Irrotational Region Research Articles

Generalized scaling laws for the irrotational motions bordering a turbulent region.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_{2} much bigger than the integral scale L in the nearby turbulent region (x_{2}≫L), the variance of the velocity fluctuations 〈u_{i}^{2}〉 (i=1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k)∼k^{n} [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n=4 (Batchelor turbulence) and n=2 (Saffman turbulence) have been previously derived, with 〈u_{i}^{2}〉∼x_{2}^{-4} and 〈u_{i}^{2}〉∼x_{2}^{-3}, for n=4 and n=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], we extend these results by including any other value of n. In particular, we obtain 〈u_{i}^{2}〉∼x_{2}^{-2} and 〈u_{i}^{2}〉∼x_{2}^{-4}, for n=1 and n≥5, respectively, while n=3 yields 〈u_{i}^{2}〉∼x_{2}^{-4}ln(x_{2}). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

Entrainment at multi-scales in shear-dominated and Rayleigh–Taylor turbulence

A partially turbulent flow continuously incorporates irrotational fluid into the turbulent region, a phenomenon known as entrainment. Although entrainment locally acts at viscous scales, the thin interface separating the turbulent from the irrotational region is extremely convoluted, and twisted in such a way that renders the global entrainment flux scale-independent. Despite turbulent entrainment being widely recognized as a multi-scale process, the theoretical basis for quantifying the entrainment flux at multi-scales is lacking. In this paper we derive an equation that allows us to quantify the local entrainment velocity at multi-scales. This is done by defining the local entrainment velocity as the propagation speed of an iso-surface of filtered enstrophy relative to the coarse-grained velocity field, and using the filtered enstrophy budget to split the total velocity into its individual components, i.e. viscous, inviscid, baroclinic and sub-filter. The equation is used to investigate the entrainment at multi-scales in simulated turbulent mixing layers, where turbulence is sustained by either a mean shear or an unstable buoyancy gradient (Rayleigh–Taylor turbulence).

Toward a robust detection of viscous and turbulent flow regions using unsupervised machine learning

We propose an invariant feature space for the detection of viscous-dominated and turbulent regions (i.e., boundary layers and wakes). The developed methodology uses the principal invariants of the strain and rotational rate tensors as input to an unsupervised Machine Learning Gaussian mixture model. The selected feature space is independent of the coordinate frame used to generate the processed data, as it relies on the principal invariants of the strain and rotational rate, which are Galilean invariants. This methodology allows us to identify two distinct flow regions: a viscous-dominated, rotational region (a boundary layer and a wake region) and an inviscid, irrotational region (an outer flow region). We have tested the methodology on a laminar and a turbulent (using Large Eddy Simulation) case for flows past a circular cylinder at Re = 40 and Re = 3900 and a laminar flow around an airfoil at Re=1×105. The simulations have been conducted using a high-order nodal Discontinuous Galerkin Spectral Element Method. The results obtained are analyzed to show that Gaussian mixture clustering provides an effective identification method of viscous-dominated and rotational regions in the flow. We also include comparisons with traditional sensors to show that the proposed clustering does not depend on the selection of an arbitrary threshold, as required when using traditional sensors.

Paul Andrews Libby Contribution to Zone-Conditioned Average Transport Equations in Intermittent Turbulent Flows

ABSTRACT Professor Paul A. Libby has made lasting contributions to the theory and modeling of turbulent premixed flames. A less known subject of his research relates to the conditioning of the local and instantaneous Navier-Stokes equations for either the turbulent or the irrotational flow regions separated by a thin interface. He postulated an evolution equation for the intermittency function, a generalized function introduced by experimentalists in the decades of 1960 and 1970, which is unity in the vorticity-containing turbulent flow and zero in the surrounding irrotational flow. This intermittency function equation allowed the derivation of transport equations for average variables conditioned either to the turbulent or the vorticity-free regions. Paul A. Libby formalism is explained in this paper. Further research triggered by Libby’s seminal work is then reported. An exact expression is obtained for his “intermittency creation” term, which allows a simple physical interpretation of the entrainment and zone interactions. This methodology is applied to an intermittent scalar in a turbulent flow of a variable density fluid. Various types of intermittent flows with zonal discrimination, based on vorticity, scalar and scalar-gradient criteria, are presented. The analogy of turbulent/nonturbulent interfaces with propagating turbulent premixed flames is remarked.

