Wake Research Articles

Flow through horizontal axis propeller turbines in a triangular array

When two horizontal rotors are put side-by-side, with slight gaps between them (less than two diameters), the flow velocity near the centerline is higher than the free stream. In this paper, we employ experimental and computational methods to examine the turbulent wake flow of a single turbine, the interactions between two side-by-side rotors, and the power output of a turbine inside a triangular arrangement (with two rotors upstream and one downstream). The experiments are carried out in a wind tunnel using 1:10 scale models. The wake flow is characterized by applying the hot-wire anemometer. Numerical simulations are employed to characterize a single turbine’s near-wake flow and guide side-by-side rotor investigations. The results demonstrate that more power can be converted by a group of three horizontal axis turbines arranged in a triangular frame than by three separate turbines. We show that the RANS turbulence model accurately computes mean velocity but not Turbulence Intensity (TI). We propose a new URANS post-processing approach that improves TI calculations at the wake region. Our findings suggest that wind, tidal current, and hydrokinetic farms may be able to convert more power adopting triangular arrays than they can in standard aligned or staggered row designs.

Fountain Flow Visualization in Quadrotor Wake Decreasing Rotor Thrust In-Ground Effect

Wake visualizations and thrust measurements of a quadrotor model were conducted to clarify the relationship between thrust and wake flow structure in-ground effects. The adjacent rotor distance, rotor height above ground, and the presence of a plate representing a generic quadrotor centerbody were varied. Thrust decreased when lowering the quadrotor to the ground when the adjacent rotor distance was over 2.2 times the rotor radius. Laser light sheet flow visualization showed quadrotor wake flow structures. Furthermore, visualization using particle image velocimetry showed an averaged vector map of wakes and fountain flow at the center of the quadrotor wake, which caused circulation with rotor passing flow and decreased rotor thrust. The center plate increased the sum of the rotor thrust and plate lift; however, circulation flow formed under the plate and caused the rotor thrust to decrease the in-ground effect. The results clarified that fountain flow development decreased the quadrotor thrust in-ground effect. Reducing the adjacent rotor distance weakened the development of fountain flow in the quadrotor wake and eliminated the decrease in rotor thrust near the ground.

Optimal waveform for fast synchronization of airfoil wakes

We obtain an optimal actuation waveform for fast synchronization of periodic airfoil wakes through the phase reduction approach. Using the phase reduction approach for periodic wake flows, the spatial sensitivity fields with respect to the phase of the vortex shedding are obtained. The phase sensitivity fields can uncover the synchronization properties in the presence of periodic actuation. This study seeks a periodic actuation waveform using phase-based analysis to minimize the time for synchronization to modify the wake shedding frequency of NACA0012 airfoil wakes. This fast synchronization waveform is obtained theoretically from the phase sensitivity function by casting an optimization problem. The obtained optimal actuation waveform becomes increasingly non-sinusoidal for higher angles of attack. Actuation based on the obtained waveform achieves rapid synchronization within as low as two vortex shedding cycles irrespective of the forcing frequency, whereas traditional sinusoidal actuation requires ${O}(10)$ shedding cycles. Further, we analyse the influence of actuation frequency on the vortex shedding and the aerodynamic coefficients using force-element analysis. The present analysis provides an efficient way to modify the vortex lock-on properties in a transient manner with applications to fluid–structure interactions and unsteady flow control.

Model Verification and Experimental Study of The Turbomachinery Wake Flow Field Reconstruction

Abstract A clear understanding of the turbomachinery wake flow field is one of the key problems in developing turbomachinery aerodynamics. The theoretical model of helical vortices is established in cylindrical coordinates (r,θ,z), and the model corresponds to the experimental scheme, which verifies the feasibility of reconstructing flow field by interpolation in r-z plane under different θ. This model shows that theta should not exceed 20 degrees in order to reconstruct the flow field more accurately. Taking rotors as the representative of the turbomachinery, Particle image velocimetry (PIV) is used to measure the velocity field in the rotor wake. Interpolating reconstruction of spacing between different measurement planes, the reconstruction results are relative to the theory, which plane spacing should be less than 20 deg. Using the vorticity weighted average method to calculate the central position of the vortex core, the wandering motion of the tip vortex is obtained. On this basis, a correct conditional average algorithm is proposed to eliminate this effect. Through the analysis method of the circulation, it is proved that the point where the second derivative of the circulation with respect to the radius is 0 corresponds to the radius of the vortex core, and the evolution law of the growth of the vortex core radius is proportional to the square root of the vortex ages. The results provide a reliable experimental method for the quantitative study of the spatio-temporal evolution of complex vortex structures in the three-dimensional flow of turbomachinery wakes.

