Nonlinear Vortex Research Articles

Rotor-Fuselage-Intake Aerodynamics and Icing Using Vortex and Eulerian–Lagrangian Computational Fluid Dynamics Methods

Rotorcraft rotor-fuselage-intake aerodynamics and icing present unique challenges associated with rotor-wake dynamics and the interaction of rotor wake with the fuselage and the intake. The effects of the rotor wake are dominant in low forward flight, and performing high-fidelity simulations of the rotor-fuselage-intake simultaneously is expensive. This study presents a novel hybrid nonlinear vortex–computational fluid dynamics (CFD) approach to rotor-fuselage-intake aerodynamics and icing. The method combines nonlinear vortex–lattice, Lagrangian vortex–particle, and Eulerian CFD methods on airflow and droplet impingement with a PDE-based ice-accretion model. The Lagrangian description of rotor wake preserves the wake structure independently of the Eulerian grid, whereas the Eulerian description of the flowfield naturally computes nonlinear flow phenomena and surface properties. The algorithm allowed the ice accretion to be computed much faster than existing methods. The method was validated by considering airflow, surface pressure, and ice accretion around a model rotorcraft. We investigated ice accretion with strong rotor wakes for different advance ratios and rotor thrust coefficients. We also investigated the effects of the suction of airflow in the intake and the differences between with and without the rotor. It was found that the advance ratio had a dominant effect compared to the rotor thrust coefficient.

A vorticity budget for theoretical and convectively coupled equatorial Rossby waves: Dynamical propagation and growth mechanisms

AbstractConvectively coupled equatorial Rossby waves (CCERWs) are westward‐propagating tropical weather systems that can trigger extreme precipitation and flooding. Here, vorticity budgets are used to determine their dynamical mechanisms of propagation and growth. First, an analytical solution to the vorticity budget of theoretical dry equatorial Rossby waves is presented. Westward propagation arises entirely from the planetary vorticity advection () term, where high‐magnitude planetary vorticity is advected equatorward from higher latitudes to the west of cyclonic perturbations in the Rossby‐wave structure. This is the classical Rossby‐wave propagation mechanism. There is one other non‐zero term in the vorticity budget: the vortex stretching () term has a (weak) eastward propagation tendency, mainly due to the convergence in the meridional wind structure to the east of the cyclonic perturbations. This acts to slow the overall westward propagation down. Both these terms are in quadrature with the vorticity structure and hence the theoretical waves are neutral. A vorticity budget of observed CCERWs is then presented, using reanalysis data. The primary westward propagation mechanism is still the planetary vorticity advection term. However, the convergence centres are now aligned with the cyclonic vorticity centres, rather than a quarter cycle to the east. Hence the vortex stretching () term is now in phase with the vorticity, leading to growth of CCERWs. There is an even stronger growth contribution from the nonlinear vortex stretching term. Horizontal vorticity advection and subgrid‐scale processes both act to damp the CCERW. The total source term is one of westward propagation and growth. This diagnostic vorticity‐budget approach can be applied to inform the assessment of forecast skill and model development.

Nonlinear Vortex Dichroism in Chiral Molecules

AbstractThe recent discovery that linearly polarized light with a helical wavefront can exhibit vortex dichroism (also referred to as helical dichroism) has opened up new horizons in chiroptical spectroscopy with structured chiral light. Recent experiments have now pushed optical activity with vortex beams into the regime of nonlinear optics. Here the theory of two‐photon absorption (TPA) of focused optical vortices by chiral molecules: nonlinear vortex dichroism (NVD) is presented. It is discovered that highly distinct features arise in the case of TPA with focused vortex beams, including the ability to probe chiral molecular structure not accessible to current methods and that the differential rate of TPA is significantly influenced by the orientation of the state of linear polarization. This study provides strong evidence that combining nonlinear optical activity with structured light provides new and improved routes to studying molecular chirality.

