Vortex-stretching Research Articles

Forgetfulness of turbulent energy cascade associated with different mechanisms

The small scales of high Reynolds number turbulence exhibit the statistical universality by forgetting about the large scales during the energy cascade. In this study, we revisit this schematic description with an information-theoretic point of view. Our objective is to understand the importance of different cascade mechanisms in this process. To this end, we compute the “information flux”, the information-theoretic measure of causality formulated by one of the authors, of the decomposed inter-scale energy transfer. For the kinetics, the ratio of the inertial-range inter-scale energy transfer between the strain self-amplification (SSA) and the vortex stretching (VS) mechanisms is 5 : 3. However, for the information-flux, the VS contribution is roughly twice as large as the SSA. We also find several deviations between the kinetics and the informatics, highlighting the nontrivial nature of information distributed among different scales and mechanics in turbulence. This result infers that the SSA is a less efficient mechanism than the VS in terms of information transfer, and contributes to losing the large-scale information.

Arctic Sea Ice Loss Modulates the Surface Impact of Autumn Stratospheric Polar Vortex Stretching Events

AbstractThe cold Eurasia has been proposed to be closely linked to the weakening of the stratospheric polar vortex (SPV), however, how the Arctic sea ice modulates the surface impacts of the weak SPV is unclear. This study explores the critical modulating role of reduced Arctic sea ice in the surface cooling response to SPV stretching events in autumn. Here, through ERA5 reanalysis and Whole Atmosphere Community Climate Model simulations, we show that Eurasian cold events are more likely (45%) to occur in days 30–50 after the onset of SPV stretching events under lower Barents‐Kara Seas (BKS) sea ice conditions, in contrast to under heavy BKS sea ice conditions when robust surface cooling is absent. The stratospheric and tropospheric pathways explain 46.8% and 53.2% of the total variance of Siberian coldness, respectively. The downward extension of anomalous stratospheric wave‐2 ridge to the troposphere intensifies the Arctic‐North European high, favoring the subsequent colder Siberia.

Locality of Vortex Stretching for the 3D Euler Equations

We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.

Intrinsic Consistency Among Three-Dimensional Instability, Additional Vorticity Generation and Vortex Stretching and Twisting Under Specific Conditions

Intrinsic Consistency Among Three-Dimensional Instability, Additional Vorticity Generation and Vortex Stretching and Twisting Under Specific Conditions

Control Possibility of Explosive Vortex Stretching in Vortex Reconnection

Control Possibility of Explosive Vortex Stretching in Vortex Reconnection

On the Effects of Advection and Vortex Stretching

We prove finite-time singularity formation for De Gregorio's model of the three-dimensional vorticity equation in the class of $L^p\cap C^\alpha(\mathbb{R})$ vorticities for some $\alpha>0$ and $p<\infty$. We also prove finite-time singularity formation from smooth initial data for the Okamoto-Sakajo-Wunsch models in a new range of parameter values. As a consequence, we have finite-time singularity for certain infinite-energy solutions of the surface quasi-geostrophic equation which are $C^\alpha$-regular. One of the difficulties in the models we consider is that there are competing \emph{nonlocal} stabilizing effects (advection) and destabilizing effects (vortex stretching) which are of the same size in terms of scaling. Hence, it is difficult to establish the domination of one effect over the other without having strong control of the solution. We conjecture that strong solutions to the De Gregorio model exhibit the following behavior: for each $0<\alpha<1$ there exists an initial $\omega_0\in C^\alpha(\mathbb{R})$ which is compactly supported for which the solution becomes singular in finite-time; on the other hand, solutions to De Gregorio's equation are global whenever $\omega_0\in L^p\cap C^{1}(\mathbb{R})$ for some $p<\infty$. Such a dichotomy seems to be a genuinely non-linear effect which cannot be explained merely by scaling considerations since $C^\alpha$ spaces are scaling subcritical for each $\alpha>0$.

Effects of Vortex Stretching and Merging on Flame Propagation Speed in Vortex Bursting

Effects of Vortex Stretching and Merging on Flame Propagation Speed in Vortex Bursting

Geostrophic Spirals Generated by the Horizontal Diffusion of Vortex Stretching in the Yellow Sea

Horizontal velocity spirals with a clockwise rotation (downward looking) rate of 1.7° m−1, on average, were observed in the western and northern Yellow Sea from December 2006 to February 2007. With the observed thermal wind relation, the beta-spiral theory was used to explain the dynamics of spirals. It was found that the horizontal diffusion of geostrophic vortex stretching is likely to be a major mechanism for generating geostrophic spirals. Vertical advection associated with surface/bottom Ekman pumping and topography-induced upwelling is too weak to support these spirals. Strong wind stirring and large heat loss in wintertime lead to weak stratification and diminish the effects of vertical advection. The cooling effect and vertical diffusion are offset by an overwhelming contribution of horizontal diffusion in connection with vortex stretching. The Richardson number-dependent vertical eddy diffusivity reaches a magnitude of 10−4 m2 s−1 on average. An eddy diffusivity of 2870 m2 s−1 is required for dynamic balance by estimating the residual term. This obtained value of 10−4 m2 s−1 is in good agreement with the estimation in terms of observed eddy activities. The suppressed and unsuppressed diffusivities in the observation region are 2752 and 2881 m2 s−1, respectively, which supports a closed budget for velocity rotation.