Experimental and numerical investigations on the performance and wake characteristics of a tidal turbine under yaw

This paper presents an extensive examination of the wake characteristics and hydrodynamic performance of a 1:60 scale horizontal axis tidal stream turbine under yawed inflow conditions. Experimental investigations were conducted in a laboratory flume, while numerical simulations utilized the actuator line method and large-eddy simulation technique. The turbine was subjected to an inflow turbulence intensity of 6% and was tested at five different yaw angles (5°, 10°, 15°, 20°, and 30°). The findings demonstrate a substantial reduction in the power coefficient as the yaw angle increases, with a notable drop of 47.1% recorded at a yaw angle of 30°. Furthermore, numerical simulations of wake characteristics, including mean velocity and turbulence intensity, were examined and compared with measurements, yielding satisfactory agreement. The yawed wake flow exhibited asymmetrical distributions of mean velocity and deviations from the centerline. Additionally, distinct deformations of the yawed wake in the y-z cross sections were observed, indicating a discernible curled kidney shape that intensified with larger yaw angles. Moreover, interactions between the turbine wake and support structures affected the width and turbulence intensity of the near wake, introducing additional unsteadiness that accelerated wake recovery.

Fluid-structure interaction analysis of the propeller-shafting system in a non-uniform wake

The hydroelastic analysis of the propeller-shafting system in the non-uniform wake is a key step for designing a modern propeller-shafting system. The hydroelastic responses of the propeller-shafting system in the wake of ships are predicted by applying a three-dimensional time-frequency combined panel approach in conjunction with the finite element method. A fully non-penetration boundary condition applied on the deformed blade surface is conducted. The correction of both the incoming flow velocities and the normal vectors imposed on the blade surface of the transient vibration and the equilibrium positions is considered. The added-mass and -damping matrices due to strongly coupled fluid-structure interaction are derived. By comparing the present findings to numerical solutions calculated using the commercial tool Ansys Mechanical, the accuracy of the suggested technique is verified. It is observed that the added damping is higher, and the amplitudes of bearing forces are smaller, by applying the fully non-penetration boundary condition compared with the results obtained by imposing the other two simplified non-penetration conditions. This indicates that the designers need to imply the fully non-penetration condition on the deformed surfaces to predict the hydroelastic dynamics of the propeller-shafting system, especially in the case of high skew propellers. In addition, the amplitudes of the exciting forces after considering the fluid and propeller-shaft system interaction can be larger or smaller than those ignoring the interaction. The results depend on the phase difference and the mode shape.

The Effect of the Layout of a Rigid Splitter Plate on the Flow-Induced Vibration of a Downstream Cylinder Subjected to Wake Flow

In this study, the effect of additional positions of rigid splitter plates on the response characteristics of tandem cylinders at a Reynolds number of 150 and a fixed distance ratio of 5.0 was numerically investigated via the computational fluid dynamics (CFD) method. Four layouts for the cylinder–plate body, including a downstream cylinder (DC), a downstream cylinder–plate body with a wake side plate (DCP), a downstream plate–cylinder body with an incoming flow side plate (DPC), and a downstream plate–cylinder–plate body with a double-sided plate (DPCP), are considered. The results show that the splitter plate attached to the incoming flow side or the wake side can suppress the vibration of the downstream cylinder in a specific reduced velocity range (4.0 < Ur ≤ 10.0). Compared with the DC, the maximum response amplitude of the DPC and DCP in the lock-in region is reduced by 30.8% and 47.4%, and the lock-in bandwidth is also significantly narrower. The layer separation point of the upstream cylinder moves downstream upon adding splitter plates to both the incoming flow and wake sides, and the resulting splitter shear layer of the DPCP is completely parallel to the free flow, while the maximum response amplitude is reduced by 93.6%, which realizes the best effect of stream-induced vibration suppression.

