Vorticity Density Research Articles

Study of Flow Characteristics and Anti-Scour Protection Around Tandem Piers Under Ice Cover

The impact of an ice-covered environment on the local flow characteristics of a bridge pier was studied through a series of flume tests, and the dominant factors affecting the scour pattern were found to grasp the change laws of the local hydrodynamic characteristics of the bridge pier under the ice cover. At the same time, because the scour problem of the pier foundation is a technical problem throughout the life-cycle of the bridge, to determine the optimal anti-scour protection effect on the foundation of the bridge pier, active protection scour plate was used to carry out scour protection tests, and its structural shape was optimized to obtain better anti-scour performance. The test results show that the jumping movements of sediment particles in the scour hole around the pier are mainly caused by events Q2 and Q4, which are accompanied by events Q1 and Q3 and cause the particle rolling phenomenon, where Q1 and Q3 events are outward and inward interacting flow regimes, and Q2 and Q4 events are jet and sweeping flow regimes, respectively. The power spectral attenuation rate in front of the upstream pier is high without masking effects, while strong circulation at the remaining locations results in strong vorticity and high spectral density, in particular, when the sampling time series is 60 s (i.e., f = 1/60), the variance loss rates under ice-covered conditions at the front of the upstream pier, between the two piers, and at the tail end of the downstream pier are 0.5%, 4.6%, and 9.8%, respectively, suggesting a smaller contribution of ice cover to the variance loss.

Simultaneous emergence of active turbulence and odd viscosity in a colloidal chiral active system

Active fluids display collective phenomena such as active turbulence or odd viscosity, which refer to spontaneous complex and transverse flow. The simultaneous emergence of these seemingly separate phenomena is here reported in experiment for a chiral active fluid composed of a carpet of standing and spinning colloidal rods, and in simulations for synchronously rotating hard discs in a hydrodynamic explicit solvent. Experiments and simulations reveal that multi-scale eddies emerge, a hallmark of active turbulence, with a power-law decay of the kinetic-energy spectrum, a feature of self-similar dynamics. Moreover, the particles are dragged to the centre of the vortices, a telltale sign of odd viscosity. The weak compressibility of the system enables an explicit measurement of the odd viscosity in bulk via the relation between local vorticity and excess density. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.

A self-similar solution for the flow behind an exponential cylindrical shock in a self-gravitating mixture of non-ideal gas and a pseudo-fluid of solid particles in a rotating medium

Although the shock wave propagation in the dusty gas medium is widely used in research, astrophysics, military, and industrial applications, the shock wave in a self-gravitating mixture of van der Waals gas and a pseudo-fluid of inert solid particles in a rotating medium, is not well understood. In the present paper, the strong exponential shock wave propagation in a self-gravitating mixture of non-ideal gas and a pseudo-fluid of small solid particles is modelled for unsteady adiabatic and isothermal flows in a rotating medium. In our model, the solid particles are considered as chemically inert pseudo-fluid, and the equilibrium flow conditions hold in the entire flow field region. The similarity solutions are derived for isothermal and adiabatic flows. The vorticity vector components, and isothermal and adiabatic compressibility's are also taken into account. It is shown that the zero-temperature gradient supposition brings the reflective changes in pressure, axial vorticity vector, density, and compressibility distributions in contrast to the adiabatic flow. The shock strength decreases, and the compressibility increases due to the zero-temperature gradient consideration. Also, the effects of the problem parameters on shock waves and the distributions of the flow variables velocity, density, etc., are discussed in detail. It is remarkable to note that due to the consideration of a self-gravitating mixture or with an increase in the ratio of the density of solid particles to the initial density of the gas, the shock strength increases; whereas due to the consideration of non-idealness of the gas or rotating medium the shock strength decreases.

Poster Session 1

Although the shock wave propagation in the dusty gas medium is widely used in research, astrophysics, military, and industrial applications, the shock wave in a self-gravitating mixture of van der Waals gas and a pseudo-fluid of inert solid particles in a rotating medium, is not well understood. In the present paper, the strong exponential shock wave propagation in a self-gravitating mixture of non-ideal gas and a pseudo-fluid of small solid particles is modelled for unsteady adiabatic and isothermal flows in a rotating medium. In our model, the solid particles are considered as chemically inert pseudo-fluid, and the equilibrium flow conditions hold in the entire flow field region. The similarity solutions are derived for isothermal and adiabatic flows. The vorticity vector components, and isothermal and adiabatic compressibility's are also taken into account. It is shown that the zero-temperature gradient supposition brings the reflective changes in pressure, axial vorticity vector, density, and compressibility distributions in contrast to the adiabatic flow. The shock strength decreases, and the compressibility increases due to the zero-temperature gradient consideration. Also, the effects of the problem parameters on shock waves and the distributions of the flow variables velocity, density, etc., are discussed in detail. It is remarkable to note that due to the consideration of a self-gravitating mixture or with an increase in the ratio of the density of solid particles to the initial density of the gas, the shock strength increases; whereas due to the consideration of non-idealness of the gas or rotating medium the shock strength decreases.

