Vorticity Spectra Research Articles

Machine learning-based vorticity evolution and super-resolution of homogeneous isotropic turbulence using wavelet projection

A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are trained with a time series of direct numerical simulation (DNS) data of homogeneous isotropic turbulence at the Taylor microscale Reynolds number 92. The predicted results are assessed by using the flow visualization of vorticity and statistics, e.g., probability density functions of vorticity and enstrophy spectra. It is found that the predicted results are in good agreement with DNS results. The small-scale flow topology considering the second and the third invariants of the velocity gradient tensor likewise shows an approximate match. Furthermore, we apply the pre-trained neural networks to coarse-grained vorticity data using super-resolution. It is shown that the super-resolved flow field well agrees with the reference DNS field, and thus small-scale information and vortex tubes are well regenerated.

Spectral analysis of the evolution of energy-containing eddies

Energy-containing eddies (energy-eddies) are the elementary structures of wall turbulence that carry most of the kinetic energy and momentum. Despite the consensus that energy-eddies can self-sustain at each relevant length scale, their precise origin and spatial evolution are currently not well understood. In this study, we examine the spatial evolution of energy-eddies by quenching them at the inflow of a turbulent channel flow. Our study shows that the eddies involved in the energy cascade cannot be sustained without the energy-eddies. The streamwise velocity spectra of the evolving flow start to recover at a spanwise wavelength of $\lambda _z^+ \simeq 100$ , equal to the near-wall spacing of streaks in the buffer layer located at $y^+ \simeq 15$ , whereas there are no active vortical motions in the streamwise vorticity spectra until the energy at the streak location is re-established. Hence, the present study demonstrates that in a spatially evolving flow, the formation of near-wall streaks is the primary process necessary in the recovery of energy-eddies.

Headland Rip Very Low Frequency Fluctuations and Surfzone Eddies During High-Energy Wave Events

Abstract A wave-group-resolving model is used to investigate the driving mechanisms and the spatiotemporal variability of very low frequency (VLF) fluctuations of a headland deflection rip, measured during a 4-m oblique wave event. Surfzone eddies (SZE) occurring in the presence of a strongly sheared longshore current V at a longshore-uniform beach are first modeled. The spectral signature and the variability of SZE are displayed and compared with the literature. The model is then used to explore the dynamics of vorticity in the surf zone and against a headland under energetic oblique wave conditions. The resulting weakly sheared V is found to host large-scale SZE propagating toward the headland at a speed decreasing seaward. Vorticity animations and spectral diagrams indicate that VLF fluctuations of the deflection rip are driven by the deflection of the upstream SZE. In line with measurements, periods from 40 min to 1 h dominate the spectrum hundreds of meters from the headland at low tide. At high tide, vorticity spectra in the rip are much narrower than in the surf zone, suggesting that the headland enforces the merging of SZE. This mechanism is further analyzed using idealized simulations with varying headland lengths, aiming at extending traditional deflection patterns at the VLF scale. Finally, we discuss the existence of a continuum in SZE driving mechanisms, going from fully wave-group-driven to both wave-group- and shear-instability-driven SZE for weakly and strongly sheared V, respectively. This continuum suggests the importance of wave groups to produce SZE under energetic wave conditions.

Sensitivity tests of cosmic velocity fields to massive neutrinos

ABSTRACT We investigate impacts of massive neutrinos on the cosmic velocity fields, employing high-resolution cosmological N-body simulations provided by the information-optimized CUBE code, where cosmic neutrinos are evolved using collisionless hydrodynamics and their perturbations can be accurately resolved. In this study, we focus, for the first time, on the analysis of massive-neutrino-induced suppression effects in various cosmic velocity field components of velocity magnitude, divergence, vorticity, and dispersion. By varying the neutrino mass sum Mν from 0 to 0.4 eV, the simulations show that the power spectra of vorticity – exclusively sourced by non-linear structure formation that is affected by massive neutrinos significantly – are very sensitive to the mass sum, which potentially provide novel signatures in detecting massive neutrinos. Furthermore, using the χ2 statistic, we quantitatively test the sensitivity of the density and velocity power spectra to the neutrino mass sum. Indeed, we find that the vorticity spectrum has the highest sensitivity, and the null hypothesis of massless neutrinos is incompatible with both vorticity and divergence spectra from Mν = 0.1 eV at high significance (P-value = 0.03 and 0.07, respectively). These results demonstrate clearly the importance of peculiar velocity field measurements, in particular of vorticity and divergence components, in determination of neutrino mass and mass hierarchy.

