Initial Vortex Research Articles

Transient growth in Poiseuille-Rayleigh-Bénard flows of binary fluids with Soret effect

The transient growth due to non-normality is investigated for the Poiseuille-Rayleigh-Benard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = −0.1, it is found that a large transient growth can be obtained by the non-normal interaction of the two least-stable-modes, i.e., the upstream and downstream modes, which determine the linear critical boundary curves for small Reynolds numbers. The transient growth is so strong that the optimal energy amplification factor G(t) is up to 102 ~ 103. While for positive separation factors such as ψ = 0.1, the transient growth is weak with the order O(1) of the amplification factor, which can even be computed by the least-stable-mode. However, for both cases, the least-stable-mode can govern the long-term behavior of the amplification factor for large time. The results also show that large Reynolds numbers have stabilization effects for the maximum amplification within moderate wave number regions. Meanwhile, much small negative or large positive separation factors and large Rayleigh numbers can enlarge the maximum transient growth of the pure streamwise disturbance with the wavenumber α = 3.14. Moreover, the initial and evolutionary two-dimensional spatial patterns of the large transient growth for the pure streamwise disturbance are exhibited with a plot of the velocity vector, spanwise vorticity, temperature, and concentration field. The initial three-layer cell vorticity structure is revealed. When the amplification factor reaches the maximum Gmax, it develops into one cell structure with large amplification for the vorticity strength.

Instability and electrical response of small laminar coflow diffusion flames under AC electric fields: Toroidal vortex formation and oscillating and spinning flames

Dynamical and electrical responses of a small coflow diffusion flame were investigated by applying a high-voltage alternating current (AC), to a fuel jet nozzle. High-speed imaging and electrical diagnostics were adopted to capture flame dynamics and electrical signals, such as voltage (Vac), frequency (fac) and current (Iac). In the Vac–fac domain of 0–5kV and 0–5kHz, AC-driven instabilities, resulting in various flame modes such as an oscillation, pinch-off and spinning of flames were identified. Characteristic frequency of each mode was determined and a visualization of near-nozzle flow structures suggested a close causality of initial counter-rotating vortices (inner and outer toroidal vortices – ITV and OTV), to the other observed flame. An axisymmetric ITV shedding was identified within oscillating and pinch-off modes, while asymmetric ITV shedding was identified with the spinning mode. Integrated electric power over several AC periods correlated well with variation in the flame surface area for these instabilities, demonstrating that measured electric power is a potential indicator of combustion instabilities in electric-field-assisted combustion.

Effect of ring size on the side force over ogive-cylinder body at subsonic speed

ABSTRACTExperiments and computations have been made to obtain the details of the flow field over a slender body at high angles of attack at a freestream velocity of 17 m/s corresponding to a Reynolds number of 2.9×104based on the base diameter. Experiments indicated that the existence of side force at higher angles of attack is mainly due to the presence of asymmetric vortices in the leeward side. A rectangular cross-section circular ring placed at an axial distance of 3.5 times the base diameter reduced the side force at all the angles of attack. Investigations were made to obtain the effect of the height of the ring at an angle-of-attack of 50° where the side force experienced is relatively large. A ring placed at a distance of 3.5 times the base diameter alters the initial vortices and hence helps in substantial reduction of the side force. Studies with rings of different heights indicate that a ring having a height of 3% of the local diameter reduced the side force at almost all the angles of attack for the present flow conditions and provided the least disturbance to the lift and drag of the body.

Self-similar roll-up of a vortex sheet driven by a shear flow: Hyperbolic double spiral

In this paper, we consider the roll-up of an infinite vortex sheet and investigate its self-similar behavior. We address the question of whether the unsteady double spiral produced by the curvature singularity in finite time exhibits self-similar behavior. We find a self-similar solution of the double-spiral vortex sheet, which in fact, is a hyperbolic spiral. The radius of the spiral asymptotically grows with time and is proportional to the inverse of the angle from the spiral center. The curvature singularity plays the role of triggering spiral formation, but the source of vorticity for forming the spiral is the initial vorticity of the sheet. We show analytically that the self-similar solution satisfies the Birkhoff-Rott equation asymptotically. Numerical validation is also given by applying the blob-regularization model to the vortex sheet with a periodic perturbation. We examine various asymptotic relations among primitive variables for the spiral turns and find agreement of numerical results of the inner turns of the vortex sheet with the analytic solution. Our study clarifies contrasting results on the existence of the self-similar double-spiral of a large structure in the previous studies. Our solution also suggests the possibility of bifurcation of the self-similar solution of the double-spiral as the sheet strength varies.