Visualization of flow field of a liquid ejector pump using embedded LES methodology

The understanding of entrainment and mixing phenomenon in the ejector pump is of pivotal importance for designing and performance estimation. In this paper, the existence of turbulent vortical structures due to Kelvin–Helmholtz instability at the free surface between the motive and the entrained fluids streams is visualized using Embedded LES methodology. The efficacy of Embedded LES for simulation of complex flow field of ejector pump is evaluated using ANSYS Fluent® 15.0. The enhanced mixing and entrainment process due to breaking down of larger eddies into smaller ones as a consequence of Vortex Stretching phenomenon is captured in this study. Moreover, the flow field characteristics of ejector pump like pressure and velocity fields are also analyzed and the results are validated against experimental results.

Variation of enstrophy production and strain rotation relation in a turbulent boundary layer

The production of enstrophy is strongly coupled to the vortex stretching process that is of inherent importance to the cascading process, one of the driving processes of turbulence in a flow. In this work the enstrophy production mechanism is investigated to identify its variation in the wall-normal direction for the case of a turbulent boundary layer. Production is decomposed into its core quantities including the ratio of the principal strains and the alignment of vorticity with the eigenvectors of the strain rate tensor. The strong variations of these quantities with the wall distance are presented and explained. A self-similar shape of the probability distribution of the enstrophy production is found for regions above the buffer layer. Based on these findings we propose a modification to an existing vortex stretch model that accounts for the wall-normal variation in enstrophy production in a boundary layer. A characteristic decomposition is applied on the turbulence field that allows for the study of the individual production mechanisms of the separate structure types. This analysis reveals a potential backscatter mechanism that transfers kinetic energy from smaller scales towards larger ones, for a structure type described as unstable vortices.

Single-Particle Motion and Vortex Stretching in Three-Dimensional Turbulent Flows.

Three-dimensional turbulent flows are characterized by a flux of energy from large to small scales, which breaks the time reversal symmetry. The motion of tracer particles, which tend to lose energy faster than they gain it, is also irreversible. Here, we connect the time irreversibility in the motion of single tracers with vortex stretching and thus with the generation of the smallest scales.

2개의 블레이드로 구성된 회전익 끝와류들의 간섭 특성

Key Words: Rotor Blade(로터블레이드), Wake Age(후류시기), Tip Vortex(끝와류), Vortex Filament(와류필라멘트), LDV(레이저도플러유속계), Vortex Stretching(와류이완)초록: 대칭익형단면에미세한피치각의차이를가지는두개의로터블레이드의끝에서발생하는와류들의상호간섭을관측하기위하여2차원LDV를활용하여끝와류의회전속도성분과축방향속도성분들을후류시기에따라서측정하였다. 선행블레이드는끝와류축방향성분이정규분포를나타내는상사성을위배한반면, 후행블레이드는회전속도성분이복합와류를나타내는Vatistas' n=2 모형의상사성을위배하는것으로관찰되었다. 또한, 후류시기200~240도근방에서두끝와류의궤적이근접되어상호간섭을나타내는것으로밝혀졌으며이시기동안후행블레이드의와류이완현상이발생하는것으로확인이되었다. 이러한후류간섭은관절형허브를가지는로터에서도발생될것으로예측된다.Abstract: In order to observe the wake interaction between tip vortices generated by a two-bladed rotor withslightly different pitch angles, the velocity components of the tip vortices were measured by using atwo-dimensional LDV system. It was observed that the swirl velocity components of the ensuing bladedeviated from the Vatistas' n = 2 vortex model and the axial velocity components of the preceding bladedeviated from the Gaussian profile. It was also found that in the wake-age range of 200o to 240o, thefilament of the ensuing blade tip vortex was stretched as result of the closing in of two vortices. The resultsfrom these observations suggest the possibility that a similar wake interaction is generated in actual rotorblades, especially, in the ones with articulated hubs.

Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

A pair of perturbed antiparallel quantum vortices, simulated using the three-dimensional Gross-Pitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K(∇ψ) being converted into interaction energy E(I) and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons, and the creation of an approximately -5/3 kinetic energy spectrum at high wave numbers. All of the wave generation and reconnection steps follow from interactions between the two original vortices. A four vortex example is given to demonstrate that some of these steps might be general.