Investigation on shear layer instabilities and generation of vortices during shock wave and boundary layer interaction

The interaction of a reflected shock with the boundary layer inside the shock tubes is an important engineering problem. Studies related to shock wave mitigation and attenuation are performed inside the shock tubes. A proper understanding of the flow behind the reflected shock and the separated zone involving multiple vortical structures is highly essential for estimating the effectiveness of the shock wave mitigation/ attenuation. Such complex flows consist of Lambda shock, shear layer originating from the triple point, multiple shocklets, Mach stems, and vortices. Experimentally the shock structures are obtained through optical techniques. The vortices present in the compressible flow can be obtained through numerical simulations. The complex flows consisting of the above- mentioned features have been simulated numerically so far for the Reynolds numbers up to 1000 [ Zhou G, Xu K, Liu F. Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube. Phys Fluids 2018;30(016102):1-21.]. In the present investigation, the shock-wave boundary-layer interaction is simulated for the Reynolds numbers of 1000 and 2500 using a 13th order hybrid scheme to discern the distinct flow features. First, the solver [Kundu A, De S. Navier-Stokes simulation of shock-heavy bubble interaction: Comparison of upwind and WENO schemes. Comput Fluids 2017;157:131-145.] was validated with the benchmark wall density data for a Reynolds number of 1000. Next, the simulations were performed using 50 and 109.5 million cells for the Reynolds number of 2500. The density gradients, vorticity, wall density, and Fourier spectra were used for comparing the flow field for the Reynolds numbers of interest. The Lambda shock, Kelvin-Helmholtz (K-H) vortices in the shear layer, shocklets, the height of lambda shock, and Mach stems were obtained using a grid-mesh of 109.5 million cells. It is observed that the number of vortices generated inside the separated flow region increased with the increase in Reynolds number from 1000 to 2500. Furthermore, the triple point height and the number of K-H vortices generated at the shear layer also increase with an increase in Reynolds number. The present simulations revealed the formation of vortices close to the wall at a Reynolds number of 2500. Such flow structures have an important role in shock / blast wave mitigation and the associated aeroacoustics.

The Effect of Vortex Shedding in Film-Cooling Processes

Film cooling using coolant jets is effective for increasing the cooling effectiveness of turbines. In the present study, large eddy simulation was employed for predicting small-scale vortices in the film-cooling process with different blowing ratios (BRs). The counter-rotating vortex pair (CRVP) was compared with the hairpin vortex, and results indicated the CRVP was the cross section of hairpin vortex. The results of a spectral analysis indicated a high correlation between the shedding period of the CRVP and the film-cooling effectiveness, and the dominant frequencies of the temperature and vorticity spectra were both identical to the shedding frequency of the CRVP when BR is less than 0.75. Furthermore, a higher shedding frequency of CRVP will suck the hot cross-flow into the core region more frequently, which will lead to a worse film-cooling effectiveness.

Interactions between barotropic tides and mesoscale processes in deep ocean and shelf regions

The interactions between barotropic tides and mesoscale processes were studied using the results of a numerical model in which tidal forcing was turned on and off. The research area covered part of the East Atlantic Ocean, a steep continental slope, and the European Northwest Shelf. Tides affected the baroclinic fields at much smaller spatial scales than the barotropic tidal scales. Changes in the horizontal patterns of the M2 and M4 tidal constituents provided information about the two-way interactions between barotropic tides and mesoscale processes. The interaction between the atmosphere and ocean measured by the work done by wind was also affected by the barotropic tidal forcing. Tidal forcing intensified the transient processes and resulted in a substantial transformation of the wave number spectra in the transition areas from the deep ocean to the shelf. Tides flattened the sea-surface height spectra down to ~ k−2.5 power law, thus reflecting the large contribution of the processes in the high-frequency range compared to quasi-geostrophic motion. The spectra along sections parallel or normal to the continental slope differ from each other, which indicates that mesoscale turbulence was not isotropic. An analysis of the vorticity spectra showed that the flattening was mostly due to internal tides. Compared with the deep ocean, no substantial scale selectivity was observed on the shelf area. Particle tracking showed that the lengths of the Lagrangian trajectories increased by approximately 40% if the barotropic tidal forcing was activated, which contributed to changed mixing properties. The ratio between the horizontal and vertical scales of motion varied regionally depending on whether barotropic tidal forcing was included. The overall conclusion is that the barotropic tides affect substantially the diapycnal mixing.