Distributional Enstrophy Dissipation Via the Collapse of Three Point Vortices

Dissipation of enstrophy in 2D incompressible flows in the zero viscous limit is considered to play a significant role in the emergence of the inertial range corresponding to the forward enstrophy cascade in the energy spectrum of 2D turbulent flows. However, since smooth solutions of the 2D incompressible Euler equations conserve the enstrophy, we need to consider non-smooth inviscid and incompressible flows so that the enstrophy dissipates. Moreover, it is physically uncertain what kind of a flow evolution gives rise to such an anomalous enstrophy dissipation. In this paper, in order to acquire an insight about the singular phenomenon mathematically as well as physically, we consider a dispersive regularization of the 2D Euler equations, known as the Euler-\(\alpha \) equations, for the initial vorticity distributions whose support consists of three points, i.e., three \(\alpha \)-point vortices, and take the \(\alpha \rightarrow 0\) limit of its global solutions. We prove with mathematical rigor that, under a certain condition on their vortex strengths, the limit solution becomes a self-similar evolution collapsing to a point followed by the expansion from the collapse point to infinity for a wide range of initial configurations of point vortices. We also find that the enstrophy always dissipates in the sense of distributions at the collapse time. This indicates that the triple collapse is a mechanism for the anomalous enstrophy dissipation in non-smooth inviscid and incompressible flows. Furthermore, it is an interesting example elucidating the emergence of the irreversibility of time in a Hamiltonian dynamical system.

Analytical solution for multi-singular vortex Gaussian beams: the mathematical theory of scattering modes

We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre–Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre–Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.

Wavelet characterization of 2D turbulence and intermittency in magnetized electron plasmas

A study of the free relaxation of turbulence in a two-dimensional (2D) flow is presented, with a focus on the role of the initial vorticity conditions. Exploiting a well-known analogy with 2D inviscid incompressible fluids, the system investigated here is a magnetized pure electron plasma. The dynamics of this system are simulated by means of a 2D particle-in-cell code, starting from different spiral density (vorticity) distributions.A wavelet multiresolution analysis is adopted, which allows the coherent and incoherent parts of the flow to be separated. Comparison of the turbulent evolution in the different cases is based on the investigation of the time evolution of statistical properties, including the probability distribution functions and structure functions of the vorticity increments. It is also based on an analysis of the enstrophy evolution and its spectrum for the two components.In particular, while the statistical features assess the degree of flow intermittency, spectral analysis allows us not only to estimate the time required to reach a state of fully developed turbulence, but also estimate its dependence on the thickness of the initial spiral density distribution, accurately tracking the dynamics of both the coherent structures and the turbulent background. The results are compared with those relevant to annular initial vorticity distributions (Chen et al 2015 J. Plasma Phys. 81 495810511).

Wind Impact on Single Vortices and Counterrotating Vortex Pairs in Ground Proximity

Wall-resolved large eddy simulations are employed to investigate the behaviour of wake vortices and single vortices in ground proximity at a variety of wind conditions. The six considered strengths of wind, ranging between 0.5 and 4 times the initial wake vortex descent speed, w 0, include practically and theoretically significant wind speeds. A crosswind of 0.5 w 0 may lead to windward stall posing a potential hazard to subsequently landing aircraft, whereas theoretical considerations predict that at 4 w 0 the rebound of the luff vortex is completely suppressed. The same range of wind speeds is also used to investigate the effects of headwind and diagonal wind in order to discriminate between effects of environmental turbulence increasing with wind speed and the direction of the wind shear. The study has been complemented by a number of single vortex computations in order to differentiate between effects related to the mutual interaction of the vortex pair and the individual vortices with the turbulent boundary layer flow. It is shown that vortex ascent, descent, rebound and decay characteristics are controlled by (i) the interaction of the vortices with secondary vorticity detaching from the ground, (ii) the redistribution of vorticity of the boundary layer which is altering the path of the primary vortices by mutual velocity induction, and (iii) the interaction of the vortices with the environmental turbulence.