The Role of Bottom Vortex Stretching on the Path of the North Atlantic Western Boundary Current and on the Northern Recirculation Gyre

Abstract The mechanisms affecting the path of the depth-integrated North Atlantic western boundary current and the formation of the northern recirculation gyre are investigated using a hierarchy of models, namely, a robust diagnostic model, a prognostic model using a global 1° ocean general circulation model coupled to a two-dimensional atmospheric energy balance model with a hydrological cycle, a simple numerical barotropic model, and an analytic model. The results herein suggest that the path of this boundary current and the formation of the northern recirculation gyre are sensitive to both the magnitude of lateral viscosity and the strength of the deep western boundary current (DWBC). In particular, it is shown that bottom vortex stretching induced by a downslope DWBC near the south of the Grand Banks leads to the formation of a cyclonic northern recirculation gyre and keeps the path of the depth-integrated western boundary current downstream of Cape Hatteras separated from the North American coast. Both south of the Grand Banks and at the crossover region of the DWBC and Gulf Stream, the downslope DWBC induces strong bottom downwelling over the steep continental slope, and the magnitude of the bottom downwelling is locally stronger than surface Ekman pumping velocity, providing strong positive vorticity through bottom vortex-stretching effects. The bottom vortex-stretching effect is also present in an extensive area in the North Atlantic, and the contribution to the North Atlantic subpolar and subtropical gyres is on the same order as the local surface wind stress curl. Analytic solutions show that the bottom vortex stretching is important near the western boundary only when the continental slope is wider than the Munk frictional layer scale.

Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations

We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition \cite{Kerr93}[Phys. Fluids {\bf 5} (1993), 1725]. We use a pseudo-spectral method with resolution up to $1536\times 1024 \times 3072$ to resolve the nearly singular behavior of the Euler equations. Our numerical results demonstrate that the maximum vorticity does not grow faster than double exponential in time, up to $t=19$, beyond the singularity time $t=18.7$ predicted by Kerr's computations \cite{Kerr93,Kerr04}. The velocity, the enstrophy and enstrophy production rate remain bounded throughout the computations. As the flow evolves, the vortex tubes are flattened severely and turned into thin vortex sheets, which roll up subsequently. The vortex lines near the region of the maximum vorticity are relatively straight. This local geometric regularity of vortex lines seems to be responsible for the dynamic depletion of vortex stretching.

Depicting Vortex Stretching and Vortex Relaxing Mechanisms

Different from many existing studies on the parametrization ofvortices, we investigate the effectiveness of two new parameters foridentifying the vortex stretching and vortex relaxing mechanisms.These parameters are invariants and identify three-dimensional flowstructures only, i.e. they diminish in two-dimensional flows. This isalso unlike the existing vortex identification approaches which deliverinformation in two-dimensional flows. The present proposals have beensuccessfully applied to identify the stretching and relaxing vorticesin compressible mixing layers and natural convection flows.

Dilatation and Vortex Stretching Effects on Turbulence in One-Dimensional/Axisymmetric Flows

A theoretical analysis is carried out to predict the amplie cation of turbulence in e ows experiencing onedimensionaland axisymmetric dilatations. When threerepresentativevorticesaretracked,thevariationsofvortex radius and vorticity arecalculated, and then the amplie cation of turbulenceis obtained from them. When a vortex istracked, conservation lawsof mass and angular momentum of thevortex are used. For a one dimensionally compressed e ow, the present analysis slightly underestimates the amplie cation of velocity e uctuations and turbulent kinetic energy, relative to that of rapid distortion theory in the solenoidal limit. For an axisymmetrically distorted e ow, the amplie cation of velocity e uctuations and turbulent kinetic energy and the anisotropy depend not only on the density ratio, but also on the ratio of streamwise mean velocities, which represents streamwise vortex contraction/stretching. Theamplie cation predicted by thepresent analysis is in excellent agreement with that by the rapid distortion theory. In both e ows, the amplie cation of turbulence is dictated by the mean density ratio, whereas the anisotropy is primarily dictated by the e ow boundary. However, streamwise vortex stretching/contraction alters the amplie cation slightly and the anisotropy signie cantly in the axisymmetric e ow.

Vortex Inhibition Effect of Surfactant Solutions in a Vortex Stretching Flow.

Vortex stretching flow was investigated using an orifice-type and a rotating-nozzle device. The surfactant solutions showed remarkable vortex inhibition effect. It was indicated that the high resistance of the stretching flow for twisting shear produced the vortex inhibition. In the rotating-nozzle device, a core region of twisting shear appeared along the centerline. The method of viscometry was derived for the twisting shear in the nozzle core. In turbulent flow, the high resistance of the stretching flow for the twisting shear would have influence on energy cascade from large scale to small scale turbulence and have a close relationship to the suppression of transverse turbulence.

An Experiment of Vortex Stretching and Filaments

An Experiment of Vortex Stretching and Filaments

Lagrangian Frozen-in Hypothesis for Vortex Stretching

A nonlinear ordinary differential equation for peak vorticity is proposed phenomenologically for 3D inviscid flows. This typically predicts that the peak vorticity behaves approximately as \(\sqrt {A}[\sin\,\{r\sqrt {A}(t_{\ast}-t)\}]^{-1}\) and the peak strain as \(\sqrt {A}[\tan\,\{r\sqrt {A}(t_{\ast}-t)\}]^{-1}\), where r , A and t * are constants. Numerical study of 3D Euler equations performed both in physical and Langrangian marker spaces is, at early stages consistent with assumptions underlying the above predictions, giving an alternative interpretation of apparently exponential growth of vorticity. It is not known if this evolution persists, leading to a finite-time singularity.