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In this paper, we study the long-time evolutions of the single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions by using the vortex sheet model. Applying a spectrally accurate numerical method, we investigate the effects of surface tension and density jump on the instability in various regimes of parameters. Complex phenomena of pinching, capillary waves, elongation, and roll-up appear at the interfaces. For a single-mode interface, surface tension retards the growths of bubble and spike. The effect of surface tension on the bubble and spike velocity is generally small but is large for a spike of an infinite density ratio. For multi-mode interfaces, we focus on an infinite density ratio. We show that bubbles grow with the scaling law h = α A g t 2 even in the presence of surface tension, while spikes follow the scaling law weakly. It is found that both the growth rates of bubbles and spikes decrease with surface tension and the growth rate of spikes decreases larger than that of bubbles. The growth rate of the bubble front is in agreements with results of previous numerical simulations and experiments.

In an incompressible inviscid flow system, helical symmetry means invariance though combined axial translation and rotation about the same axis. In helical symmetry, the axial vorticity is materially conserved if the velocity components along the helical lines are proportional to 1/(1+epsilon^2r^2), where e is the pitch and r is the distance from the z-axis. Linear instability analysis shows that a circular helical vortex patch centered at the origin is neutrally stable. We present the evolution of a family of helically symmetric vortices using contour dynamics, a Lagrangian technique to compute the motion of vortices via contour integrals. For contours perturbed by both lower and high modes, the first mode always becomes the most unstable mode for large time. We can inspect the features induced by the lower perturbed mode. We take mode 4 and mode 9 as examples in this work. Adding a vortex sheet on the boundary of the shifted contour accelerates the twisting and rotating process. The distribution of vortex sheet forms a sharpening shock in the evolution and may lead to the discontinuity.

In this Paper, the integrated propeller–wing system design space is investigated to gain insight into the influence of propeller diameter, location, and rotation direction. To conduct this investig...

At a finite temperature, the stable equilibrium states of a coupled two-component superfluid with the same mass in both non-rotating and rotating cases can be obtained by studying its real time dynamics via holography, the equilibrium state is the final stable state that does not change in time anymore in the evolution process . Without rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant $\eta>\eta_c=0.05$ when the Josephson coupling $\epsilon$ is turned off. While a finite $\epsilon$ will always prevent the two species to be separated spatially. Under rotation, with vanishing $\epsilon$, the quantum fluid reveals many equilibrium structures of vortex states by varying the $\eta$ from negative to positive, the interlaced vortex lattices undergo a phase transition to vortex sheets with each component made up of chains of single quantized vortices., Comment: 7pages,6 figures. The vortex diagram was added

A large variety of gusts that develop in the atmospheric boundary layer affect aerial vehicles. This study, performed in water tow tanks, compares the response of a flat plate wing to transverse ve...

We study weak solutions of the two-dimensional (2D) filtered Euler equations for measure-valued initial vorticity. The filtered Euler equations are a regularized model based on a spatial filtering to the Euler equations and have a unique global weak solution for initial vorticity in the space of a finite Radon measure. In this paper, we treat the vortex sheet problem and the point-vortex problem on the 2D filtered Euler equations. We prove that vortex sheet solutions of the 2D filtered Euler equations converge to those of the 2D Euler equations in the limit of the filtering parameter when initial vortex sheet has a distinguished sign. In addition, we make it clear what kind of condition should be imposed on the spatial filter to show the convergence and, according to the condition, our result is applicable to well-known regularized models such as the Euler- $$\alpha $$ model and the vortex blob model. We also show that filtered point vortices converge to a solution of the point-vortex system provided that collision of point vortices does not occur.

This paper presents a framework for the estimated state regulation of the lift force for a maneuvering wing during a transverse gust encounter. An expression for the effective angle of attack of th...