Stochastic Noise Sources for Computational Aeroacoustics of a Vehicle Side Mirror

<div>The broadband aeroacoustics of a side mirror is investigated with a stochastic noise source method and compared to scale-resolving simulations. The setup based on an already existing work includes two geometrical variants with a plain series side mirror and a modified mirror with a forward-facing step mounted on the inner side. The aeroacoustic near- and farfield is computed by a hydrodynamic–acoustic splitting approach by means of a perturbed convective wave equation. Aeroacoustic source terms are computed by the Fast Random Particle-Mesh method, a stochastic noise source method modeling velocity fluctuations in time domain based on time-averaged turbulence statistics. Three RANS models are used to provide input data for the Fast Random Particle-Mesh method with fundamental differences in local flow phenomena. Results of aeroacoustics simulations excited by the Fast Random Particle-Mesh method based on well-matching RANS data are in good agreement to the scale-resolving simulations in the integral acoustic Delta on the side window induced by the different side mirror geometries. For relative levels in between the variations, the robustness of the Fast Random Particle-Mesh method can be shown with secondary influences on the choice of the integral length scale. Absolute levels are only achieved with an adaptation of the length scale from literature. Two different RANS models with a missing separation bubble on the mirror or an overestimated wake flow show a good agreement with the plain series side mirror. However, they fail at computing the Delta to the step variant due to the missing amplification of the local turbulent kinetic energy interacting with the step and downstream mirror surfaces. Computational aeroacoustics simulations excited by the Fast Random Particle-Mesh method method based on RANS data only needs 14% of the computational effort compared to the conventional hybrid RANS-LES approach. This reveals its enormous potential for aeroacoustic broadband noise optimization purposes.</div>

A GPU-Accelerated Method for 3D Nonlinear Kelvin Ship Wake Patterns Simulation

The study of ship waves is important for ship detection, coastal erosion and wave drag. This paper proposed a highly paralleled numerical computation method for efficiently simulating three-dimensional nonlinear kelvin waves. First, a numerical model for nonlinear ship waves is established based on potential flow theory, the Jacobian-free Newton–Krylov (JFNK) method and the boundary integral method. To reduce the amount of data stored in the JFNK method and improve the computational efficiency, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU)-based parallel computing framework is designed, and we used the Compute Unified Device Architecture (CUDA) language to develop a GPU solution. Finally, numerical simulations of 3D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved, and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

Efficient numerical model for sediment transport on vortex ripple bed in wave-induced oscillatory flow

Sediment motion on rippled bed under wave action plays an important role in coastal landforms, but the application of traditional numerical model is limited by large computational work or bottom sediment condition due to unsteady effects. A single-phase model is proposed to maintain low computation and high accuracy for the vortex structure development and suspended sediment motion on vortex rippled bed in wave-induced oscillatory flow. The 2D bottom sediment condition takes into account the acceleration effect and asymmetric boundary layer development under nonlinear waves as well as the sediment phase-lag. The particle inertia and wake flow around sediment particle are considered in sediment turbulence, and the SST k-ω turbulence model which is suitable for inverse pressure gradient flow on rippled bed is selected to close the Reynolds stress. The single-phase model well predicts the velocity on vortex ripples, periodic concentration at fixed points and vertical distribution of averaged sediment concentration. The results show qualitative formation, development and ejection of vortex, and demonstrate quantitative development of vortex center, radius and strength in symmetric and asymmetric flows. In addition, the model well performs the development of sediment cloud referring to vortex structure.

Experimental investigation on the turbulent wake flow in fully established transonic buffet conditions