The nonlinear behavior of generic tail fins for small wind turbines

This paper describes analysis and measurements of the yaw response of tail fins for small wind turbines. It is based on an extension of unsteady slender body theory (USBT) to cover non-slender fins and high angles of incidence, both of which make the theory nonlinear. We provide three main additions to the substantial literature on linearized USBT for tail fins. First, USBT is extended to high angles by modeling the nonlinear vortex dynamics. Second, the restriction to slender bodies is removed by modeling the chordwise load variation. Third, we consider the effect of time-varying wind speed. The extended theory is compared to wind tunnel measurements of the yaw behavior of delta, elliptical, and rectangular tail fins without a rotor and nacelle. The fins were released from initial yaw angles of −40° and −80°; the latter is of sufficient magnitude to show the importance of the nonlinear yaw dynamics. Generally good agreement was found between the theory and measurements, and the theory was shown to be more accurate than a “polar” or quasi-steady model which uses only the lift and drag of a delta planform. Of the three planforms, the rectangular one showed the lowest accuracy in terms of frequency but the damping was accurately predicted. Overall, the results demonstrate the importance of nonlinearity in the response of a yawing tail fin, particularly for the higher aspect ratio fins at large yaw angles.

Caudal peduncle-inspired two-degree-of-freedom elastic coupling fin propulsion method

Marine animals orchestrate the swimming process through the coordinated interplay of body musculature, the caudal peduncle, and the caudal fin. However, understanding the coordinated action of these components to achieve high propulsive performance remains a significant challenge. The study proposes a self-propulsive physical model with two-degree-of-freedom (DoF) elastic coupling inspired by the caudal peduncle, where the caudal peduncle exhibits spring-like behaviors influencing the tail's motion along heave/pitch directions. The complex nonlinear fluid–structure interaction issues are addressed via the nonlinear vortex sheet method. The study primarily compares the propulsive performance of the two-DoF elastic coupling caudal fin model with the pitch caudal fin model. Numerical results show that the peak efficiency of the proposed model is nearly eight times that of the pitch caudal fin model. Additionally, the study reveals that the high-propulsive mechanism lies in generating the figure of a butterfly phase diagram for the hydrodynamic forces and exploiting vortices to decrease energy consumption. These findings offer novel perspectives for the future design of high-efficiency underwater robots.

Nonlinear parametric generation and optical vortex transfer in graphene ensemble under Landau quantization

We explore the dynamics of nonlinear parametric generation and light beam propagation in a Landau-quantized graphene structure with three energy levels interacting with two laser pulses, utilizing the Maxwell-Bloch equations. By applying a laser field to one transition of the graphene sample while keeping the second beam initially absent, the distinctive preparation of the graphene sample, coupled with its weak interaction with laser radiation, results in the parametric generation of a new laser beam in a different transition. We investigate the influence of diverse system parameters on both the efficiency of the generated beam and the propagation dynamics of both beams. Our findings reveal that manipulating these parameters can induce oscillations in the intensity of propagated beams, mitigate absorption losses during propagation allowing for earlier relaxation, and enhance the efficiency of energy transfer from the initial to the generated beam. Additionally, we demonstrate the transfer of optical vortices within the graphene ensemble by introducing an optical vortex to the initial beam. This scheme holds promise for applications in high-dimensional quantum information processing.

Magnetic vortex polarity reversal induced gyrotropic motion spectrum splitting in a ferromagnetic disk

We investigate the gyrotropic motion of the magnetic vortex core in a chain of a few micron-sized Permalloy disks by electrical resistance measurement with amplitude-modulated magnetic field. We observe a distinctive splitting of the resistance peak due to the resonant vortex-core motion under heightened radio frequency (RF) magnetic field excitation. Our micromagnetic simulation identifies the splitting of the resonant peak as an outcome of vortex polarity reversal under substantial RF amplitudes. This study enhances our understanding of nonlinear magnetic vortex dynamics amidst large RF amplitudes and proposes a potential pathway for spintronic neural computing thanks to their unique and controllable magnetization dynamics.