Turbulent entrainment in viscoelastic fluids

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

Flow pressure evaluation on generic surfaces by robotic volumetric PTV

An experimental approach for the measurement of the time-average fluid flow pressure over the surface of generic three-dimensional objects is presented. The method is based on robotic volumetric PTV measurements followed by the integration of the pressure gradient. The domain for pressure evaluation is subdivided in two parts: in the irrotational region the static pressure is obtained following Bernoulli relation; in the turbulent wake and close to the object the pressure gradient is integrated. An approach based on the total pressure distribution is proposed to estimate the boundary between these two regions. The method is first assessed with experiments around a sphere equipped with pressure taps. A criterion for minimum spatial resolution is formulated in terms of maximum ratio between bin size and local radius of curvature of the object. An experimental database from a three-dimensional problem of higher geometrical complexity is considered: the time-averaged flow field around a full-scale cyclist. The surface pressure distribution is discussed in connection to the topological features of near-surface streamlines and streamwise vortices.

Coherent structures in turbulent boundary layers over an airfoil

This preliminary study is concerned with the identification of three-dimensional coherent structures, defined as intense Reynolds-stress events, in the turbulent boundary layer developing over the suction side of a NACA4412 airfoil at a Reynolds number based on the chord lenght and the incoming velocity of Rec = 200, 000. The scientific interest for such flows originates from the non-uniform adverse pressure gradient that affects the boundary-layer development. Firstly, we assess different methods to identify the turbulent-non-turbulent interface, in order to exclude the irrotational region from the analysis. Secondly, we evaluate the contribution of the considered coherent structures to the enhanced wall-normal velocity, characteristic of adverse pressure gradients. Our results show that it is necessary to limit the detection of coherent structures to the turbulent region of the domain, and that the structures reveal qualitative differences between the contributions of intense events to the wall-normal velocity in adverse-pressure-gradient and zero-pressure-gradient turbulent boundary layers.

Steady Streaming Induced by Asymmetric Oscillatory Flows over a Rippled Bed

The flow induced by progressive water waves propagating over a rippled bed is reproduced by means of the numerical solution of momentum and continuity equations to gain insights on the steady streaming induced in the bottom boundary layer. When the pressure gradient that drives the flow is given by the sum of two harmonic components an offshore steady streaming is generated within the boundary layer which persists in the irrotational region. This steady streaming depends on the Reynolds number and on the geometrical characteristics of the ripples. Nothwithstanding the presence of a steady velocity component, the time-average of the force on the ripples vanishes.

On the large difference between Benjamin’s and Hanratty’s formulations of perturbed flow over uneven terrain

Flow over an uneven terrain is a complex phenomenon that requires a chain of approximations in order to be studied. In addition to modelling the intricacies of turbulence if present, the problem is classically first linearized about a flat bottom and a locally parallel flow, and then asymptotically approximated into an interactive representation that couples a boundary layer and an irrotational region through an intermediate inviscid but rotational layer. The first of these steps produces a stationary Orr–Sommerfeld equation; since this is a one-dimensional problem comparatively easy for any computer, it would seem appropriate today to forgo the second sweep of approximation and solve the Orr–Sommerfeld problem numerically. However, the results are inconsistent! It appears that the asymptotic approximation tacitly restores some of the original problem’s non-parallelism. In order to provide consistent results, Benjamin’s version of the Orr–Sommerfeld equation needs to be modified into Hanratty’s. The large difference between Benjamin’s and Hanratty’s formulations, which arises in some wavenumber ranges but not in others, is here explained through an asymptotic analysis based on the concept of admittance and on the symmetry transformations of the boundary layer. A compact and accurate analytical formula is provided for the wavenumber range of maximum laminar shear-stress response. We highlight that the maximum turbulent shear-stress response occurs in the quasi-laminar regime at a Reynolds-independent wavenumber, contrary to the maximum laminar shear-stress response whose wavenumber scales with a power of the boundary-layer thickness. A numerical computation involving an eddy-viscosity model provides a warning against the inaccuracy of such a model. We emphasize that the range $k\unicode[STIX]{x1D708}/u_{\unicode[STIX]{x1D70F}}<10^{-3}$ of the spectrum remains essentially unexplored, and that the question is still open whether a fully developed turbulent regime, similar to the one predicted by an eddy-viscosity model, ever exists for open flow even in the limit of infinite wavelength.

