
[Sponsors] 
Publication date: Available online 1 May 2021
Source: Computers & Fluids
Author(s): Yuying HU, Peng HU, Wei Li, Weihong LIAO
Publication date: Available online 1 May 2021
Source: Computers & Fluids
Author(s): Paul Garnier, Jonathan Viquerat, Jean Rabault, Aurélien Larcher, Alexander Kuhnle, Elie Hachem
Publication date: Available online 4 May 2021
Source: Computers & Fluids
Author(s): Jasper P. Huijing, Richard P. Dwight, Martin Schmelzer
Publication date: Available online 4 May 2021
Source: Computers & Fluids
Author(s): Lucas Manueco, PierreElie Weiss, Sébastien Deck
Publication date: Available online 6 May 2021
Source: Computers & Fluids
Author(s): Yifei Yu, Pushpa Shrestha, Oscar Alvarez, Charles Nottage, Chaoqun Liu
Publication date: Available online 4 May 2021
Source: Computers & Fluids
Author(s): Aditi Sengupta, Roshan J. Samuel, Prasannabalaji Sundaram, Tapan K. Sengupta
Publication date: Available online 27 April 2021
Source: Computers & Fluids
Author(s): Raj Maddipati, Tapan K. Sengupta, Prasannabalaji Sundaram
Publication date: Available online 27 April 2021
Source: Computers & Fluids
Author(s): E.M.J. Komen, J.A. Hopman, E.M.A. Frederix, F.X. Trias, R.W.C.P. Verstappen
Publication date: Available online 1 March 2021
Source: Computers & Fluids
Author(s): Florian De Vuyst, Christophe Fochesato, Vincent Mahy, Renaud Motte, Mathieu Peybernes
Publication date: Available online 2 November 2020
Source: Computers & Fluids
Author(s): Romit Maulik, Himanshu Sharma, Saumil Patel, Bethany Lusch, Elise Jennings
We introduce a parallel cell‐centered finite volume lattice Boltzmann method on 3D unstructured grids for incompressible flow simulations. The proposed method is validated by three benchmark problems and the results agree well with the published data. The parallel algorithm scales well on a supercomputer with a large number of processors.
The standard lattice Boltzmann method, which employs certain regular lattices coupled with discrete velocities as the computational grid, is limited in its flexibility to simulate flows in irregular geometries. To simulate large‐scale complex flows, we present a cell‐centered finite volume lattice Boltzmann method for incompressible flows on three‐dimensional (3D) unstructured grids and its corresponding parallel algorithm. The advective fluxes are calculated by the low‐diffusion Roe scheme, and the gradients of the particle distribution functions are computed with a least squares method. The presented scheme is validated by three benchmark flows: (a) a 3D Poiseuille flow, (b) cubic cavity flows with Reynolds numbers Re = 100 and 400, and (c) flows past a sphere with Re = 50, 100, 150, 200, and 250. Some parallel performance results are presented to show the scalability of the method, which reveal that the proposed parallel algorithm has considerable scalability and that the parallel efficiency is higher than 87% on 3840 processor cores. It can be seen that the presented parallel solver has significant potential for the accurate simulation of flows in complex 3D geometries.
We introduce a phase‐field formulation of an existing fictitious domain method and a corresponding collision model in order to simulate rigid particulate flows interacting with arbitrary solid structures. The phase‐field framework enables the consideration of both the particulate flow and the structure on a fix Cartesian grid. It also enables the consideration of phase transition within the boundary structure, for example, due to grain growth, making it change its shape during runtime.
A distributed Lagrange multiplier/fictitious domain method in a phase‐field formulation for the simulation of rigid bodies in incompressible fluid flow is presented. The phase‐field method yields an implicit representation of geometries and thus rigid body particulate flows within arbitrary geometries can be simulated based on a fixed Cartesian grid. Therefore, a phase‐field based collision model is introduced in order to address contact of particles with arbitrary solid structures as boundaries. In addition, grain growth within the boundary geometry can be considered leading to changes in its shape during the simulation. The method is validated on benchmark problems and a convergence study is performed. Multiple numerical experiments are carried out in order to show the methods' capability to simulate problems with differently shaped rigid bodies and particulate flows involving complex boundary geometries like foam structures.
A variationally approach for deriving residual‐based closure models for incompressible Navier–Stokes equations is presented. Variational consistency of the model lends itself to rigorous linearization that results in quadratic rate of convergence of the method in the nonlinear solution strategy. The method is shown to work for a family of linear and quadratic hexahedral and tetrahedral elements as well as composite discretizations that are comprised of hexahedral and tetrahedral elements in the same computational domain.