Comparison between Density and Velocity Fields in Burst Modulation of a Dielectric-Barrier-Discharge Plasma Actuator

The flow field produced by a dielectric-barrier-discharge plasma actuator using burst modulation was experimentally investigated in quiescent air from two viewpoints: density and vorticity fields. A wide range of burst signal parameters were evaluated using particle-image velocimetry and background-oriented schlieren measurements. Four types of flow-field patterns were found: Type 1 was a wall jet, similar to continuous operation; Type 2 was a periodical, independent vortex moving along the wall surface; Types 3 and 4 demonstrated a feature wherein the periodic shedding of the vortex pair (primary and secondary vortices) occurred while moving over the surface. While Types 3 and 4 demonstrated a shared feature, they had different density and vorticity structures. The change of the flow-field pattern from Type 1 to Type 4 was triggered by a lower burst frequency and ratio, as well as a higher base frequency. In addition, the vorticity strength and density were strongly negatively correlated and depended on the rate of power consumption to generate one vortex.

A topological realization of spin polarization through vortex formation in collisions of Bose–Einstein condensates

The global spin polarization of hadrons in heavy ion collisions has been measured in the solenoidal tracker at relativistic heavy ion collider experiments, which opens up a new window in the study of the hottest, least viscous, and most vortical fluid that has ever been produced in the laboratory. We present a different approach to spin polarization from conventional ones: a topological realization of spin polarization through quantum vortex formation in collisions of Bose–Einstein condensates. This approach is based on the observation that the vortex is a topological excitation in a superfluid in the presence of local orbital angular momentum and is an analog of spin degrees of freedom. The formation processes of vortices and vortex–antivortex pairs are investigated by solving the Gross–Pitaevskii equation with a large-scale parallel algorithm on a graphics processing unit to very high precision. In a rotating environment, the primary vortex with winding number one is stable against perturbation, which has minimal energy and fixed orbital angular momentum (OAM), but the vortices with larger winding numbers are unstable and will decay into primary vortices through a redistribution of the energy and vorticity. The injection of OAM can also be realized in non-central collisions of self-interacting condensates, part of the OAM of the initial state will induce the formation of vortices through concentration of energy and vorticity density around topological defects. Different from a hydrodynamical description, the interference of the wave function plays an important role in the transport of energy and vorticity, reflecting the quantum nature of the vortex formation process. The study of the vortex formation may shed light on the nature of particle spin and spin–orbit couplings in strong interaction matter produced in heavy-ion collisions.

Sub-grid-scale model for studying Hall effects on macroscopic aspects of magnetohydrodynamic turbulence

A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful since this term often influences not only sub-ion-scales but also macroscopic scales. Our new sub-ion-scale sub-grid-scale model for large eddy simulations of Hall magnetohydrodynamic turbulence is developed in order to overcome the difficulties. Large eddy simulations by the use of the new model successfully reproduce statistical signatures such as the energies and probability density functions of the vorticity and current density, keeping some signatures intrinsic to Hall magnetohydrodynamic turbulence. Our new sub-grid-scale model enables numerical simulations of homogeneous and isotropic Hall magnetohydrodynamic turbulence with a small computational cost, improving the effective resolution of an LES from that carried out with earlier models, and retaining the ion-electron separation effects by the Hall term in the grid scales.

Vortex dynamics on a Möbius strip

We consider the dynamics of a two-dimensional incompressible perfect fluid on a Möbius strip embedded in $\mathbb {R}^{3}$ . The vorticity–stream function formulation of the Euler equations is derived from an exterior-calculus form of the momentum equation. The non-orientability of the Möbius strip and the distinction between forms and pseudo-forms this introduces lead to unusual properties: a boundary condition is provided by the conservation of circulation along the single boundary of the strip, and there is no integral conservation for the vorticity density or for any odd function thereof. A finite-difference numerical implementation is used to illustrate the Möbius-strip realisation of familiar phenomena: translation of vortices along boundaries, shear instability and decaying turbulence.

