Lagrangian-averaged Vorticity Deviation Research Articles

Experimental study on low-speed streaks in a turbulent boundary layer at low Reynolds number

Abstract

Role of Surface-Layer Coherent Eddies in Potential Vorticity Transport in Quasigeostrophic Turbulence Driven by Eastward Shear

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.

Fast Computations for the Lagrangian-averaged Vorticity Deviation Based on the Eulerian Formulations

We propose an efficient Eulerian approach to compute the Lagrangian-averaged vorticity deviation (LAVD) of given flow fields. Traditional approaches need to solve [Formula: see text] ordinary differential equations (ODEs) for a [Formula: see text]-dimensional flow. Furthermore, if the velocity data are discrete, interpolation is required to obtain the velocity and vorticity data along the particle trace of any sampling point, which could be quite time-consuming and even affect the accuracy of the solutions. In contrast, our proposed Eulerian approach only needs to solve one single partial differential equation (PDE) in order to obtain the LAVD field and no interpolation is required. Based on the doubling technique, we also propose an efficient iterative Eulerian-type algorithm to compute the long-time LAVD for periodic flows. After that, relation between the long-time LAVD and the coherent ergodic partition is briefly discussed. Numerical examples will show the accuracy, efficiency and effectiveness of our proposed Eulerian approaches.

Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current

In this paper, we employ the theory of Lagrangian coherent structures for three-dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical Lagrangian coherent structures (VLCSs), a fully automated three-dimensional extraction algorithm for multiple flow structures based on the so-called Lagrangian-averaged vorticity deviation method is implemented. The size, the orientation and the shape of the VLCSs are analysed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, consequently affecting the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.

Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

ABSTRACT The quiet Sun exhibits a wealth of magnetic activities that are fundamental for our understanding of solar magnetism. The magnetic fields in the quiet Sun are observed to evolve coherently, interacting with each other to form prominent structures as they are advected by photospheric flows. The aim of this paper is to study supergranular turbulence by detecting Lagrangian coherent structures (LCS) based on the horizontal velocity fields derived from Hinode intensity images at disc centre of the quiet Sun on 2010 November 2. LCS act as transport barriers and are responsible for attracting/repelling the fluid elements and swirling motions in a finite time. Repelling/attracting LCS are found by computing the forward/backward finite-time Lyapunov exponent (FTLE), and vortices are found by the Lagrangian-averaged vorticity deviation method. We show that the Lagrangian centres and boundaries of supergranular cells are given by the local maximum of the forward and backward FTLE, respectively. The attracting LCS expose the location of the sinks of photospheric flows at supergranular junctions, whereas the repelling LCS interconnect the Lagrangian centres of neighbouring supergranular cells. Lagrangian transport barriers are found within a supergranular cell and from one cell to other cells, which play a key role in the dynamics of internetwork and network magnetic elements. Such barriers favour the formation of vortices in supergranular junctions. In particular, we show that the magnetic field distribution in the quiet Sun is determined by the combined action of attracting/repelling LCS and vortices.

Revisiting coherent structures in low-speed turbulent boundary layers

Coherent structures are essential for the momentum exchange and turbulence production in wall-bounded turbulent flows. Diversified coherent structures have been observed in turbulent boundary layers, and hairpin-based vortices dominate most of the relevant literature. However, there is no consensus yet on the origin and forming mechanism of hairpin vortices. Herein, five cornerstones pertaining to the framework of hairpin-based coherent structures are reviewed, and three different hairpin generation mechanisms are clarified. Next, the time-resolved tomographic particle image velocimetry (Tomo-PIV) is used in an early turbulent boundary layer (Reθ= 420) to investigate the origin of hairpin vortices. The timelines reveal a triangular bulge in the low-speed streak (LSS), and the initial roll-up occurs at two sides of it. Meanwhile, the material surfaces manifest as a three-dimensional (3D) wave structure in the LSS, which may support the model of a soliton-like coherent structure (SCS). Subsequently, the method of Lagrangian-averaged vorticity deviation is used to detect early vortices. We find that the 3D wave structure is flanked by two vortices, thus confirming the roll-up of timelines and demonstrating the advantage of the Lagrangian criteria in capturing structures in complex flows. These results suggest that various coherent structures may evolve from the metamorphosis of 3D wave structures and their later interaction. Finally, the limitations of traditional experimental and post-processing tools are discussed.