Turbulence statistics in smooth wall oscillatory boundary layer flow

Turbulence characteristics of an asymmetric oscillatory boundary layer flow are analysed through two-component laser-Doppler measurements carried out in a large oscillatory flow tunnel and direct numerical simulation (DNS). Five different Reynolds numbers, $R_{\unicode[STIX]{x1D6FF}}$, in the range 846–2057 have been investigated experimentally, where $R_{\unicode[STIX]{x1D6FF}}=\tilde{u} _{0max}\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ with $\tilde{u} _{0max}$ the maximum oscillatory velocity in the irrotational region, $\unicode[STIX]{x1D6FF}$ the Stokes length and $\unicode[STIX]{x1D708}$ the fluid kinematic viscosity. DNS has been carried out for the lowest three $R_{\unicode[STIX]{x1D6FF}}$ equal to 846, 1155 and 1475. Both experimental and numerical results show that the flow statistics increase during accelerating phases of the flow and especially at times of transition to turbulent flow. Once turbulence is fully developed, the near-wall statistics remain almost constant until the late half-cycle, with values close to those reported for steady wall-bounded flows. The higher-order statistics reach large values within a normalized wall distance of approximately $y/\unicode[STIX]{x1D6FF}=0.2$ at phases corresponding to the onset of low-speed streak breaking, because of the intermittency of the velocity fluctuations at these times. In particular, the flatness of the streamwise velocity fluctuations reaches values of the order of ten, while the flatness of the wall-normal velocity fluctuations reaches values of several hundreds. Far from the wall, at locations where the vertical gradient of the streamwise velocity is zero, the skewness is approximately zero and the flatness is approximately equal to 3, representative of a normal distribution. At lower elevations the distribution of the fluctuations deviate substantially from a normal distribution, but are found to be well described by other standard theoretical probability distributions.

The behaviour of the scalar gradient across the turbulent/non-turbulent interface in jets

The dynamics of a passive scalar field near a turbulent/non-turbulent interface is analysed through direct numerical simulations of turbulent planar jets, with Reynolds numbers ranging from 142≤Reλ≤246, and Schmidt numbers from 0.07≤Sc≤7.0. A scalar-gradient turbulent/non-turbulent interface (SG-TNTI) forms at the outer edge of the jet, which does not coincide with the vorticity turbulent/non-turbulent interface (VO-TNTI) for the lower Schmidt number cases (Sc = 0.07 and 0.7). Specifically, for Sc = 0.07 and 0.7, the scalar gradient maxima, and thus the bulk of the mixing takes place in the irrotational region, between 10 and 30 Kolmogorov micro-scale distances from the start of the VO-TNTI. For these moderate Schmidt number cases, the SG-TNTI exhibits an irrotational-diffusive superlayer, where the scalar gradient diffusion dominates, while the production is negligible, followed by an irrotational-straining sublayer where the scalar gradient production dominates. In contrast for Sc = 7.0, the SG-TNTI consists of a viscous-convective superlayer that closely matches the viscous superlayer from the VO-TNTI and an inertial-convective sublayer, where scalar gradient production dominates, which is much smaller than the turbulent sublayer of the VO-TNTI. The scaling laws and mean thicknesses of each one of these (sub)layers are briefly discussed. This work presents a systematic study of the effects of the Schmidt number on the scalar gradient evolution and of the SG-TNTI characteristics.

Small-scale entrainment in inclined gravity currents

We investigate the effect of buoyancy on the small-scale aspects of turbulent entrainment by performing direct numerical simulation of a gravity current and a wall jet. In both flows, we detect the turbulent/nonturbulent interface separating turbulent from irrotational ambient flow regions using a range of enstrophy iso-levels spanning many orders of magnitude. Conform to expectation, the relative enstrophy isosurface velocity v_n in the viscous superlayer scales with the Kolmogorov velocity for both flow cases. We connect the integral entrainment coefficient E to the small-scale entrainment and observe excellent agreement between the two estimates throughout the viscous superlayer. The contribution of baroclinic torque to v_n is negligible, and we show that the primary reason for reduced entrainment in the gravity current as compared to the wall-jet are 1) the reduction of v_n relative to the integral velocity scale u_T; and 2) the reduction in the surface area of the isosurfaces.

The turbulent/nonturbulent interface in penetrative convection

ABSTRACTThe effect of buoyancy on the turbulent/nonturbulent interface (TNTI) and viscous superlayer are studied by performing direct numerical simulation of penetrative convection. In this flow, rising turbulent thermals alternate with unmixed fluid entrained from above, forming a TNTI between the turbulent and irrotational flow regions. We detect the TNTI using a broad range of enstrophy iso-levels, from the very low levels of the outer fringes of the turbulent flow region to high levels located in the turbulent flow region. We study the local entrainment velocity vn by which the TNTI propagates outwards relative to the fluid flow while entraining unmixed fluid into the turbulent region. The relative entrainment velocity is decomposed into a viscous, an inertial and a baroclinic torque term, respectively. For low enstrophy levels we find a viscous superlayer (VSL) where viscous diffusion dominates, while inertial and baroclinic torque terms are small. It is only for higher iso-levels in the buffer region of the TNTI, which extends from the edge of the VSL to the threshold for which vn = 0, that the inertial enstrophy production term plays a significant role. Penetrative convection does not feature a turbulent core where vn > 0 (i.e. inward moving enstrophy isosurfaces) that has been previously identified in other entraining flows such as jets or gravity currents. Surprisingly, the baroclinic torque remains inactive throughout the whole range of enstrophy iso-levels. The smallness of the baroclinic torque against viscous effects in the TNTI is supported by a dimensional argument which predicts that at high Reynolds number the baroclinic torque term will be negligible.