Self-intersecting Interfaces for Stationary Solutions of the Two-Fluid Euler Equations

We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly with a small gravity constant, that feature a splash singularity. More precisely, in the solutions we construct the interface is a $$\mathcal {C}^{2,\alpha }$$ smooth curve that intersects itself at one point, and the vorticity density on the interface is of class $$\mathcal {C}^\alpha $$ . The proof consists in perturbing Crapper’s family of formal stationary solutions with one fluid, so the crux is to introduce a small but positive second-fluid density. To do so, we use a novel set of weighted estimates for self-intersecting interfaces that squeeze an incompressible fluid. These estimates will also be applied to interface evolution problems in a forthcoming paper.

Numerical Analysis of Flows of Stratified and Homogeneous Fluids near Horizontal and Inclined Plates

The structure and dynamics of flows near a horizontal and inclined plates in stratified and homogeneous fluids in a transient vortex regime are studied for various angles of inclination of the plate to the horizon and various geometrical modifications of its front and rear edges. This study is based on high-precision numerical modeling of the fundamental system of equations, which allows calculations of both stratified and homogeneous viscous liquids in a unified formulation. Instantaneous patterns of the vorticity fields, pressure gradient, and density, as well as the values of forces and moments acting on the surface of the plate are analyzed at different inclination angles, curvature radii of the front edge of the plate, and sharpness coefficients of the rear part. The pressure field consists of multi-scale spotted structures with a negative values of pressure, corresponding to the positions of vortical elements of the flow, whose spatial and time scales, geometric features, manifestation level, and dissipation rate essentially depend on the angle of inclination of the plate to the horizon, geometrical modification of its edges, and the type of the fluid. Special attention is paid to the fine structure of the flow near the front edge of the plate, which is the area with the most diverse scales of the flow, in which both large-scale and small-scale vertical structures form and actively interact.

Generation of bulk vorticity and current density in current-vortex sheet models

Matsuoka et al. [1] present a set of equations governing the evolution of two-dimensional MHD flows using current-vortex sheets. In the resulting model the vorticity ω and current density j are zero except on the current-vortex sheets. We show that this is not true in general and that the term Δ(B × u) in the evolution equation for j does not vanish, leading to the generation of j and ω in the bulk. This means that the evolution of the system is not governed solely by the dynamics of quantities on the current-vortex sheets. A perturbative solution is derived that shows this explicitly.

Impact of Surface Potential Vorticity Density Forcing over the Tibetan Plateau on the South China Extreme Precipitation in January 2008. Part I: Data Analysis

The external source/sink of potential vorticity (PV) is the original driving force for the atmospheric circulation. The relationship between surface PV generation and surface PV density forcing is discussed in detail in this paper. Moreover, a case study of the extreme winter freezing rain/snow storm over South China in January 2008 is performed, and the surface PV density forcing over the eastern flank of the Tibetan Plateau (TP) has been found to significantly affect the precipitation over South China in this case. The TP generated PV propagated eastward in the middle troposphere. The associated zonal advection of positive absolute vorticity resulted in the increasing of cyclo-nic relative vorticity in the downstream region of the TP. Ascending air and convergence in the lower troposphere developed, which gave rise to the development of the southerly wind. This favored the increasing of negative meridio-nal absolute vorticity advection in the lower troposphere, which provided a large-scale circulation background conducive to ascending motion such that the absolute vorticity advection increased with height. Consequently, the ascending air further strengthened the southerly wind and the vertical gradient of absolute vorticity advection between the lower and middle troposphere in turn. Under such a situation, the enhanced ascending, together with the moist air transported by the southerly wind, formed the extreme winter precipitation in January 2008 over South China.

Impact of Surface Potential Vorticity Density Forcing over the Tibetan Plateau on the South China Extreme Precipitation in January 2008. Part ll: Numerical Simulation