Characteristics of the turbulent energy dissipation rate in a cylinder wake

This work aims to improve our understanding of the turbulent energy dissipation rate in the wake of a circular cylinder. Ten of the twelve velocity derivative terms which make up the energy dissipation rate are simultaneously obtained with a probe composed of four X-wires. Measurements are made in the plane of mean shear at$x/d=10$, 20 and 40, where$x$is the streamwise distance from the cylinder axis and$d$is the cylinder diameter, at a Reynolds number of$2.5\times 10^{3}$based on$d$and free-stream velocity. Both statistical and topological features of the velocity derivatives as well as the energy dissipation rate, approximated by a surrogate based on the assumption of homogeneity in the transverse plane, are examined. The spectra of the velocity derivatives indicate that local axisymmetry is first satisfied at higher wavenumbers while the departure at lower wavenumbers is caused by the Kármán vortex street. The spectral method proposed by Djenidi & Antonia (Exp. Fluids, vol. 53, 2012, pp. 1005–1013) based on the universality of the dissipation range of the longitudinal velocity spectrum normalized by the Kolmogorov scales also applies in the present flow despite the strong perturbation from the Kármán vortex street and violation of local isotropy at small$x/d$. The appropriateness of the spectral chart method is consistent with Antoniaet al.’s (Phys. Fluids, vol. 26, 2014, 45105) observation that the two major assumptions in Kolmogorov’s first similarity hypothesis, i.e. very large Taylor microscale Reynolds number and local isotropy, can be significantly relaxed. The data also indicate that vorticity spectra are more sensitive, when testing the first similarity hypothesis, than velocity spectra. They also reveal that the velocity derivatives$\unicode[STIX]{x2202}u/\unicode[STIX]{x2202}y$and$\unicode[STIX]{x2202}v/\unicode[STIX]{x2202}x$play an important role in the interaction between large and small scales in the present flow. The phase-averaged data indicate that the energy dissipation is concentrated mostly within the coherent spanwise vortex rollers, in contrast with the model of Hussain (J. Fluid Mech., vol. 173, 1986, pp. 303–356) and Hussain & Hayakawa (J. Fluid Mech., vol. 180, 1987, p. 193), who conjectured that it resides mainly in regions of strong turbulent mixing.

Vortex pairing and reverse cascade in a simulated two-dimensional rocket motor-like flow field

Two-dimensional large eddy simulation of a flow experiment intended for studying and understanding transition and parietal vortex shedding has brought to light some interesting features that have never been seen in previous similar simulations and have implications for future computational work on combustion instabilities in rocket motors. The frequency spectrum of pressure at head end shows a peak at the expected value associated with parietal vortex shedding but an additional peak at half this frequency emerges at downstream location. Using vorticity spectra at various distances away from the wall, it is shown that the frequency halving is due to vortex pairing as hypothesized by Dunlap et al. [“Internal flow field studies in a simulated cylindrical port rocket chamber,” J. Propul. Power 6(6), 690–704 (1990)] for a similar experiment. As the flow transitions to turbulence towards the nozzle end, inertial range with Kolmogorov scaling becomes evident in the velocity spectrum. Given that the simulation is two-dimensional, such a scaling could be associated with a reverse energy cascade as per Kraichnan-Leith-Bachelor theory. By filtering the simulated flow field and identifying where the energy backscatters into the filtered scales, the regions with a reverse cascade are identified. The implications of this finding on combustion modeling are discussed.