Objective Lagrangian Vortex Detection in the Solar Photosphere

Abstract Vortices in the solar photosphere can be linked to a wide range of events, such as small-scale solar eruptions, wave excitation, and heating of the upper part of the solar atmosphere. Despite their importance in solar physics, most of the current studies on photospheric vortices are based on methods that are not invariant under time-dependent translations and rotations of the reference frame and are Eulerian; i.e., they are based on single snapshots of a velocity field and, therefore, do not convey information on the true long-term motion of fluid particles on a time-varying field. Another issue with methods for vortex detection is that typically they provide false identifications in highly compressible flows. This Letter presents a novel criterion that effectively removes wrong detections based on the geometry of the streamlines of the displacement vector of fluid elements and can be readily applied to other astrophysical flows. The new criterion is applied to the Lagrangian-averaged vorticity deviation (LAVD), which is a recently developed frame invariant vortex detection method. The advantage of LAVD is that it delimits the vortices’ outer boundaries precisely by following up the trajectories of fluid elements in space and time. The proposed method is compared with two other techniques using horizontal velocity fields extracted from Hinode satellite data.

Transport by Lagrangian Vortices in the Eastern Pacific

AbstractRotationally coherent Lagrangian vortices (RCLVs) are identified from satellite-derived surface geostrophic velocities in the eastern Pacific (180°–130°W) using the objective (frame invariant) finite-time Lagrangian coherent structure detection method of Haller et al. based on the Lagrangian-averaged vorticity deviation. RCLVs are identified for 30-, 90-, and 270-day intervals over the entire satellite dataset, beginning in 1993. In contrast to structures identified using Eulerian eddy-tracking methods, the RCLVs maintain material coherence over the specified time intervals, making them suitable for material transport estimates. Statistics of RCLVs are compared to statistics of eddies identified from sea surface height (SSH) by Chelton et al. RCLVs and SSH eddies are found to propagate westward at similar speeds at each latitude, consistent with the Rossby wave dispersion relation. However, RCLVs are uniformly smaller and shorter-lived than SSH eddies. A coherent eddy diffusivity is derived to quantify the contribution of RCLVs to meridional transport; it is found that RCLVs contribute less than 1% to net meridional dispersion and diffusion in this sector, implying that eddy transport of tracers is mostly due to incoherent motions, such as swirling and filamentation outside of the eddy cores, rather than coherent meridional translation of eddies themselves. These findings call into question prior estimates of coherent eddy transport based on Eulerian eddy identification methods.

An accurate vortex feature extraction method for Lagrangian vortex visualization on high-order flow field data

As vortex is of great significance to structure analysis and mechanism research in flow field, vortex feature extraction has always been a hot research topic in flow field visualization. We investigate the data precision and numerical algorithm accuracy impact on vortex feature area extraction of Lagrangian Averaged Vorticity Deviation (LAVD). Then, an LAVD-based high-order accurate vortex extraction algorithm is proposed, which incorporates vorticity computation of cell-vertexed data by Weighted Essentially Non-Oscillatory (WENO) scheme, vorticity and velocity computation of off-grid point by candidate stencil weight-based high-order polynomial interpolation method, flow map computation by 4th-order Runge–Kutta (RK) method and integration by compound Simpson rule. We perform vortex feature extraction and visualization on both analytical flow field and high-order unsteady flow field. The experiment results demonstrate that the proposed algorithm can practically reflect the vortex feature of high-order flow field and accurately describe small scale vortex structure, which is unavailable by low-order method.

Defining coherent vortices objectively from the vorticity

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two- and three-dimensional flows.