An inviscid vortex shedding model for separated vortices from a solid body is studied. The model describes the separated vortices by vortex sheets and the attached flow via conformal mapping. We develop a computational model to simulate the vortex shedding of a moving body, with varying angle. An unsteady Kutta condition is imposed on the edges of the plate to determine the edge circulations and velocities. The force on the plate is obtained by integrating the unsteady Blasius equation. We apply the model to two representative cases of an accelerated plate, with impulsive start and uniform acceleration, and investigate the dynamics for large angles of attack. For both cases, the vortex force is dominant in the lift over times. The lift coefficients are initially high and decrease in four chord lengths of displacement, in general. For large angles of attack, the appearance of a peak of lift at an early time depends on the power-law velocity, which differs from the behavior for small angles of attack. The lift and drag from the model are in agreement with the Navier–Stokes simulation and experiment for moderate Reynolds numbers. We also demonstrate the vortex shedding of hovering and flapping plates. In the hovering motion, the large increase in lift at the early backward translation is due to the combined effect of the vortex force and added mass force. In the flapping plate, our model provides an improvement in the prediction for the induced force than other shedding models.

An interesting physical phenomenon was recently observed when a fresh-water basin is covered by a thin ice film that has properties similar to that of a rubber membrane. Surface waves can be generated under the action of wind on the air-water interface that contains an ice film. The modulation property of hydro-elastic waves (HEWs) in deep water covered by thin ice film blown by the wind with a uniform vertical profile is studied here in terms of the air-flow velocity versus a wavenumber. The modulation instability of HEWs is studied through the analysis of coefficients of the nonlinear Schrödinger (NLS) equation with the help of the Lighthill criterion. The NLS equation is derived using the multiple scale method in the presence of airflow. It is demonstrated that the potentially unstable hydro-elastic waves with negative energy appear for relatively small wind speeds, whereas the Kelvin–Helmholtz instability arises when the wind speed becomes fairly strong. Estimates of parameters of modulated waves for the typical conditions are given.

A simplified formulation, based on treating the ratio of the heat release to the postshock thermal enthalpy as a small parameter, accommodating arbitrary chemistry descriptions, is shown to reproduce computationally the same variety of phenomena as more complex formulations for oblique detonations with supersonic postshock flow. The resulting small relative variations of velocity and thermodynamic properties across the reaction region are described by linearized Euler equations written in characteristic form, supplemented by the linearized Rankine-Hugoniot jump conditions across the leading shock. The simplified formulation is used to analyze the interaction of the oblique detonation with a weak vortex sheet, for an Arrhenius irreversible reaction with an activation energy large compared with the postshock thermal enthalpy. The analysis reveals that, as ß, the product of the activation energy and the heat release divided by the square of the postshock thermal enthalpy, increases through values of order unity, decaying spatial oscillations, found for small values, are replaced by persistent nonlinear oscillations of finite amplitude for larger values. Beyond a critical value of ß the growth of the oscillation amplitude leads to the development of a singularity at the shock, an explosion, consistent with the formation of a triple point. Many related problems can be clarified with this formulation. The work of D.M.-R. and C.H. was supported by the Spanish Ministry of Science through Grant No. ENE2015-65852-C2-1-R) and by the Fundación Iberdrola España through Grant No. BYNVua37crdy. The work of A.L.S. and F.A.W. was supported by the U.S. AFOSR Grant No. FA9550-16-1-0443.

General expressions are derived in this paper for the aerodynamic force and moment on an arbitrary set of pitching and heaving foils from the vortical impulse theory in the limit of linearized pote...

A characteristic feature of flows past many oscillating airfoils and wings is the leading-edge vortex (LEV). Although considerable progress has been made in the low-order modeling of LEV formation ...