The transonic flight regime is often dominated by transonic buffet, a highly unsteady and complex shock-wave/boundary-layer interaction involving major parts of the flow field. The phenomenon is associated with a large-amplitude periodic motion of the compression shock coupled with large-scale flow separation and intermittent re-attachment. Due to the resulting large-scale variation of the global flow topology, also the turbulent wake of the airfoil or wing is severely affected, and so are any aerodynamic devices downstream on which the wake impinges. To analyze and understand the turbulent structures and dynamics of the wake, we performed a comprehensive experimental study of the near wake of the supercritical OAT15A airfoil in transonic buffet conditions at a chord Reynolds number of 2×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ imes 10^{6}$$\\end{document}. Velocity field measurements reveal severe global influences of the buffet mode on both the surface-bound flow field on the suction side of the airfoil and the wake. The flow is intermittently strongly separated, with a significant momentum deficit that extends far into the wake. The buffet motion induces severe disturbances and variations of the turbulent flow, as shown on the basis of phase-averaged turbulent quantities in terms of Reynolds shear stress and RMS-values. The spectral nature of downstream-convecting fluctuations and turbulent structures are analyzed using high-speed focusing schlieren sequences. Analyses of the power spectral density pertaining to the vortex shedding in the direct vicinity of the trailing edge indicate dominant frequencies one order of magnitude higher than those associated with shock buffet (Stc=O(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({1})$$\\end{document}) vs. Stc=O(0.1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({0.1})$$\\end{document}). It is shown that the flapping motion of the shear layer is accompanied by the formation of a von Kármán-type vortex street of fluctuating strength. These wake structures and dynamics will impact any downstream aerodynamic devices affected by the wake. Our study, therefore, allows conclusions regarding the incoming flow of devices such as the tail plane.

Transient Model for the Hydrodynamic Force in a Hydraulic Capsule Pipeline Transport System

The hydraulic capsule pipeline (HCP) is an eco-friendly and sustainable pipeline transport option. The freight-carrying capsule is driven by hydraulic pipe flow. Fluid drag is generated by the principal dynamic force effect on the capsule, which could influence the capsule’s motion speed. To make the HCP more efficient, a transient model for the hydrodynamic force in an HCP was developed in this study. From a numerical simulation, the coherent vortex structures of fluctuating modes were observed, and the velocity iso-surfaces of the coherent vortex of the wake flow exhibited an annular trend in circumferential connection. Then, the hydrodynamic force was analyzed: the steady component and transient component were resolved, and the general trend in forces in terms of the transient components was that the maximum amplitude of forces reduced with an increase in mode order. Through short-term Fourier transform, the frequency components and their variations in terms of the entire time range could be acquired. The transient model in this study provided a perspective to build the connection between the flow structures and the hydrodynamic force. By the transient model, the transient component of hydrodynamic force can be explained as the fluctuation of coherent vortex structures.

Data-Driven Discovery of Anomaly-Sensitive Parameters from Uvula Wake Flows Using Wavelet Analyses and Poincaré Maps

This study presents a data-driven approach to identifying anomaly-sensitive parameters through a multiscale, multifaceted analysis of simulated respiratory flows. The anomalies under consideration include a pharyngeal model with three levels of constriction (M1, M2, M3) and a flapping uvula with two types of kinematics (K1, K2). Direct numerical simulations (DNS) were implemented to solve the wake flows induced by a flapping uvula; instantaneous vortex images, as well as pressures and velocities at seven probes, were recorded for twelve cycles. Principal component analysis (PCA), wavelet-based multifractal spectrum and scalogram, and Poincaré mapping were implemented to identify anomaly-sensitive parameters. The PCA results demonstrated a reasonable periodicity of instantaneous vortex images in the leading vector space and revealed distinct patterns between models with varying uvula kinematics (K1, K2). At higher PCA ranks, the periodicity gradually decays, eventually transitioning to a random pattern. The multifractal spectra and scalograms of pressures in the pharynx (P6, P7) show high sensitivity to uvula kinematics, with the pitching mode (K2) having a wider spectrum and a left-skewed peak than the heaving mode (K1). Conversely, the Poincaré maps of velocities and pressures in the pharynx (Vel6, Vel7, P6, P7) exhibit high sensitivity to pharyngeal constriction levels (M1–M3), but not to uvula kinematics. The parameter sensitivity to anomaly also differs with the probe site; thus, synergizing measurements from multiple probes with properly extracted anomaly-sensitive parameters holds the potential to localize the source of snoring and estimate the collapsibility of the pharynx.