Computational investigations of Ka-226T helicopter coaxial rotor aerodynamics in the vortex ring state

The vortex ring states are observed when the rotor is flowed at positive angles of attack. For the main rotor, these conditions are realized during a steep descent of the helicopter at low speeds. The rotor vortex ring states are affected by significant phenomena related to the behavior of its aerodynamics, including negative phenomena. The latter is, firstly, referred to decrease in rotor thrust, increase in the required power, pulsations of thrust and torque, unsteady flapping blade motion, etc. In terms of helicopter piloting, it means a sharp loss of altitude, increase in the control force, a high level of vibration, defocusing attenuation of rotor spinning cone, as well as controllability deterioration. All these factors determine the relevance of research on these modes and the importance of solving a problem of defining their boundaries. Recently, due to the rapid development of computer technologies and computational models, it has become practical to perform numerical research of the rotor aerodynamics in vortex ring states. The paper presents the study results of Ka-226T helicopter coaxial rotor aerodynamics in steep descent modes in the field of vortex ring states. The angles of rotor attack αВ = 90...30° and the range of vertical descent velocities Vу = 0...26 m/s are considered. The original nonlinear bladed vortex model of the rotor developed at the Moscow Aviation Institute (MAI) was used. The total and distributed aerodynamic rotor characteristics were calculated. The shapes of the vortex wake and the rotor flow patterns were analyzed. The boundaries of the vortex ring states in velocity coordinates “Vx − Vу” were constructed according to various criteria reflecting the known features of these states. The results obtained significantly complement the existing experience of experimental and numerical research in this field.

Analysis of MAV Rotors Optimized for Low Noise and Aerodynamic Efficiency with Operational Constraints

The rapid growth of drone use in urban areas has prompted authorities to review airspace regulations, forcing drone manufacturers to anticipate and reduce the noise emissions during the design stage. Additionally, micro air vehicles (MAVs) are designed to be aerodynamically efficient, allowing them to fly farther, longer and safer. In this study, a steady aerodynamic code and an acoustic propagator based on the non-linear vortex lattice method (NVLM) and Farassat’s formulation-1A of the Ffowcs Williams and Hawkings (FW-H) acoustic analogy, respectively, are coupled with pymoo, a python-based optimization framework. This tool is used to perform a multi-objective (noise and aerodynamic efficiency) optimization of a 20 cm diameter two-bladed rotor under hovering conditions. From the set of optimized results, (i.e., the Pareto front), three different rotors are 3D-printed using a stereolithography (SLA) technique and tested in an anechoic room. Here, an array of far-field microphones captures the acoustic radiation and directivity of the rotor, while a balance measures the aerodynamic performance. Both the aerodynamic and aeroacoustic performance of the three different rotors, in line with what has been predicted by the numerical codes, are compared and guidelines for the design of aerodynamically and aeroacoustically efficient MAV rotors are extracted.

Second harmonic generation of visible vortex laser based on a waveguide-grating emitter in LBO.

In this work, we propose a practical solution to visible vortex laser emission at 532 nm based on second harmonic generation (SHG) in a well-designed waveguide-grating structure. Such an integrated structure is fabricated by femtosecond laser direct writing (FsLDW) in an LBO crystal. Confocal micro-Raman spectroscopy is employed for detailed analysis of FsLDW-induced localized crystalline damage. By optical excitation at 1064 nm, the guiding properties, SHG performance, as well as vortex laser generation of the waveguide-grating hybrid structure are systematically studied. Our results indicate that FsLDW waveguide-grating emitter is a reliable design holding great promise for nonlinear vortex beam generation in integrated optics.

Numerical investigation on non-linear streaming effects in a two-stage coaxial pulse tube cryocooler

Stirling pulse tube cryocoolers (PTC) are widely used in aerospace applications for the cooling of infrared sensors and for filtering background thermal noise in the astro-imaging devices, etc. Present investigation aims to use numerical methods to demonstrate the nonlinear fluid flow, heat transfer, and vortex generation phenomena in a two-stage coaxial type inertance pulse tube cryocooler. The numerical simulation is conducted using commercially available Fluent® code for both single-stage and multi-stage configurations to show nonlinear processes with varying heat load conditions. It has been noticed that the width of the vortex produced inside the pulse tube grows with an increase in heat load capacity. This undesirable flow conditions yields an adverse effect in the cooling behavior and reduces overall performance of cryocooler with higher heat load. Additionally, streamlines, stream function, pressure and temperature variation plots are given for both stages with different heat load capacity to substantiate our results.