An oblique shock impinging on a shear layer that separates two uniform supersonic streams, of Mach numbers $M_{1}$ and $M_{2}$, at an incident angle $\unicode[STIX]{x1D70E}_{i}$ can produce regular and irregular interactions with the interface. The region of existence of regular shock refractions with stable flow structures is delineated in the parametric space $(M_{1},M_{2},\unicode[STIX]{x1D70E}_{i})$ considering oblique-shock impingement on a supersonic vortex sheet of infinitesimal thickness. It is found that under supercritical conditions, the oblique shock fails to deflect both streams consistently and to provide balanced flow properties downstream. In this circumstance, the flow renders irregular configurations which, in the absence of characteristic length scales, exhibit self-similar pseudosteady behaviours. These cases involve shocks moving upstream at constant speed and increasing their intensity to comply with equilibrium requirements. Differences in the variation of propagation speed among the flows yield pseudosteady configurations that grow linearly with time. Supercritical conditions are described theoretically and reproduced numerically using highly resolved inviscid simulation.

A depth sensitized Rossiter mode expression for compressible resonant cavity flows is derived based on simple shear layer and acoustic concepts. The physics-based result is compared to relevant experiment measurements and empirical models and shows reasonable agreement. Though simple, the cavity depth sensitized Rossiter mode estimate demonstrates the connection between shear layer flow and cavity acoustics; moreover, the model provides a useful analytically-based validation metric for detailed resonant cavity simulations.

Nonlinear motion of vortex sheets with non-uniform current is investigated taking the magnetohydrodynamic Richtmyer–Meshkov instability (MHD RMI) and the magnetohydrodynamic Kelvin–Helmholtz instability (MHD KHI) as the examples. As the ratio of the magnetic force to the convective force increases, Alfven oscillations appear and the nonlinear growth of the interface as a vortex sheet is suppressed. We show that the turbulent energy possessing the interface flows into the magnetic energy, which causes the strong magnetic field amplification for both instabilities. We also discuss the difference of the temporal evolution of the interface between MHD RMI and MHD KHI.

A twin-jet vortex-sheet model is applied to study the axisymmetric screech modes, generated by simply converging nozzles, for low supersonic Mach numbers. This allows for the identification of the different waves supported by the flow for different conditions. Propagative regions for the upstream-propagating neutral guided jet mode are observed to vary both as a function of solution symmetry, SS and SA, and the jet separation, whilst bounding the screech tones. The A1 screech mode is observed to be cut-off sharply by the SS lower bound. Screech frequency predictions are performed using the wavenumbers obtained from the vortex-sheet model, which provided a good qualitative agreement with the experimental data. Additional A1 and A2 screech tones were observed in the acoustic spectrum as the jet separation was increased, pointing to the existence of new resonance cycles associated with the different symmetries of the flow. These additional tones exist simultaneously and are seen to merge together as increases leaving only a single A1 and A2 tone.

Fish schools are ubiquitous in marine life. Although flow interactions are thought to be beneficial for schooling, their exact effects on the speed, energetics and stability of the group remain elusive. Recent numerical simulations and experimental models suggest that flow interactions stabilize in-tandem formations of flapping foils. Here, we employ a minimal vortex sheet model that captures salient features of the flow interactions among flapping swimmers, and we study the free swimming of a pair of in-line swimmers driven with identical heaving or pitching motions. We find that, independent of the flapping mode, heaving or pitching, the follower passively stabilizes at discrete locations in the wake of the leader, consistent with the heaving foil experiments, but pitching swimmers exhibit tighter and more cohesive formations. Further, in comparison to swimming alone, pitching motions increase the energetic efficiency of the group while heaving motions result in a slight increase in the swimming speed. A deeper analysis of the wake of a single swimmer sheds light on the hydrodynamic mechanisms underlying pairwise formations. These results recapitulate that flow interactions provide a passive mechanism that promotes school cohesion, and afford novel insights into the role of the flapping mode in controlling the emergent properties of the school.