Investigation of the wake flow and the oscillation process of two free-to-rotate tandem cylinders due to a flow disturbance

This paper presents an exploratory analysis of the oscillation process of a set of two circular cylinders (D = 25 mm) mounted with a fixed pitch-to-diameter ratio P/D = 1.26 and attached to a free-to-rotate circular table submitted to a turbulent crossflow in a wind tunnel. Measurements were performed with hot wire anemometers placed in the wake of the cylinders synchronized with a high-speed digital camera. Flow visualizations with static cylinders in a water channel were performed to investigate the wake formation around the cylinders. The analysis of the results was made through Fourier and wavelet transforms. The main objective is to address the observed phenomenon with its causing physical mechanism. Wind tunnel results showed that, depending on the imposed mean flow velocity, the set starts oscillating with a low steady amplitude. When the flow is disturbed, an increase in the oscillation amplitude is observed, remaining in this steady regime even after removing the disturbance. Although the interaction between the flow and cylinder set generates two stable states, the properties of the oscillation phenomena (frequency and amplitude) remained the same, pointing out an intrinsic property of the dynamical system. The vortex shedding is identified to be the primary mechanism responsible for initiating the small amplitude oscillation, while the flow passing through the gap between the cylinders is the cause of the high amplitude oscillation. The flow visualization corroborated the wake analysis described in the wind tunnel experiments. No evidence of coherence between the vortex shedding from the first cylinder and the oscillation process was identified. Considering the results in the present work, the configuration analyzed may work as a vortex-shedding suppressor.

Research on the impact of air-blowing on aerodynamic drag reduction and wake characteristics of a high-speed maglev train

The maglev train fills the speed gap between ground transportation and airplanes. However, the increasing train speed results in greater energy losses due to increased aerodynamic drag, impeding the green and sustainable development of high-speed railways. This study employs the numerical simulation method to explore the effects of installing air-blowing slots on the surface of the TR08 maglev train's tail car and blowing air along three different directions at two different speeds on drag reduction and the characteristics of the wake flow field. Among them, only blowing air along the streamwise direction at speeds of 12 m/s (X12) and 24 m/s (X24) shows drag reduction effects of 2.06% and 6.53%, respectively. However, considering the energy efficiency, only X12 achieves a net energy saving of 58.96%, while the energy consumption by blowing air and saving by reducing drag in X24 are roughly balanced. Air-blowing reduces the aerodynamic lift of the tail car (Cl), with blowing air along the perpendicular direction at 24 m/s (Z24) reducing the Cl by 99.57%. Additionally, Z24 reduces the maximum velocity value of the train-induced air flow (Usmax¯) by 61.91%. The research findings provide new insight and data support for the development of blowing/suction drag reduction techniques.

Flow control for aerodynamic drag reduction of a high-speed train with diversion slots on bogie regions

A diversion slot is one of the potential mechanical devices to reduce high-speed train underbody aerodynamic resistance. This research aims to investigate the effectiveness of using diversion slots as a means of passive flow control to reduce the resistance of a high-speed train. Two different diversion slot designs, i.e., the big diversion slot (Bds) and the small diversion slot (Sds), placed at two installation locations near the bogie cabin end walls in six configurations are used. The results indicate that drag of the tail car is significantly reduced by 7.8%, 5.5%, 9.0%, and 9.4% using the configurations in cases 2 and 4–6, while an increase in 0.4% is experienced in case 3. Consequently, the total train aerodynamic resistance reduces by 1.9%, 0.2%, 3.0%, 4.2%, and 0.4% in cases 2–6, respectively, as compared to case 1. By evaluating the flow structure, we found that the diversion slots trigger flow separation, deflecting the airflow from entering the bogie regions, increasing flow turbulence and reducing the flow velocity. It efficiently improves the wake flow structure by reducing the wake strength, thereby increasing the tail nose surface pressure, thus reducing the tail car's aerodynamic drag. This study proposes a novel approach for reducing aerodynamic drag in high-speed trains, improving the underbody flow and wake characteristics.