Highly efficient nonlinear vortex beam generation by using a compact nonlinear fork grating

Vortex beams with an orbital angular momentum (OAM) are extremely important in optical trapping, optical micromachining, high-capacity optical communications, and quantum optics. Nonlinear generation of such a vortex beam enables vortex beams to be obtained at new wavelengths, which opens up new possibilities for all-optical switching and manipulation of vortex beams. However, previous nonlinear vortex beam generation suffers from either low efficiency or low-level integration. Here, we use the technique of ultraviolet photolithography-assisted inductively coupled plasma (ICP) etching to realize a compact nonlinear fork grating for high-efficiency nonlinear vortex beam generation. In our experiment, the depth of such a compact nonlinear fork-grating structure can be precisely controlled by etching time. The vortex beams with a topological charge of l = ±1, ± 2, ± 3 can be generated in the far field, and the normalized nonlinear conversion efficiency of such nonlinear vortex beam is 189% W−1cm−2. Our method not only provides an efficient and compact method for nonlinear vortex beam manipulation but also suits for timesaving and large-area nonlinear functional device fabrication.

Dynamical nonlinear excitations induced by interaction quench in a two-dimensional box-trapped Bose–Einstein condensate

Manipulating nonlinear excitations, including solitons and vortices, is an essential topic in quantum many-body physics. A new progress in this direction is a protocol proposed in [Phys. Rev. Res. 2 043256 (2020)] to produce dark solitons in a one-dimensional atomic Bose–Einstein condensate (BEC) by quenching inter-atomic interaction. Motivated by this work, we generalize the protocol to a two-dimensional BEC and investigate the generic scenario of its post-quench dynamics. For an isotropic disk trap with a hard-wall boundary, we find that successive inward-moving ring dark solitons (RDSs) can be induced from the edge, and the number of RDSs can be controlled by tuning the ratio of the after- and before-quench interaction strength across different critical values. The role of the quench played on the profiles of the density, phase, and sound velocity is also investigated. Due to the snake instability, the RDSs then become vortex–antivortex pairs with peculiar dynamics managed by the initial density and the after-quench interaction. By tuning the geometry of the box traps, demonstrated as polygonal ones, more subtle dynamics of solitons and vortices are enabled. Our proposed protocol and the discovered rich dynamical effects on nonlinear excitations can be realized in near future cold-atom experiments.

Numerical investigation on the spanwise chord distribution effects on the performance of an H-darrieus vertical axis wind turbines

The efficiency of Darrieus wind turbines has increased significantly due to developments in blade design, albeit at the expense of the simplicity provided by simple straight blades. The purpose of this research is to gain insight into the influence of various curvatures embedded in the plan of the blade while maintaining its simple straight shape. A variation in chord length along the span defines the curvature. To assess their effect on performance and efficiency, concave, and convex Leading-Trailing Edged Blades (LTEB) are investigated and evaluated in comparison to straight blades. That is viable to gain valuable insight about these blade designs' potential advantages in various applications by studying their aerodynamic characteristics and flow characteristics. The Q-blade tool is used to simulate 3D unsteady Nonlinear Lifting Lines Free Vortex Wake (3D-NLLFVW). The virtual camber effect brought on by flow curvatures is implemented to improve the results' accuracy. According to the findings, H-Darrieus' aerodynamic efficiency climbed by 16% and 9.5% at high TSR. For the concave and convex LTEBs, the torque ripple is smoothed by 37% and 19%, respectively. Additionally, compared to the straight-bladed rotor, the chosen variations enable volume reductions of 53% and 28%.