International audience; In shock wave/boundary layer interactions, two mechanisms have been recognized to drive the low-frequency unsteadiness of the reflected shock: upstream boundary layer forcing and downstream feedback. The current work presents a quantitative analysis of the causal mechanisms underlying such flow unsteadiness. The analysis is based on a large-eddy simulation database covering approximately 300 cycles of the low-frequency shock fluctuations in a Mach 2 turbulent boundary layer. This time span enables the accurate application of frequency-domain system identification methods targeting such low frequencies. The evaluation of the spectrum in the interaction zone indicates that the broadband low-frequency unsteadiness is predominantly two-dimensional and can be isolated via spanwise averaging. Empirically derived transfer functions are computed using the averaged flow field and indicate the occurrence of a feedback between the locations downstream of the flow separation and the shock fluctuations. The results indicate that this mechanism dominates over the upstream forcing of the interaction region. Accordingly, the computed transfer functions are also used as an estimation tool to predict the shock motion accurately; for the largest streamwise separation between input and output signals, correlations above 0.6 are observed between predictions and raw data. Computation of spectral proper orthogonal decomposition modes reveals the existence of upstream traveling waves in the leading spectral mode at the main shock frequency; higher frequencies do not exhibit this trend. Furthermore, the spectral modes obtained using selected flow regions downstream of the shock enable the reconstruction of a significant portion of the energy in the interaction zone. Finally, a linear stability analysis is conducted using the mean turbulent flow, showing the existence of upstream traveling waves. Evaluation of a vortex sheet model indicates that these upstream traveling modes are of acoustic nature. The predicted modes from this local analysis present a compelling match against the spectral modes, both in terms of the shape and phase speed of the fluctuations. The combined analysis of the techniques indicates that downstream disturbances are the dominant cause of shock oscillations in the present configuration, leading to shock motion by upstream traveling acoustic modes.

We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses, for three canonical boundary conditions---both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density, or with one or both ends free). The most unstable eigenmodes generally become "wavier" at smaller mass density and smaller tension, but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions., 28 pages, 22 figures

The modulation instability of surface capillary-gravity water waves is analysed in a shear flow model with a tangential discontinuity of velocity. It is assumed that air blows along the surface of the water with a uniform profile in the vertical direction. Such a model, despite its simplicity, plays an important role in hydrodynamics as the reference model for investigating basic physical phenomena of wave–current interactions and acquiring insights into a series of complex phenomena. In certain cases where the wavelength of interfacial perturbations is much bigger than the width of the shear flow profile, the model with the tangential discontinuity in the velocity is adequate for describing physical phenomena at least within limited spatial and temporal frameworks. A detailed analysis of the air-flow conditions under which modulation instability sets in is presented. It is also shown that the interfacial waves are subject to dissipative or radiative instability when negative-energy waves appear at the interface.

We consider the rotating and translating equilibria of open finite vortex sheets with endpoints in two-dimensional potential flows. New results are obtained concerning the stability of these equilibrium configurations which complement analogous results known for unbounded, periodic and circular vortex sheets. First, we show that the rotating and translating equilibria of finite vortex sheets are linearly unstable. However, while in the first case unstable perturbations grow exponentially fast in time, the growth of such perturbations in the second case is algebraic. In both cases the growth rates are increasing functions of the wavenumbers of the perturbations. Remarkably, these stability results are obtained entirely with analytical computations. Second, we obtain and analyze equations describing the time evolution of a straight vortex sheet in linear external fields. Third, it is demonstrated that the results concerning the linear stability analysis of the rotating sheet are consistent with the infinite-aspect-ratio limit of the stability results known for Kirchhoff's ellipse (Love 1893; Mitchell & Rossi 2008) and that the solutions we obtained accounting for the presence of external fields are also consistent with the infinite-aspect-ratio limits of the analogous solutions known for vortex patches., 24 pages, 5 figures; accepted for publication in Journal of Fluid Mechanics