Platform and Across-Swath Comparison of Vorticity Spectra From QuikSCAT, ASCAT-A, OSCAT, and ASCAT-B Scatterometers

In the last few years, there has been tremendous improvement in the calibration of ocean surface vector winds from scatterometers and polarimetric radiometers. This is the first detailed investigation of across-swath consistency in scatterometer-derived (i.e., QSCAT, ASCAT-A, OSCAT, and ASCAT-B) vorticity (curl of the ocean surface vector winds). Spatial derivatives of the winds fields are very important for atmospheric boundary-layer processes, upper ocean forcing, and deep ocean forcing. Improvements in wind calibration imply improvements in derivatives of these winds; however, it does not imply consistency. This study demonstrates near consistency in across-swath vorticity and near consistency between platforms.

Enstrophy cascades in two-dimensional dense granular flows.

Employing two-dimensional molecular dynamics simulations of dense granular materials under simple shear deformations, we investigate vortex structures of particle rearrangements. Introducing vorticity fields as a measure of local spinning motions of the particles, we observe their heterogeneous distributions, where statistics of vorticity fields exhibit the highly non-Gaussian behavior and typical domain sizes of vorticity fields significantly increase if the system is yielding under quasistatic deformations. In such dense granular flows, a power-law decay of vorticity spectra can be observed at mesoscopic scale, implying anomalous local structures of kinetic energy dissipation. We explain the power-law decay, or enstrophy cascades in dense granular materials, by a dimensional analysis, where the dependence of vorticity spectra not only on the wave number, but also on the shear rate, is well explained. From our dimensional analyses, the scaling of granular temperature and rotational kinetic energy is also predicted.

Flow Unsteadiness and Pressure Pulsations in a Nuclear Reactor Coolant Pump

Unsteady flow induced by rotor-stator interaction is detrimental to the safe operation of the nuclear reactor coolant pump, so it is essential to clarify flow structures and pressure pulsation in such pumps, especially within the spherical casing. In this paper, unsteady flow characteristics in a mixed-flow nuclear reactor coolant model pump were investigated using large-eddy simulation (LES) method. Results show that at the nominal flow rate, in two particular diffuser channels near the spherical casing discharge nozzle, the flow structures are uneven compared with that in the other flow channels. The reason is associated with the position of the flow channel with respect to the spherical casing nozzle. Large- scale flow separation and backflow structures easily occur at the regions near these two channels. In the right and the middle region of the casing nozzle, due to the large-scale separate flow and high vorticity magnitude, unsteady flow structures are more complicated in comparison with the other regions. It has been found that the vorticity spectra and the pressure spectra almost have the same main excitation frequencies. Therefore, it has been confirmed that for particular regions pressure pulsations are determined by the shedding vortex wake from the diffuser blade trailing edge of the nuclear reactor coolant model pump.

Measuring Turbulent Kinetic Energy Dissipation at a Wavy Sea Surface

AbstractWave breaking is thought to be the dominant mechanism for energy loss by the surface wave field. Breaking results in energetic and highly turbulent velocity fields, concentrated within approximately one wave height of the surface. To make meaningful estimates of wave energy dissipation in the upper ocean, it is then necessary to make accurate measurements of turbulent kinetic energy (TKE) dissipation very near the surface. However, the surface wave field makes measurements of turbulence at the air–sea interface challenging since the energy spectrum contains energy from both waves and turbulence over the same range of wavenumbers and frequencies. Furthermore, wave orbital velocities can advect the turbulent wake of instrumentation into the sampling volume of the instrument. In this work a new technique for measuring TKE dissipation at the sea surface that overcomes these difficulties is presented. Using a stereo pair of longwave infrared cameras, it is possible to reconstruct the surface displacement and velocity fields. The vorticity of that velocity field can then be considered to be representative of the rotational turbulence and not the irrotational wave orbital velocities. The turbulent kinetic energy dissipation rate can then be calculated by comparing the vorticity spectrum to a universal spectrum. Average surface TKE dissipation calculated in this manner was found to be consistent with near-surface values from the literature, and time-dependent dissipation was found to depend on breaking.

Analytic structure of a drag-driven confined dust vortex flow in plasma.

