The logarithmic variance of streamwise velocity and conundrum in wall turbulence

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Design and Implement of Three-Phase Permanent-Magnet Synchronous Wave Generator using Taguchi Approach

In this paper, the design and performance analysis of a high-efficiency permanent-magnet synchronous wave generator (PSWG) are presented. A systematic approach for the design of the outer rotor was proposed as a prototype model. The magnetic field, magnetic circuit characteristics, electrical characteristics of the generator, and optimal design parameters such as the pole–arc ratio and shoe outer length were determined using the Taguchi method, finite-element analysis (FEA) software, and rotor skewing techniques. The proposed six series and six parallel-connection winding configurations can provide an evenly distributed current for practical applications. A PSWG was designed and fabricated according to the proposed methodology. According to the experimental results by implementing the optimized design, the efficiencies of the proposed PSWG which used 3.6 Ω load at 300 rpm is 86.32% and the efficiency error between simulation and experiment is less than 1.8%. It verifies the feasibility of the proposed method to PSWG and the structural reliability optimization design.

Multifractal Model of Atmospheric Turbulence Applied to Elastic Lidar Data

This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title “On a Multifractal Approach of Turbulent Atmosphere Dynamics”.

Symmetry Breaking in Stochastic Dynamics and Turbulence

Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and weight of these principles are the same as in quantum physics: dynamics of complex nonlinear statistical systems is straightforwardly dictated by their symmetry or its breaking, as we demonstrate on the example of developed (magneto)hydrodynamic turbulence and the related theoretical models. To simplify the problem, unbounded models are commonly used. However, turbulence is a mesoscopic phenomenon and the size of the system must be taken into account. It turns out that influence of outer length of turbulence is significant and can lead to intermittency. More precisely, we analyze the connection of phenomena such as behavior of statistical correlations of observable quantities, anomalous scaling, and generation of magnetic field by hydrodynamic fluctuations with symmetries such as Galilean symmetry, isotropy, spatial parity and their violation and finite size of the system.

A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, ‘a fully developed passive scalar’ refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the ‘HRAP formalism’ is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence:$u=\sum _{i=1}^{N_{z}}a_{i}$, where the instantaneous streamwise velocity fluctuation at a generic wall-normal location$z$is modelled as a sum of additive contributions from wall-attached eddies ($a_{i}$) and the number of addends is$N_{z}\sim \log (\unicode[STIX]{x1D6FF}/z)$. The HRAP model admits generalized logarithmic scalings including$\langle \unicode[STIX]{x1D719}^{2}\rangle \sim \log (\unicode[STIX]{x1D6FF}/z)$,$\langle \unicode[STIX]{x1D719}(x)\unicode[STIX]{x1D719}(x+r_{x})\rangle \sim \log (\unicode[STIX]{x1D6FF}/r_{x})$,$\langle (\unicode[STIX]{x1D719}(x)-\unicode[STIX]{x1D719}(x+r_{x}))^{2}\rangle \sim \log (r_{x}/z)$, where$\unicode[STIX]{x1D719}$is the streamwise velocity fluctuation,$\unicode[STIX]{x1D6FF}$is an outer length scale,$r_{x}$is the two-point displacement in the streamwise direction and$\langle \cdot \rangle$denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for$\unicode[STIX]{x1D719}$being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

Compact UWB microstrip antenna with quadruple band-notched characteristics for short distance wireless tele-communication applications

In this paper, the design and simulation of a compact ultra-wide band (UWB) microstrip antenna with quadruple band-notched characteristics for short-distance wireless telecommunication applications were explored. The design process of the antenna is carried on FR4 substrate with dielectric constant 4.4, loss tangent 0.02, thickness of 0. 8mm and the size of the proposed antenna are 30×20 mm2. The rectangular monopole antenna endures a rectangular radiating patch with chamfered bevel slots on the top side, and a defective ground planed on the bottom side of the substrate. To realize single, dual, triple and quadruple band notch characteristics, slot-1 is created on the patch to achieve first notch at 3.5 GHz, which eliminates WIMAX signal, slot-2 is created on the patch to achieve second notch at 4.6 GHz, which eliminates INSAT signal, slot-3 is created on the patch to achieve third notch at 5.5 GHz, which eliminates WLAN signal and also fourth notch is created at 9.5GHz which eliminates X-band frequency with slot-1 outer length. The proposed antenna is well miniaturized and can be easily integrated with any compact devices. The simulated result shows that proposed antenna gain a good range of UWB from (2.6 GHz to 13.4 GHz).

A multifractal model for the momentum transfer process in wall-bounded flows

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation $\unicode[STIX]{x1D70F}_{l}^{\prime }$, where $l$ is the filtering length scale. According to the multifractal formalism, $\langle {\unicode[STIX]{x1D70F}^{\prime }}^{2}\rangle \sim \log (Re_{\unicode[STIX]{x1D70F}})$ and $\langle \exp (p\unicode[STIX]{x1D70F}_{l}^{\prime })\rangle \sim (L/l)^{\unicode[STIX]{x1D701}_{p}}$ in the log-region, where $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, $p$ is a real number, $L$ is an outer length scale and $\unicode[STIX]{x1D701}_{p}$ is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at $Re_{\unicode[STIX]{x1D70F}}=4200$.

Generalized logarithmic law for high-order moments in turbulent boundary layers

High-Reynolds-number data in turbulent boundary layers are analysed to examine statistical moments of streamwise velocity fluctuations ${u}^{\prime } $. Prior work has shown that the variance of ${u}^{\prime } $ exhibits logarithmic behaviour with distance to the surface, within an inertial sublayer. Here we extend these observations to even-order moments. We show that the $2p$-order moments, raised to the power $1/ p, $ also follow logarithmic behaviour according to $\langle \mathop{({u}^{\prime + } ){}^{2p} \rangle }\nolimits ^{1/ p} = {B}_{p} - {A}_{p} \ln (z/ \delta )$, where ${u}^{\prime + } $ is the velocity fluctuation normalized by the friction velocity, $\delta $ is an outer length scale and ${B}_{p} $ are non-universal constants. The slopes ${A}_{p} $ in the logarithmic region appear quite insensitive to Reynolds number, consistent with universal behaviour for wall-bounded flows. The slopes differ from predictions that assume Gaussian statistics, and instead are consistent with sub-Gaussian behaviour.