On the Existence for the Free Interface 2D Euler Equation with a Localized Vorticity Condition

We prove a local-in-time existence of solutions result for the two dimensional incompressible Euler equations with a moving boundary, with no surface tension, under the Rayleigh---Taylor stability condition. The main feature of the result is a local regularity assumption on the initial vorticity, namely $$H^{1.5+\delta }$$H1.5+� Sobolev regularity in the vicinity of the moving interface in addition to the global regularity assumption on the initial fluid velocity in the $$H^{2+\delta }$$H2+� space. We use a special change of variables and derive a priori estimates, establishing the local-in-time existence in $$H^{2+\delta }$$H2+�. The assumptions on the initial data constitute the minimal set of assumptions for the existence of solutions to the rotational flow problem to be established in 2D.

Impact of Satellite Radiance Data on Simulations of Bay of Bengal Tropical Cyclones Using the WRF-3DVAR Modeling System

This study attempts to evaluate whether assimilating radiance observations in the Weather Research and Forecasting (WRF) model could improve track, intensity, and precipitation forecasts of tropical cyclones (TCs) that occurred over the Bay of Bengal. The bias correction coefficients obtained from offline statistics, along with the quality control for radiances, were computed in the variational assimilation system. For this study, three numerical experiments named CNTL (no assimilation), GTS (with Global Telecommunication System observations), and RAD (radiance data along with GTS observations) were carried out with ten different model initial conditions for two TCs. The averaged root-mean-square errors of the analysis were relatively lower in the RAD experiments in comparison to the GTS experiments for all assimilation cycles of the meteorological variables. The mean initial position errors of TCs were reduced by 30%–47% in the RAD runs over the other runs. The results indicate that the assimilation of radiance data has a positive impact on the prediction of track, intensity, thermodynamic structures, and reflectivity associated with the storms. Improvements in mean landfall position errors were shown to range from 40% to 70% in the RAD experiments as compared to the CNTL and GTS simulations. This is because the RAD analyses are able to successfully reproduce the initial vortex and vertical structures as well as the prominent synoptic features associated with TC storms; therefore, the performance of the WRF modeling system is enhanced for simulations of track, structures, and intensity of TCs.

Gas dynamics and flow characteristics of highly turbulent under-expanded hydrogen and methane jets under various nozzle pressure ratios and ambient pressures

The current study used large eddy simulations to investigate the sonic and mixing characteristics of turbulent under-expanded hydrogen and methane jets with various nozzle pressure ratios issued into various ambient pressures including elevated conditions relevant to applications in direct injection gaseous-fuelled internal combustion engines. Due to the relatively low density of most gaseous fuels such as hydrogen and methane, DI requires high injection pressures to achieve suitable mass flow rates for fast in-cylinder fuel delivery and rapid fuel-air mixing. Such pressures typically form an under-expanded fuel jet past the nozzle exit. Test cases of hydrogen injection with nozzle pressure ratio (NPR) of 10 issued into quiescent air with pressure P∞ ≈ 1, 5 and 10 bar were simulated. Direct comparison between hydrogen and methane jets with NPR = 8.5 and P∞ ≈ 1 was also made. The effect of ambient pressure on features of transient development of the near-nozzle shock structure and tip vortices (vortex ring) was investigated. It was observed that at constant NPR, higher ambient pressure resulted in slightly faster formation of the Mach reflection and shorter Mach disk settlement time. Different mechanisms were observed between hydrogen and methane with regards to transient formation of their initial tip vortex rings. It was found that the initial transient tip vortices of hydrogen jets may also contribute to the flow instabilities at the boundary of the intercepting shock and, unlike for methane, promote fuel-air mixing before the Mach reflection. It was also shown that the near-nozzle shock structure was only affected by NPR regardless of the ambient pressure. Furthermore, no flow recirculation zone was found just downstream of the Mach disk, a finding comparable to all previous experimental investigations. Also, it was observed that a locally richer mixture was created for jets with higher NPR or with higher ambient pressure at constant NPR. Based on the results of the current study, correlations were proposed for the shock cell spacing and jet tip penetration of highly under-expanded jets issued from millimetre-size circular nozzles.

Algebraic spiral solutions of the 2d incompressible Euler equations

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The regions of positive and negative vorticity form algebraic spirals.