The evolution of the boundary layer vortex sheet on a rotating and translating accelerating circular cylinder at Reynolds numbers of 10 000 and 20 000 is investigated using planar particle image velocimetry. The vortex sheet is decomposed into contributions resulting from translation and rotation as well as from local and far-field vorticity. Their individual development is explored to understand the overall time history of the boundary layer as well as its evolution at the unsteady separation point. The boundary layer vortex sheet distribution changes considerably throughout the motion as well as between different kinematic cases. The same is observed for the vortex sheet strength at the unsteady separation point. A non-dimensional parameter is proposed which removes the effect of rotation rate, instantaneous velocity and shed vorticity accumulating in the far field. It was found that this was successful at collapsing the vortex sheet strength at the unsteady separation point during cylinder motion as well as for the individual kinematic test cases investigated. This confirms that cylinder kinematics and far-field vorticity are driving factors contributing to the development of the unsteady boundary layer and its strength at the separation point.

We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (AM,2021). These surfaces avoid the Kelvin-Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff,2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface, or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution's stability breaks the Euler dynamics' time reversibility. We interpret this as dynamic irreversibility. We have also represented the enstrophy as a surface integral, conserved in the Navier-Stokes equation in the turbulent limit, with vortex stretching and viscous diffusion terms exactly canceling each other on the CVS surfaces. We have studied the CVS equations for the cylindrical vortex surface for an arbitrary constant background strain with two different eigenvalues. This equation reduces to a particular version of the stationary Birkhoff-Rott equation for the 2D flow with an extra nonanalytic term. We study some general properties of this equation and reduce its solution to a fixed point of a map on a sphere, guaranteed to exist by the Brouwer theorem., Comment: 19 pages, 1 figure. Modified CVS theory, with a totally different solution for the surface

International audience; Some recent developments in the Lamb-vector-based aerodynamic force breakdown used the concept of vortex force to define the lift and to decompose the drag into lift-induced drag and profile drag. However, the Lamb vector formulation involves moment transformations, and the associated force breakdown may depend on the reference point adopted for their computation. Yet, the force acting on an airplane cannot be dependent on this point. Thus, a systematic method based on the far-field flow symmetries is here proposed to eliminate this dependence. Those symmetries also allow for a better understanding of the progressive invariance of the drag decomposition with respect to the size of the integration domain. Finally, a reference-point-invariant formulation is defined and tested for a 2-D transonic flow around an OAT15A airfoil and a 3-D flow around the NASA Common Research Model under cruise flight conditions.

In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $\Omega$, such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor., Comment: 31 pages, 4 figures

International audience; In this theoretical work, the existing links between the vortex-force theory, Kutta-Joukowski lift theorem and Maskell's lift-induced drag formula is emphasized. A compressibility correction is identified and it is proven that it gradually vanishes in the far wake. This theoretical equivalence is further tested on subsonic and transonic RANS computations around the M6 wing.

The problem of the accuracy improving is considered for vortex method. The general Galerkin-type approach is considered for the numerical solution of the boundary integral equation. It is shown that the airfoil surface line representation as a polygon consisting of rectilinear panels can lead to incorrect behavior of the numerical solution of the boundary integral equation with respect to unknown vortex sheet intensity, especially in case of considerably different lengths of the neighboring panels. However, in this case, the exact analytical formulae are derived for the coefficients of the linear algebraic system, which approximate the integral equation. The approach is developed which makes it possible to take into account explicitly the curvature of the airfoil surface line. The approximate analytical formulae are derived for the coefficients of the linear system, which are expressed through the integrals of the fractions, which denominators can be equal to zero. Numerical example is considered for the elliptic airfoil in the incident flow at its essentially non-uniform discretization. The suggested algorithm has acceptable numerical complexity, however it permits to obtain rather good numerical results.