A velocity decomposition approach for three-dimensional unsteady flow

A velocity decomposition method is developed for the solution of three-dimensional, unsteady flows. The velocity vector is decomposed into an irrotational component (viscous-potential velocity) and a vortical component (vortical velocity). The vortical velocity is selected so that it is zero outside of the rotational region of the flow field and the flow in the irrotational region can thus be solely described by the viscous-potential velocity. The formulation is devised to employ both the velocity potential and the Navier–Stokes-based numerical methods such that the field discretization required by the Navier–Stokes solver can be reduced to only encompass the rotational region of the flow field and the number of unknowns that are to be solved by the Navier–Stokes solver is greatly reduced. A higher-order boundary-element method is used to solve for the viscous potential by applying a viscous boundary condition to the body surface. The finite-volume method is used to solve for the total velocity on a reduced domain, using the viscous-potential velocity as the boundary condition on the extent of the domain. The two solution procedures are tightly coupled in time. The viscous-potential velocity and the total velocity are time dependent due to the unsteadiness in the boundary layer and the wake. The solver is applied to solve three-dimensional, laminar and turbulent unsteady flows. For turbulent flows, the solver is applied for both Unsteady-Reynolds-Averaging-Navier–Stokes and Large-Eddy-Simulation computations.

A numerical investigation of acceleration-skewed oscillatory flows

Numerical simulations of wall-bounded acceleration-skewed oscillatory flows are here presented. The relevance of this type of boundary layer arises in connection with coastal hydrodynamics and sediment transport, as it is generated at the bottom of sea waves in shallow water. Because of the acceleration skewness, the bed shear stress during the onshore half-cycle is larger than in the offshore half-cycle. The asymmetry in the bed shear stress increases with increasing acceleration skewness, while an increase of the Reynolds number from the laminar regime causes the asymmetry first to decrease and then increase. Low- and high-speed streaks of fluid elongated in the streamwise direction emerge near the wall, shortly after the beginning of each half-cycle, at a phase that depends on the flow parameters. Such flow structures strengthen during the first part of the accelerating phase, without causing a significant deviation of the streamwise wall shear stress from the laminar values. Before the occurrence of the peak of the free stream velocity, the low-speed streaks break down into small turbulent structures causing a large increase in wall shear stress. The ratio of the root-mean-square (r.m.s.) of the fluctuations to the mean value (relative intensity) of the wall shear stress is approximately 0.4 throughout a relatively wide interval of the flow cycle that begins when breaking down of the streaks has occurred in the entire fluid domain. The acceleration skewness and the Reynolds number determine the phase at which this time interval begins. Both the skewness and the flatness coefficients of the streamwise wall shear stress are large when elongated streaks are present, while values of approximately 1.1 and 5.4 respectively occur just after breaking has occurred. The trend of both the relative intensity and the flatness of the spanwise wall shear stress are qualitatively similar to those of the wall shear in the streamwise direction. As a result of the acceleration skewness, the period-averaged Reynolds stress does not vanish. Consequently, an offshore directed steady streaming is generated which persists into the irrotational region.

On the evolution of the invariants of the velocity gradient tensor in single-square-grid-generated turbulence

Direct numerical simulations were performed to investigate the topological evolution of turbulence generated by a single square grid. Immediately behind the single square grid (i.e., in the irrotational dissipation region), the conditional mean trajectories (CMTs) of R and Q are distinctly different from those in homogeneous isotropic turbulence (HIT), where R and Q are the third and second invariants, respectively, of the velocity gradient tensor. In this region, the non-local influence of the pressure Hessian is dominant, which causes irrotational viscous dissipation. The anisotropic part of the pressure Hessian may be responsible for the irrotational viscous dissipation found at the turbulent/nonturbulent interface in turbulent jets [C. B. da Silva and J. C. F. Pereira, “Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets,” Phys. Fluids 20, 055101 (2008) and Watanabe et al., “Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet,” J. Fluid Mech. 758, 754 (2014)]. In the transition region, the CMTs of R and Q gradually acquire an evolution pattern similar to that in HIT. The expansion of the (R, Q) map at Q > 0 is associated with the effects of the restricted Euler term. Finally, in the fully turbulent region, the CMTs of R and Q demonstrate a clockwise evolution toward a point close to the origin. However, the cyclic spiraling seen in HIT is not found. The lack of the cyclic evolution may be attributed to the considerably large effect of the viscous term owing to the relatively small local Reynolds number. On average, the combined influences of the restricted Euler term and anisotropic part of the pressure Hessian contribute to the generation of small-scale motions, and the viscous term tends to remove small-scale motions.

Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet

Lagrangian statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of Lagrangian statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The Lagrangian statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using Eulerian statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.

Effects of mean shear on the local turbulent entrainment process

AbstractWe report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity ${v}_{n} = - (\mathrm{D} {\omega }^{2} / \mathrm{D} t)/ (\partial {\omega }^{2} / \partial {\hat {x} }_{n} )$, where ${\omega }^{2} $ is enstrophy and ${\hat {x} }_{n} $ is the coordinate normal to the TNTI. The quantity ${v}_{n} $ is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effects.

Non bonded interaction between BnNn (stator) and [formula omitted] (rotor) systems: A quantum rotation in IR region

The electromagnetic non-bonded interactions of BN(-,0,+)B molecule as a quantum rotor inside several of BnNn molecular rings as a stator has been investigated by using EPR-II and EPR-III basis sets. Optimized structures, relative stability and hyperfine spectroscopic parameters, have been calculated.In this study, we have shown that the BnNn–BNB systems can be works as a nano rotor–stator molecular motor for the biological systems.Although in our previous works, we have discussed (Monajjemi et al. (2010) [20] and Monajjemi and Boggs (2013) [18]) of the stability and electromagnetic properties of some kind of BnNn rings, using of these systems as a detector are much more significant and have investigated in this work.The study for the BnNn–BN(-,0,+)B systems and then for Adenine–Thymine and Guanine–Cytosine base pairs coupled with BN(-,0,+)B inside the BnNn (n=8,12,15,16,18,20,24) have been investigated. Three quantized rotational frequencies in cationic, radical, and anionic forms have been calculated and all frequencies appeared in the IR rotational region.

Kinetic energy budgets near the turbulent/nonturbulent interface in jets

The dynamics of the kinetic energy near the turbulent/nonturbulent (T/NT) interface separating the turbulent from the irrotational flow regions is analysed using three direct numerical simulations of turbulent planar jets, with Reynolds numbers based on the Taylor micro-scale across the jet shear layer in the range Reλ ≈ 120–160. Important levels of kinetic energy are already present in the irrotational region near the T/NT interface. The mean pressure and kinetic energy are well described by the Bernoulli equation in this region and agree with recent results obtained from rapid distortion theory in the turbulent region [M. A. C. Teixeira and C. B. da Silva, “Turbulence dynamics near a turbulent/non-turbulent interface,” J. Fluid Mech. 695, 257–287 (2012)]10.1017/jfm.2012.17 while the normal Reynolds stresses agree with the theoretical predictions from Phillips [“The irrotational motion outside a free turbulent boundary,” Proc. Cambridge Philos. Soc. 51, 220 (1955)]10.1017/S0305004100030073. The use of conditional statistics in relation to the distance from the T/NT interface allow a detailed study of the build up of kinetic energy across the T/NT interface, pointing to a very different picture than using classical statistics. Conditional kinetic energy budgets show that apart from the viscous dissipation of kinetic energy, the maximum of all the mechanisms governing the kinetic energy are concentrated in a very narrow region distancing about one to two Taylor micro-scales from the T/NT interface. The (total and fluctuating) kinetic energy starts increasing in the irrotational region by pressure-velocity interactions – a mechanism that can act at distance, and continue to grow by advection (for the total kinetic energy) and turbulent diffusion (for the turbulent kinetic energy) inside the turbulent region. These mechanisms tend to occur preferentially around the core of the large-scale vortices existing near T/NT interface. The production of turbulent kinetic energy then becomes the dominating mechanism and the so called “peak production” is located at about one Taylor micro-scale from the T/NT interface. Simple analytical estimates are given for the peaks of pressure strain, turbulent diffusion, and production near the T/NT interface. The growth of kinetic energy across the T/NT interface is an inertial process, since the viscous terms (diffusion and dissipation) are negligible during this process. The present results highlight the importance of the region near the T/NT interface in the entire jet development.