The surface air convergence on the eastern flank of the Tibetan Plateau (TP) can increase the in situ surface potential vorticity density (PVD). Since the elevated TP intersects with the isentropic surfaces in the lower troposphere, the increased PVD on the eastern flank of TP thus forms a PVD forcing to the intersected isentropic surface in the boundary layer. The influence of surface PVD forcing over the TP on the extreme freezing rain/snow over South China in January 2008 is investigated by using numerical experiments based on the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL). Compared with observations, the simulation results show that, by using a nudging method for assimilating observation data in the initial flow, this model can reasonably reproduce the distribution of precipitation, atmospheric circulation, and PVD propagation over and downstream of the TP during the extreme winter precipitation period. In order to investigate the impact of the increased surface PVD over the TP on the extreme precipitation in South China, a sensitivity experiment with surface PVD reduced over the TP region was performed. Compared with the control experiment, it is found that the precipitation in the TP downstream area, especially in Southeast China, is reduced. The rainband from Guangxi Region to Shandong Province has almost disappeared. In the lower troposphere, the increase of surface PVD over the TP region has generated an anomalous cyclonic circulation over southern China, which plays an important role in increasing southerly wind and the water vapor transport in this area; it also increases the northward negative absolute vorticity advection. In the upper troposphere, the surface PVD generated in eastern TP propagates on isentropic surface along westerly wind and results in positive absolute vorticity advection in the downstream areas. Consequently, due to the development of both ascending motion and water vapor transport in the downstream place of the TP, extremely heavy precipitation occurs over southern China. Thereby, a new mechanism concerning the influence of the increased surface PVD over the eastern TP slopes on the extreme weather event occurring over southern China is revealed.

Approaching Earth’s core conditions in high-resolution geodynamo simulations

SUMMARY The geodynamo features a broad separation between the large scale at which Earth’s magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer core. Here, the properties of this scale separation are analysed using high-resolution numerical simulations that approach closer to Earth’s core conditions than earlier models. The new simulations are obtained by increasing the resolution and gradually relaxing the hyperdiffusive approximation of previously published low-resolution cases. This upsizing process does not perturb the previously obtained large-scale, leading-order quasi-geostrophic (QG) and first-order magneto-Archimedes-Coriolis (MAC) force balances. As a result, upsizing causes only weak transients typically lasting a fraction of a convective overturn time, thereby demonstrating the efficiency of this approach to reach extreme conditions at reduced computational cost. As Earth’s core conditions are approached in the upsized simulations, Ohmic losses dissipate up to 97 per cent of the injected convective power. Kinetic energy spectra feature a gradually broadening self-similar, power-law spectral range extending over more than a decade in length scale. In this range, the spectral energy density profile of vorticity is shown to be approximately flat between the large scale at which the magnetic field draws its energy from convection through the QG-MAC force balance and the small scale at which this energy is dissipated. The resulting velocity and density anomaly planforms in the physical space consist in large-scale columnar sheets and plumes, respectively, co-existing with small-scale vorticity filaments and density anomaly ramifications. In contrast, magnetic field planforms keep their large-scale structure after upsizing. The small-scale vorticity filaments are aligned with the large-scale magnetic field lines, thereby minimizing the dynamical influence of the Lorentz force. The diagnostic outputs of the upsized simulations are more consistent with the asymptotic QG-MAC theory than those of the low-resolution cases that they originate from, but still feature small residual deviations that may call for further theoretical refinements to account for the structuring constraints of the magnetic field on the flow.

Local approach to the study of energy transfers in incompressible magnetohydrodynamic turbulence.

We present a local approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter ℓ. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which provides a local form of Politano and Pouquet's 4/3 law, without any assumption of homogeneity or isotropy. Our approach is exact and nonrandom, and we show its connection to the usual statistical results of turbulence. Its implementation on data obtained via a three-dimensional direct numerical simulation of the forced incompressible MHD equations from the John Hopkins turbulence database constitutes the main part of our study. First, we show that the local Kármán-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers are studied next, their means and standard deviations being maximum at inertial scales and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, which can be observed over the whole available range of scales. As ℓ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Finally, we highlight their quasi-one-dimensional (filamentlike) or quasi-two-dimensional (sheetlike or ribbonlike) nature and show that they appear in areas of strong vorticity or electric current density.

Influence of Transonic Flutter on the Conceptual Design of Next-Generation Transport Aircraft

Transonic aeroelasticity is an important consideration in the conceptual design of next-generation aircraft configurations. This paper develops a low-order physics-based flutter model for swept high-aspect-ratio wings. The approach builds upon a previously developed flutter model that uses the flowfield’s lowest moments of vorticity and volume-source density perturbations as its states. The contribution of this paper is a new formulation of the model for swept high-aspect-ratio wings. The aerodynamic model is calibrated using offline two-dimensional unsteady transonic computational-fluid-dynamics simulations. Combining that aerodynamic model with a beam model results in a low-dimensional overall aeroelastic system. The low computational cost of the model permits its incorporation in a conceptual design tool for next-generation transport aircraft. The model’s capabilities are demonstrated by finding transonic flutter boundaries for different clamped-wing configurations and investigating the influence of transonic flutter on the planform design of next-generation transport aircraft.