This work concentrates on the study of flow dynamics of swirl vortex rings at the Reynolds number Re = 20 000 using a combination of the planar- and stereo-particle image velocimetry (PIV) measurements and dynamic delayed detached-eddy simulation. Particular attention is paid to the identification of the large-scale azimuthal modes in the vortex ring propagation process. In the experiments, vortex rings are issued from piston-driven axial swirlers with the swirl number ranges from S = 0 to 1.10. The stroke ratio L/D = 1.5 is used to produce a compact vortex ring without a trailing jet. PIV measurements are conducted in a water tank, while the in-plane component flow velocities on the longitudinal center plane and the three-component flow velocities on the cross section plane at several downstream locations according to the ring trajectories are obtained. In the simulation, the axial swirlers are also included, while the piston motion is realized by imposing a time-dependent inflow condition. Two types of dynamic effects in the vortex ring propagation process are captured by the planar-PIV measurement: the arriving time effect and the azimuthal effect, which induce parallel shift of the vortex ring core and the radial tilting of the vortex sheet, respectively. These modes are identified using the stereo-PIV results by applying the fast Fourier transform in the azimuthal direction, followed by the proper orthogonal decomposition on the radial and temporal directions. It shows that both m = 0 and 1 modes (m is the azimuthal wave number) coexist in the weakly swirled vortex rings, while the m = 2 mode arises and the m = 0 mode decays at high swirl numbers. The simulation also identifies the m = 1 and 2 modes, while the m = 2 mode has a large pitch with respect to the formation time.

The receptivity of an under-expanded supersonic impinging jet flow at a sharp nozzle lip to acoustic impulse disturbances is investigated as a function of geometric and flow parameters. The under-expanded supersonic jets emanate from an infinite-lipped nozzle, i.e. the nozzle exit is a circular hole in a flat plate. Two specific cases have been investigated corresponding to nozzle-to-wall distances of h = 2d and 5d, where d is the jet diameter, at a nozzle pressure ratio of 3.4 and a Reynolds number of 50 000. Receptivity in this study is defined as originally coined by Morkovin (Tech. Rep. AFFDL TR, 1969, pp. 68-149; see also Reshotko, AGARD Special Course on Stability and Transition of Laminar Flow, N84-33757 23-34) as the internalisation of an external disturbance into the initial condition that either initiates or sustains a vortical fluid dynamic instability. Notionally, receptivity can be considered as a transfer function between the external disturbance and the initial conditions of the vortical instability. In the case of under-expanded supersonic impinging jet flow subjected to an acoustic disturbance, this transfer function is located at the nozzle lip and, thus, is amenable to an impulse response analysis using the linearised compressible three-dimensional Navier-Stokes equations. In this study, the transfer function at the nozzle lip is defined as the ratio of the output flow energy to the input acoustic energy of the acoustic disturbance. The sensitivity of this transfer function to the angular acoustic disturbance location, its azimuthal mode number and Strouhal number has been investigated for the two under-expanded supersonic impinging jet flow cases. It is found that for both the h = 2d and 5d cases, acoustic disturbances located at angles greater than 80° from the jet centreline, with Strouhal numbers in the range between 0.7 and 6.5, have the highest receptivity for all azimuthal mode numbers investigated, except the azimuthal mode number 2 in the case of h = 5d. The case with h = 5d is found to also have high receptivity to acoustic disturbances located at angles between 15° and 50° from the jet centreline for acoustic disturbances of all azimuthal mode numbers.

We study the large-amplitude flutter of membranes (of zero bending rigidity) with vortex-sheet wakes in 2D inviscid fluid flows. We apply small initial deflections and track their exponential decay or growth and subsequent large-amplitude dynamics in the space of three dimensionless parameters: membrane pretension, mass density, and stretching modulus. With both ends fixed, all the membranes converge to steady deflected shapes with single humps that are nearly fore-aft symmetric, except when the deformations are unrealistically large. With leading edges fixed and trailing edges free, the membranes flutter with very small amplitudes and high spatial and temporal frequencies at small mass density. As mass density increases, the membranes transition to periodic and then increasingly aperiodic motions, and the amplitudes increase and spatial and temporal frequencies decrease. With both edges free, the membranes flutter similarly to the fixed-free case but also translate vertically with steady, periodic, or aperiodic trajectories, and with nonzero slopes that lead to small angles of attack with respect to the oncoming flow., 34 pages, 25 figures