Remarks on the Cauchy problem for the axisymmetric Navier-Stokes equations

Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity ω θ is integrable with respect to the two-dimensional measure dr dz, where (r, θ, z) denote the cylindrical coordinates in R 3 , we show the existence of a unique global solution, which converges to zero in L 1 norm as t → ∞. The proof of local well-posedness follows exactly the same lines as in the two-dimensional case, and our approach emphasizes the similarity between both situations. The solutions we construct have infinite energy in general, so that energy dissipation cannot be invoked to control the long-time behavior. We also treat the more general case where the initial vorticity is a finite measure whose atomic part is small enough compared to viscosity. Such data include point masses, which correspond to vortex filaments in the three-dimensional picture.

Development and Nondevelopment of Binary Mesoscale Vortices into Tropical Cyclones in Idealized Numerical Experiments

Abstract The evolution of two symmetric midlevel mesoscale vortices situated above a warm ocean is examined with a basic cloud-resolving model. Idealized numerical experiments provide insight into how the evolution may vary with the initial vortex separation distance D and other parameters that influence the time scale for an isolated vortex to begin rapid intensification. The latter parameters include the ambient middle-tropospheric relative humidity (RH) and the initial midlevel wind speed of each vortex. At relatively low RH, there exists an interval of D where binary midlevel vortex interaction prevents tropical cyclone formation. While tropical cyclones generally develop at high RH, similar values of D can delay the process if the vortices are initially weak. Prevention or inhibition of tropical cyclone formation occurs in association with the outward expulsion of lower-tropospheric potential vorticity anomalies as the two vortices merge in the middle troposphere. It is proposed that the primary mechanism for midlevel merger and low-level potential vorticity expulsion involves the excitation of rotating misalignments in each vortex. An analog model based on this premise provides a good approximation for the range of D in which the merger–expulsion scenario occurs. Relatively strong vortices in high-RH environments promptly develop vigorous convection and begin rapid intensification. Differences between the interaction of such diabatic vortices and their adiabatic counterparts are briefly illustrated. In systems that generate tropical cyclones, the mature vortex properties (size and strength) are found to vary significantly with D.

Real-time prediction of movement, intensity and storm surge of very severe cyclonic storm Hudhud over Bay of Bengal using high-resolution dynamical model

Tropical cyclone (TC) ‘Hudhud’ (October 2014) over the Bay of Bengal was the first TC to strike the Port city, Vishakhapatnam, with intensity of 100 knots (180 km h−1) since 1891. The advanced research weather research and forecasting (ARW) model with 9-km grid spacing is coupled offline with dynamical storm surge model and is used for real-time prediction of Hudhud. In the current study, the successful story of prediction of Hudhud is substantiated. The ARW model was able to predict the genesis in advance of 3 days with reasonable accuracy in position and strength. The mean initial vortex position and intensity errors are 46 km and 6 knots, respectively. The model predictions showed that Hudhud would intensify to a very severe cyclonic storm (max. sustained wind speed ~97 knots from all the experiments) in advance of ~4 days which is consistent with the observation. The mean absolute intensity forecast error is significantly less (18 knots) up to 96-h forecast. The model could reproduce the upper-level warming of ~7.5 °C at ~50 km radial distance similar to that of satellite observation. The ARW model showed appreciable performance in track prediction (with errors ≤150 km up to 96-h forecast). On the landfall day, the rainfall patterns are realistic and consistent with IMD rainfall observation. The dynamical storm surge model, forced with the outputs of the ARW model, was able to predict realistic surge ranging between 1.4–2.2 m in 24- to 96-h forecast lengths. This study highlights the importance and need of high-resolution numerical models for operational TC and associated surge forecast over the region.

The growth characteristics of a starting axisymmetric turbulent jet

This paper characterizes the growth of the initial unexcited vortical structure produced by a rapidly started axisymmetric turbulent air jet. Although previous studies have been performed primarily with water, the flows were artificially excited in order to increase the size of the vortical structures which ultimately allows for easier capture. A major finding of these studies has indicated that the leading vortex eventually ‘pinches off’ from the trailing fluid. In order to more accurately simulate wingtip vortices, smoke visualization was used on a continuous, axisymmetric turbulent jet at a Reynolds number based on diameter of 7500. The growth of the initial vortical structure diameter and overall vortical growth were measured and compared to the large-scale structures that develop in the flow trailing these initial vortical structures. The results show that when the flow is unexcited, the initial vortex does not completely ‘pinch off’. Further, the initial vortical structure reaches a size over twice that of the trailing large-scale structures and has a spread rate 1.7 times that of the trailing large-scale structures. In addition, the initial structure was observed to survive approximately 2 pipe diameters further downstream before breaking down.