Modulation of wake evolution, separation, and radiated noise by a cylinder with porous media cladding

In this paper, the effects of porous media parameters on circular cylinder wake flow and radiation noise are investigated using large eddy simulations and Ffowcs Williams–Hawkings acoustic analogy. We performed three-dimensional numerical simulations for flow around the cylinder coated with a porous layer of different pores per inch in a subcritical flow regime (ReD=4.7×104) to explore the control mechanism of porous media on wake and radiation noise. The results show that the application of porous media significantly alters the separation pattern behind the cylinder and stabilizes the shear layer detached from the cylinder. The existence of porous layers leads to the transformation of chaotic and irregular vortex structures into more orderly vortices. Moreover, this study also reveals that the cylinder coated with high pore density can provide the desired noise reduction. The analysis of vortex sound theory indicates that porous media reduces the interaction area and magnitude of the positive and negative Lamb vector divergences, which is beneficial for drag reduction and noise attenuation. In addition, the comparison of sound pressure contours shows that the application of porous media does not change the radiation mode of noise, but the porous media with high pore density helps to decrease the generation of noise and intensity of the sound source.

Large eddy simulations of flow past an inclined circular cylinder: Insights into the three-dimensional effect

The flow past an inclined cylinder is simulated using large eddy simulations to study the three-dimensional wake flow effects on the forces on the cylinder at Re = 3900. Four inclination angles of α = 0°, 30°, 45°, and 60° are considered. The validity of the independence principle (IP) at the four investigated angles is examined. The results suggest that IP can predict the vortex shedding frequency at 0° ≤ α ≤ 60°, while it fails to predict the drag, lift, and pressure coefficients variations because the three-dimensional effect is neglected for IP. A comprehensive analysis is performed to provide insights into the three-dimensional effects on the drag and lift forces caused by α. The flow velocities, the Reynolds stress, and the spanwise characteristic length of the flow structures are discussed in detail. It is found that the recirculation length reaches its maximum at α = 45°, which results in the smallest drag coefficient and lift force amplitudes. The spanwise characteristic lengths of the vortices are similar for all cases, while spanwise traveling patterns are observed only for α > 0°. A force partitioning analysis is performed to quantify the correlations between the forces and the spanwise and cross-spanwise vortices. It reveals that for α = 30°, the drag force becomes dominated by the cross-spanwise vorticity. With the increasing α, the dominant contribution gradually changes from the cross-spanwise to the spanwise vorticity, and the cross-spanwise vorticity contribution to the drag force further becomes negative at α = 60°.

Research on the interaction mechanism of multiple vortices in biological wake flow field

The vortex-ring interaction of synchronous jets has been paid more attention by predecessors, while the research of asynchronous jets (i.e. there is a time difference between the start of jets) of parallel dual nozzles has been studied less. Therefore, the interaction between vortex rings and the vortex structure evolution of the dual-nozzle asynchronous jets with different time differences (Δt) is studied in this paper. Numerical results obtained can be divided into four intervals: 1. Synchronous jets (Δt = 0); 2. Critical interval (Δt < 0.1t, where t is the jet time), having similar vortex structure evolution modes and dynamic characteristics as the synchronous jet; 3. Strong interaction interval (0.2t ≤ Δt ≤ 0.4t), in which the main vortex ring shows obvious acceleration, and the streamwise vortex structure is found in the wake; 4. weak interaction interval (Δt ≥ 0.6t), in which the interaction between vortex rings is much less strong and the streamwise vortex structure also appears in the wake. In addition, it is found that pressure on the nozzle outlet plane increases and the vortex dissipation in the downstream flow field slows down significantly due to the vortex-ring interaction on the condition of asynchronous jets.

Vortex wake patterns in superfluid 4He

Excitations in the form of quantized vortex rings are known to exist in superfluid 4He at energies and momenta exceeding those of the Landau phonon–roton spectrum. They form a vortex branch of elementary excitations spectrum which is disconnected from the Landau spectrum. Interference of vortex ring excitations determines wake patterns due to uniformly traveling sources in bulk superfluid at low speeds and pressures. The dispersion law of these excitations resembles that of gravity waves on deep water with infrared wave number cutoff. As a result, vortex wake patterns featuring elements of the Kelvin ship wake are predicted. Specifically, at lowest speeds the pattern with fully developed transverse and diverging wavefronts is present. At intermediate speeds transverse wavefronts are absent within a cone whose opening angle increases with the source velocity. At largest speeds only diverging wavefronts confined within a cone whose opening angle decreases with the source velocity are found. When experimentally observed, these changes in appearance of wake patterns serve as indicators of the beginning part of the vortex branch of elementary excitations.