Growth rates of harmonics in nonlinear vortex beams

Nonlinear effects in acoustical vortex beams were described originally in a numerical investigation by Marchiano et al. [Phys. Rev. E 77, 016605 (2008)]. The focus of the present investigation is the rate at which nonlinearly generated harmonics grow with distance in the field of a vortex beam radiated by a monofrequency or bifrequency source as a function of the topological charge. The motivation is a paper by Richard et al. [New J. Phys. 22, 063021 (2020)] suggesting that the rate of nonlinear distortion in the direction of the beam axis is increased in a vortex beam due to the lengthened propagation distance along the ray paths spiraling about the beam axis. In the present work, harmonic growth rate is characterized in terms of both amplitudes along different ray paths and total power across the beam. Growth rates are calculated and compared for harmonics generated in nonlinear vortex beams radiated by sources with different topological charges and amplitude distributions. Both unfocused and focused beams are considered. The likelihood of shock formations is also explored. [CAG is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Implementing the edge enhancement with vortex filter in both linear and nonlinear optics

The edge enhancement technique, as an effective method to represent the boundary of objects, plays an important role in image processing. Among them, the vortex filtering, which is based on the radial Hilbert transformation, has been paid great attention due to its ability to achieve isotropic and anisotropic edge enhancement. Recent years have witnessed a growing interest in the nonlinear vortex filter to skillfully realize the visualization of the object edge under invisible light irradiation. In this paper, we start from reviewing the achievements have been made with the vortex filtering technique in linear optics, and then discussed the recent processes of the scalar and vector vortex filter in nonlinear optics. We hope that the nonlinear optical vortex filter can motivate some promising applications in biological edge imaging with visible light-sensitive specimens.

Tanh-like models for analysis and prediction of time-dependent flow around a circular cylinder at low Reynolds numbers

When employing traditional low-order approximation equations to forecast the Hopf bifurcation phenomenon in the wake of a circular cylinder at low Reynolds numbers, inaccuracies may arise in estimating the phase. This is due to the fact that, in this transition process, the frequency varies with time. In this paper, we propose a method for analyzing and predicting the vortex shedding behind a cylinder at low Reynolds numbers. The proposed method is based on coordinate transformation and description function and is demonstrated using data from computational fluid dynamics simulation of flow around a cylinder at Reynolds number 100. The resulting governing equations explicitly contain the flow amplitude and implicitly contain the flow frequency. The proposed method is found to have higher accuracy compared to other methods for nonlinear identification and order reduction. Finally, the method is extended to predict nonlinear vortex shedding in the Reynolds number range of 80–200.

Finite-time blowup for the inviscid vortex stretching equation

In this paper, we will introduce the inviscid vortex stretching equation, which is a model equation for the 3D Euler equation where the advection of vorticity is neglected. We will show that there are smooth solutions of this equation which blowup in finite-time, even when restricting to axisymmetric, swirl-free solutions. This provides further evidence of the role of advection in depleting nonlinear vortex stretching for solutions of the 3D Euler equation.

Nonlinear two-photon pumped vortex lasing based on quasi-bound states in the continuum from perovskite metasurface.

The experimental observation of nonlinear two-photon pumped vortex lasing from perovskite metasurfaces is demonstrated. The vortex lasing beam is based on symmetry-protected quasi-bound states in the continuum (QBICs). The topological charge is estimated to be +1 according to the simulation result. The quality factor and lasing threshold are around 1100 and 4.28 mJ/cm2, respectively. Theoretical analysis reveals that the QBIC mode originates from the magnetic dipole mode. The lasing wavelength can be experimentally designed within a broad spectral range by changing the diameter and periodicity of the metasurface. The finite array size effect of QBIC can affect the quality factor of the lasing and be used to modulate the lasing. Results shown in this study can lead to more complex vortex beam lasing from a single chip and previously unidentified ways to obtain ultrafast modulation of the QBIC lasing via the finite array size effect.

Nonlinear Vortex Induced Vibration Analysis of Electrostatic Actuated Microbeam Based on Modified Strain Gradient Theory

Nonlinear Vortex Induced Vibration Analysis of Electrostatic Actuated Microbeam Based on Modified Strain Gradient Theory