Mesoscale-submesoscale interactions in the Gulf of Mexico: From oil dispersion to climate

In the ocean, forcing acts at planetary scales and dissipation at the microscales. In between are the mesoscales, in a lot of respects akin to nearly two-dimensional, quasi-geostrophically, balanced turbulence. Eddies and fronts, extending from ten to hundred kilometers, represent their best-known dynamical expression. At the ocean boundary layers, near the surface and at the bottom, smaller ageostrophic, coherent flow structures may appear in the form of vorticity filaments, density fronts or coherent vortices, with typical scales of hundreds of meters to few kilometers and a lifespan of few days. These so-called submesoscale circulations provide a pathway for energy transfer towards smaller scales, contribute to the global overturning budget, and impact substantially lateral and diapycnal mixing. They develop in presence of density gradients in the turbulent boundary layers, and their statistics are not well known in a global sense, but are likely to change in the future due to projected changes in near surface stratification.This perspective presents an overview of recent studies illustrating physical and biogeochemical interactions across mesoscale and submesoscale flows focusing on the Gulf of Mexico, where much modeling and observational work has been taking place following the 2010 Deepwater Horizon blow-out. The physical interpretation of several biogeochemical data-sets illustrates how mesoscale and submesoscale circulations impact the dispersion of biologically and climatically relevant tracers, from coral larvae to carbon.The ultimate goal is present the reader with examples of spatial and temporal multiscale interactions in a complex, chaotic system such as the ocean that is key to the future evolution of the climate system with its enormous storage capacity of heat and carbon.

A local tensor that unifies kinetic energy density and vorticity in density functional theory

We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-generalized gradient approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory. Both types of functionals can thus be subsumed as special cases of a novel functional form that is naturally placed on the third rung of Jacob's ladder. Moreover, the kinetic energy tensor is related to the exchange hole curvature, is gauge invariant, and has very clearcut N-representability conditions. The latter conditions enable the definition of an effective number of non-negligible orbitals. Whereas quantities such as the electron localization function can discriminate effective one-orbital regions from other regions, the present kinetic energy tensor can discriminate between one-, two-, three-, and four-or-more orbital regions.

Relative equilibria of point vortices and linear vortex sheets

A new exact method is presented for obtaining uniformly rotating distributions of vorticity in a two dimensional ideal fluid. The vorticity is confined to the union of a straight line and a finite collection of points; i.e., the distribution is a collection of point vortices together with a number of vortex sheets lying on the common line. The vorticity density of the vortex sheets and the velocity field of the fluid are expressed in terms of a rational function in which the point vortex positions and strengths appear as parameters. For many values of these parameters, the vortex sheet portion of the distribution is not unique, and there is a continuous family of vortex sheets which combine with the point vortices to form relative equilibria. Several examples are worked out in detail.

Numerical investigation of dual-fuel injection timing on air-fuel mixing and combustion process in a novel natural gas-diesel rotary engine

This study aimed at further improving the combustion efficiency of the diesel rotary engine (DRE), and in this regard a novel natural gas-diesel rotary engine (NG-DRE) was numerically studied. Based on the experimental validated computational fluid dynamics (CFD) model, a 3D-dynamic numerical study of the NG-DRE was carried out by adopting NG port injection plus diesel direct injection mode. The influence of natural gas injection timing (NGIT) and diesel injection timing (DIT) on air-fuel mixing, combustion and emission characteristics were explored. Simulation results showed that NG-DRE performance was better than DRE. During the entire air-fuel mixing process, NG movement was easily affected by the vorticity density due to its good diffusion characteristics, however its influence on diesel movement was relatively minimal. At assisted ignition timing, NG concentrated at the rear of the combustion chamber, and diesel concentrated at the front and middle of the combustion chamber. Delaying NGIT and DIT, the mixture became more concentrated due to a shorter mixing time. Moreover, the delayed NGIT and DIT resulted in improvement of the pressure and combustion rate, while for a further delayed DIT the pressure was decreased due to the pressure negative work. Considering the engine power and emission performance, for dual-fuel injection schemes, 340°CA BTDC and 70°CA BTDC were the preferred application schemes for NG and diesel respectively. Their peak combustion pressure (Pmax) increased by 16.34% and 27.38% respectively, but due to the richer mixture, soot value increased by 0.023% and 0.054% and CO (carbon monoxide) value also increased by 0.026% and 0.039% respectively.