Flow structure of a dust medium electrostatically suspended and confined in a plasma presents a unique setup where the spatial scale of a volumetric drive by the plasma flow might exceed that of the boundaries confining the dust. By means of a formal implementation of a two-dimensional hydrodynamic model to a confined dust flow and its analytic curvilinear solutions, it is shown that the eigenmode spectrum of the dust vortex flow can lose correlations with the driving field even at the low dust Reynolds numbers as a result of strong shear and finer scales introduced in the equilibrium dust vorticity spectrum by the boundaries. While the boundary effects can replace the desired turbulent processes unavailable in this regime, the shear observable in most of the dust vortex flows is identified to have a definite exponent of dependence on the dust viscosity over a substantially large range of the latter. These results and scalings allow quantification of the notion of dusty plasma medium as a paradigm for a wide range of natural flow processes having scales inaccessible to ordinary laboratory experiments.

Energy and vorticity spectra in turbulent superfluidHe4fromT=0toTλ

We discuss the energy and vorticity spectra of turbulent superfluid $^4$He in all the temperature range from $T=0$ up to the phase transition "$\lambda$ point", $T_\lambda\simeq 2.17\,$K. Contrary to classical developed turbulence in which there are only two typical scales, i.e. the energy injection $L$ and the dissipation scales $\eta$, here the quantization of vorticity introduces two additional scales, i.e the vortex core radius $a_0$ and the mean vortex spacing $\ell$. We present these spectra for the super- and normal-fluid components in the entire range of scales from $L$ to $a_0$ including the cross-over scale $\ell$ where the hydrodynamic eddy-cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale a bottleneck accumulation of the energy was found earlier at $T=0$. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" $\nu'$ in the entire temperature range and show agreement with numerous experimental observation for $\nu'(T)$.

The Vorticity Balance of the Ocean Surface in Hawaii from a Regional Reanalysis

AbstractThe ocean surface vorticity budget around the Hawaiian Islands is examined using an 18-month model reanalysis generated using four-dimensional variational state estimation with all available observations (satellite, in situ, and high-frequency radio). To better resolve the ocean surface currents and reduce the representation error of the radio-measured surface currents, this study developed a new vertical scheme for the Regional Ocean Modeling System. A new, detailed description of the ocean surface vorticity is created, revealing a region dominated by cyclonic (anticyclonic) vorticity to the north (south) of the mean position of the Hawaii Lee Countercurrent. Advection of vorticity is the primary process that transports the vorticity generated in the lee of the islands by the wind wake. In this island lee, the zonal wavenumber spectra show a cascade of vorticity/energy from the submesoscale toward the larger scales. Latitudinal differences in the advection of vorticity spectra indicate the propagation of a first baroclinic mode Rossby wave in the region dominated by anticyclonic vorticity to the west of the island of Hawaii, while the region dominated by cyclonic vorticity is disrupted by the wake of the smaller islands.

Intensified Diurnal Tides along the Oregon Coast

Abstract Intensified diurnal tides are found along portions of the Oregon shelf (U.S. West Coast) based on analyses of high-frequency (HF) radar surface current data and outputs of a 1-km resolution ocean circulation model. The K1 tidal currents with magnitudes near 0.07 m s−1 over a wider part of the shelf (Heceta Bank complex; 44°–44.5°N), previously predicted by Erofeeva et al., are confirmed here by newly available HF radar data. Intensified diurnal tides are also found along the narrow shelf south of Heceta Bank. In the close vicinity of Cape Blanco (42.8°N), diurnal tidal currents (K1 and O1 constituents combined) may reach 0.3 m s−1. Appreciable differences in diurnal tide intensity are found depending on whether the model is forced with tides and winds (TW) or only tides. Also, diurnal variability in wind forcing is found to affect diurnal surface velocities. For the case forced by tides alone, results strongly depend on whether the model ocean is stratified [tides only, stratified (TOS)] or not [tides only, no stratification (TONS)]. In case TONS, coastal-trapped waves at diurnal frequencies do not occur over the narrow shelf south of 43.5°N, consistent with the dispersion analysis of a linear shallow-water model. However, in case TOS, diurnal tides are intensified in that area, associated with the presence of coastal-trapped waves. Case TW produces the strongest modeled diurnal tidal motions over the entire Oregon shelf, partially due to cross-shore tidal displacement (advection) of alongshore subinertial currents. At Cape Blanco, diurnal tidal variability dominates the modeled relative vorticity spectrum, suggesting that tides may influence the separation of the alongshore coastal jet at that location.