Mechanism of Side Force Generation and Its Alleviation over a Slender Body

Experiments and computational studies were made on a slender body having a slender ratio of 16 at a freestream velocity of and Reynolds number of based on the base diameter so as to obtain the details of the flowfield that leads to the generation of side force at large angles of attack. It is observed that the large side force experienced at a high angle of attack of 50 deg is due to the presence of asymmetric vortices, which change its direction in the downstream. The vortices lift off from the surface due to the adverse pressure gradient. The major contribution of side force is mainly from an initial length limited to six times the base diameter, suggesting that efforts to reduce the side force by introducing any control method would be effective if used in the initial part of the body. Use of a circular trip having 5% height of the base diameter placed at a distance of 3.5 times the base diameter modifies the initial vortices and hence the local side force distribution over the body, which is mainly responsible for substantial reduction in the side force.

A vibration analysis used in the methods of detecting unsteady operational modes of axial compressors

We have grounded the necessity to devise a system of a compressor surge prevention at the stage of its inception and analysed possible informative parameters characterizing an unsteady flow in a compressor and the possibility of a surge. We have presented the results of numerical simulation of the flow and dynamics of the loss of gas-dynamic stability in the inter-blade channel of the axial compressor impeller.It has been determined that the process of the loss of dynamic stability begins with the appearance of the initial vortex zone on the back of the blade profile. We have carried out an experimental research with measuring the pressure pulsation and vibration, revealed that the levels of pressure fluctuations on the impeller with a frequency of rotor blades can signal of the compressor stall, and pointed out the problems of technical use of this criterion. We have experimentally researched the connection of unstable flows in the flow part and vibration levels in the compressor housing. It is proved that the harmonics of the rotating stall that is determined by the level of vibrations is stable and significantly stands out from the background noise, so it can be used to diagnose the rotating stall as a signal of the surge.The paper contains an experimentally verified dependence for determining the frequency of the rotating stall. We have studied the possibility of using the median and band filters in processing the vibrations and suggested an algorithm for identifying a pre-surge compressor state by the rate of vibrations in the compressor housing, which is aimed at devising of automatic warning systems for the surge prevention at the stage of its inception. Devising a system of an anti-surge protection with the use of the vibration signal would increase the reliability of its work and raise the operational reliability of a gas turbine engine by eliminating false positives.

Tomographic PIV measurements of a regenerating hairpin vortex

The three-dimensional formation and regeneration of a hairpin vortex in a laminar boundary layer is studied in a free-surface water channel. The vortex is generated by fluid injection through a narrow slot into a laminar boundary layer $$(Re_{\delta ^*} = 485)$$ and recorded with tomographic particle image velocimetry. The swirling strength based on the $$\lambda _2$$ criterion shows that the hairpin initially forms at the upstream edge of the elongated ring vortex produced by the injection. The elongated ring vortex decays while the hairpin vortex strengthens. Because the hairpin vortex is of sufficient strength, it forms a kink in the legs as a result of inviscid induction. A bridging structure forms between the legs initially upstream of the kink. As this structure dissipates, another bridging structure forms downstream of the kink and closes the vortex loop between the legs. This pinches off the original hairpin head such that two distinct vortices result. The formation of the secondary hairpin head does not appear to be preceded by a reduction in the spanwise gap between the legs or significant change in height above the wall as has been seen when exposed to a mean turbulent profile. Instead, the formation is preceded by the stretching of the hairpin legs downstream of the kink, exposes the ejected fluid between the legs to boundary layer flow producing conditions similar to those that formed the initial hairpin vortex.

Lagrangian solutions to the 2D Euler system with [formula omitted] vorticity and infinite energy

We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated to vector fields with gradient given by a singular integral in order to define Lagrangian solutions, for which the vorticity is transported by the flow. We prove strong stability of these solutions via strong convergence of the flow, under the only assumption of L1 weak convergence of the initial vorticity. The existence of Lagrangian solutions to the Euler system follows for arbitrary L1 vorticity. Relations with previously known notions of solutions are established.