Wavelet Analysis of Vortex Breakdown

We study the quasi-periodic turbulent bursting of a laboratory produced isolated vortex immersed in laminar flow. We analyze the experimentally measured flow field using orthogonal wavelets to observe the time evolution of the bursting. The discrete wavelet transform is used to separate the flow field into a coherent component, capturing the dynamics and statistics of the vortex during bursting, and an incoherent component, which is structureless and exhibits a different statistical behavior

Elastic Convection in Vibrated Viscoplastic Fluids

We observe a new type of behavior in a shear thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a non-dimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.Comment: 4 pages, 6 figure

Extraction of coherent structures in a rotating turbulent flow experiment

The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle Image Velocimetry (PIV) measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity fields exhibit vortex birth, merger, scattering, and destruction. We separate the flow into a low-entropy ``coherent'' and a high-entropy ``incoherent'' component by thresholding the coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWPT and DWT are necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations. The remaining small amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in PRE, last few figures appear at the end. clarifications, added references, fixed typo

Forcing-dependent dynamics and emergence of helicity in rotating turbulence

The effects of large-scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of direct numerical simulations, systematically varying the nature of the mechanical force in time. We find that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relative to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We demonstrate that the nature of the mechanical force in time and the emergence of helicity have direct implications for the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak turbulence

Coherent structures and two-dimensionalization in rotating turbulent flow

textWe study laboratory-produced fluid turbulence under the influence of rapid rotation. Three-dimensional (3D) turbulence is generated by strong pumping through sources and sinks at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter) filled with water. This flow evolves toward quasi-two-dimensional (quasi-2D) turbulence with increasing height in the tank. Digital Particle Image Velocimetry (DPIV) measurements were taken using tracer particles illuminated by a horizontal laser light-sheet. The quasi-2D flow near the top of the tank contains many long-lived coherent vortices and jets with a wide range of sizes near the top of the tank. The vertical vorticity field exhibits complex dynamics such as vortex birth, merger, scattering, and destruction. Measurements using two synchronized cameras and vertically separated light sheets revealed coherent structures that were columnar and extended vertically throughout the tank. The effect of rotation greatly increased the vertical correlation of the flow, even for small rotation rates. A gradual decay in the correlation of increasingly vertically separated vii planes was observed, rather than a sharp transition. The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) were used to extract and study the dynamics of the localized coherent structures near the top of our tank. We separated the flow into a low-entropy “coherent” and a highentropy “incoherent” component by thresholding the coefficients of the DWPT and DWT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression, the Okubo-Weiss criterion and Proper Orthogonal Decomposition (POD) were also tested. We found that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than other methods. Only about 3% of the largeamplitude coefficients of the DWPT and DWT were necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations of the measured fields. The remaining small amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can faithfully describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.Physic

Wavelet tools to study intermittency: application to vortex bursting

This paper proposes statistical tools adapted to study highly unsteady and inhomogeneous flows, such as vortex bursting. For this, we use the wavelet representation in which each coefficient keeps track of both location and scale, in contrast to Fourier representation which requires keeping the phase of all coefficients to preserve the spatial structure of the flow. Based on the continuous wavelet transform, we propose several diagnostics, such as the local spectrum and the local intermittency measure. We also use the orthogonal wavelet transform to split each flow realization into coherent and incoherent contributions, which are then analysed independently and from which we define the coherency measure. We apply these wavelet tools to analyse the bursting of a three-dimensional stretched vortex immersed in a steady laminar channel flow. The time evolution of the velocity field is measured by particle image velocimetry during several successive bursts