Mechanics of viscous vortex reconnection

This work is motivated by our long-standing claim that reconnection of coherent structures is the dominant mechanism of jet noise generation and plays a key role in both energy cascade and fine-scale mixing in fluid turbulence [F. Hussain, Phys. Fluids 26, 2816 (1983); J. Fluid Mech. 173, 303 (1986)]. To shed further light on the mechanism involved and quantify its features, the reconnection of two antiparallel vortex tubes is studied by direct numerical simulation of the incompressible Navier–Stokes equations over a wide range (250–9000) of the vortex Reynolds number, Re (=circulation/viscosity) at much higher resolutions than have been attempted. Unlike magnetic or superfluid reconnections, viscous reconnection is never complete, leaving behind a part of the initial tubes as threads, which then undergo successive reconnections (our cascade and mixing scenarios) as the newly formed bridges recoil from each other by self-advection. We find that the time tR for orthogonal transfer of circulation scales as tR≈Re−3/4. The shortest distance d between the tube centroids scales as d≈a[Re(t0−t)]3/4 before reconnection (collision) and as d≈b[Re(t−t0)]2 after reconnection (repulsion), where t0 is the instant of smallest separation between vortex centroids. We find that b is a constant, thus suggesting self-similarity, but a is dependent on Re. Bridge repulsion is faster than collision and is more autonomous as local induction predominates, and, given the associated acceleration of vorticity, is potentially a source of intense sound generation. At the higher Re studied, the tails of the colliding threads are compressed into a planar jet with multiple vortex pairs. For Re>6000, there is an avalanche of smaller scales during the reconnection, the rate of small scale generation and the spectral content (in vorticity, transfer function and dissipation spectra) being quite consistent with the structures visualized by the λ2 criterion. The maximum rate of vortex circulation transfer, enstrophy production, and dissipation scale as Re1, Re7/4, and Re−1/2, respectively. A more detailed study of subsequent reconnection of threads requires much higher-resolution simulations that are currently not feasible.

Cosmological magnetic fields from inflation in extended electromagnetism

In this work we consider an extended electromagnetic theory in which the scalar state which is usually eliminated by means of the Lorenz condition is allowed to propagate. This state has been shown to generate a small cosmological constant in the context of standard inflationary cosmology. Here we show that the usual Lorenz gauge-breaking term now plays the role of an effective electromagnetic current. Such a current is generated during inflation from quantum fluctuations and gives rise to a stochastic effective charge density distribution. Because of the high electric conductivity of the cosmic plasma after inflation, the electric charge density generates currents which give rise to both vorticity and magnetic fields on sub-Hubble scales. Present upper limits on vorticity coming from temperature anisotropies of the CMB are translated into lower limits on the present value of cosmic magnetic fields. We find that, for a nearly scale invariant vorticity spectrum, magnetic fields ${B}_{\ensuremath{\lambda}}>{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{G}$ are typically generated with coherence lengths ranging from subgalactic scales up to the present Hubble radius. Those fields could act as seeds for a galactic dynamo or even account for observations just by collapse and differential rotation of the protogalactic cloud.

Effect of a small axisymmetric contraction on grid turbulence

Measurements downstream of a grid followed by a contraction with an area ratio of 1.36 have been made with a one-component vorticity probe. The velocity data indicate that there is indeed an improvement in isotropy of the large scales when such a contraction is used. In particular, the spectrum of u loses a significant amount of low frequency energy and its peak is shifted towards that of v. Although the v spectrum is less affected than the u spectrum, the relative magnitudes of the u and v spectra satisfy isotropy more closely with than without the contraction. In particular, isotropy is most closely approximated when the contraction is used in combination with a grid designed to minimise vortex shedding. The lateral vorticity spectrum is essentially unaffected, irrespective of the grid that is used or the magnitude of the wavenumber.