we replace the nonlinear term by a combination of a stochastic forcing term and an eddy dissipation term. The stochastic forcing term plays a role in energy production by the large scales, and the eddy dissipation term plays a role in energy dissipation by the small scales. Based on the results in channel flow, we find that the models can estimate large-scale fluctuations with reasonable accuracy only when the stochastic forcing and eddy dissipation terms vary with wall distance and with the length scale of the fluctuations to be estimated. The dependence on the wall distance ensures that energy production and energy dissipation are not concentrated close to the wall but are evenly distributed across the near-wall and logarithmic regions. The dependence on the length scale of the fluctuations ensures that lower wavelength fluctuations are not excessively damped by the eddy dissipation term and hence that the dominant scales shift towards lower wavelengths towards the wall. This highlights that, on the one hand, energy extraction in wall turbulence is predominantly linear and thus physics-based linear models give reasonably accurate results. On the other hand, the absence of linearly unstable modes in wall turbulence means that the nonlinear term still plays an essential role in energy extraction and thus the modelled terms should include the observed wall distance and length scale dependencies of the nonlinear term.

Field Observations of Breaking of Dominant Surface Waves

The results of field observations of breaking of surface spectral peak waves, taken from an oceanographic research platform, are presented. Whitecaps generated by breaking surface waves were detected using video recordings of the sea surface, accompanied by co-located measurements of waves and wind velocity. Whitecaps were separated according to the speed of their movement, c, and then described in terms of spectral distributions of their areas and lengths over c. The contribution of dominant waves to the whitecap coverage varies with the wave age and attains more than 50% when seas are young. As found, the whitecap coverage and the total length of whitecaps generated by dominant waves exhibit strong dependence on the dominant wave steepness, ϵp, the former being proportional to ϵp6. This result supports a parameterization of the dissipation term, used in the WAM model. A semi-empirical model of the whitecap coverage, where contributions of breaking of dominant and equilibrium range waves are separated, is suggested.

Rotationally symmetric flow of Cu-Al2O3/water hybrid nanofluid over a heated porous boundary

This paper endeavours to provide an analysis for nanofluid boundary layer that develops beneath a generalized vortex flow subjected to viscous dissipation effects. Tangential flow high above the disk is assumed to vary with radial distance [Formula: see text] as [Formula: see text]. Hybrid nanofluid comprises alumina-[Formula: see text] and copper-[Formula: see text] nanoparticles with water as base liquid. A generalized version of von Kármán relations proposed in a recent paper is opted to present self-similar solutions. In presence of viscous dissipation term, self-similar solutions are possible only when temperature difference is proportional to [Formula: see text]. Otherwise, the solutions are only locally similar. Present model reduces to two special situations namely rigid body rotation [Formula: see text] and potential vortex [Formula: see text]. It is perceived that inclusion of nanoparticles markedly affects the boundary layer development under the prescribed vortex flow, and the associated heat transfer process. Also, viscous dissipation term has important implications on the resulting heat transfer process.

Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit–qubit interaction

The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit–qubit interaction and dissipation term is considered. The effects of the qubit–qubit interaction and the dissipation term on the dynamics of the proposed system are discussed in detail for certain values of the number of levels. The dynamical expressions of the observable operators are obtained using the Heisenberg equation of motion. The population inversion and linear entropy, as well as the concurrence formula as a measure of entanglement between the two qubits are calculated and discussed. The roles of the number of levels, the qubit–qubit coupling parameter and the dissipation rate on these quantities are also discussed. We explore the sudden birth and sudden death of the entanglement phenomena with and without the dissipation term.