We present a variationally consistent method for deriving residual‐based closure models for incompressible Navier–Stokes equations. The method is based on the fine‐scale variational structure facilitated by the variational multiscale framework where fine scales are driven by the residuals of the Euler–Lagrange equations of the resolved scales in the balance of momentum and conservation of mass equations. A bubble‐functions based approach is applied directly to the fine‐scale variational equation to derive analytical expressions for the closure model. Variational consistency of the model lends itself to rigorous linearization that results in quadratic rate of convergence of the method in the iterative solution strategy for the nonlinear equations. The method is shown to work for a family of linear and quadratic hexahedral and tetrahedral elements as well as composite discretizations that are comprised of hexahedral and tetrahedral elements in the same computational domain. Numerical tests with the proposed model are presented for various classes of turbulent flow problems to show its generality and range of applicability. The test cases investigated include Taylor–Green vortex stretching, statistically stationary wall‐bounded channel flows, and modeling the effects of the geometry of the leading edge of the plate on the instability of the boundary layer that leads to flow separation and flow reversal over flat plates of finite thickness.
A coupled lattice Boltzmann method with two types of distribution functions is used to simulate non‐Newtonian White‐Metzner fluid flows inside a lid driven square cavity. A very detailed investigation of the effect of each parameter on the behavior of the WM fluid flows is presented. The method proves to be good in simulating WM fluids and encounter the instabilities that arise in such flows.
The simulation of non‐Newtonian fluids is a challenging task from theoretical and numerical points of view. Different numerical methods has been used to study this class of fluids. In this article, a novel numerical scheme based on lattice Boltzmann method is presented for the simulation of White–Metzner (WM) fluid flows, where two types of distribution functions are defined for the evolution of momentum and stress, respectively. We study the accuracy, and the influence of different parameters on the flow on different benchmarks: we validate our model first for a two‐dimensional planar channel, and then we investigate in details the behavior of WM fluid flows in a square lid driven cavity. In the numerical results, we give a very detailed investigation to elaborate the effect over a large range of each parameter on the flow field.
In this paper, we present a front capturing method for compressible reactive flows, where a shock tracking technique is applied with level set method. In stiff reaction problems, the difficulty arises when the time scale of the source term is significantly shorter than the time scale of the homogeneous conservation law. The spurious numerical phenomenon may occur due to the smeared out shock profiles. In order to overcome the difficulty, the detonation front is captured sharply by level set technique, and a modified finite volume scheme is developed at the computational cells cut by detonation front. The mass, momentum and energy transitions are occurred on shock front for chemical reactive flows. In our method, the interface exchanges are calculated by considering a Riemann problem. Unlike the standard level set/ghost fluid method, our method can maintain the conservation on the shock discontinuity. One‐ and two‐dimensional numerical examples including stable and unstable detonation problems are illustrated to verify the good reliability and robustness of our method.
A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This ‘discretize‐then‐project’ approach requires no pressure stabilization technique (even though the pressure term is present in the ROM) nor a boundary control technique (to impose the boundary conditions at the ROM level). These are two main advantages compared to existing approaches. The fully discrete FOM is obtained by a finite volume discretization of the incompressible Navier‐Stokes equations on a collocated grid, with a forward Euler time discretization. Two variants of the time discretization method, the inconsistent and consistent flux method, have been investigated. The latter leads to divergence‐free velocity fields, also on the ROM level, whereas the velocity fields are only approximately divergence‐free in the former method. For both methods, accurate results have been obtained for test cases with different types of boundary conditions: a lid‐driven cavity and an open‐cavity (with an inlet and outlet). The ROM obtained with the consistent flux method, having divergence‐free velocity fields, is slightly more accurate but also slightly more expensive to solve compared to the inconsistent flux method. The speedup ratio of the ROM and FOM computation times is the highest for the open cavity test case with the inconsistent flux method.
The DG formulation of the velocity divergence term and the pressure gradient term is required in order to improve the stability of the scheme at small time steps. Moreover, an appropriate penalty term for pressure Poisson equation still provides inf‐sup stabilization for equal‐order polynomials. The combination of these methods is a relatively simple and effective way to improve the stability and robustness of the solver for incompressible flows with high‐Reynolds numbers.
In this work, we consider equal‐order discontinuous Galerkin (DG) solver for incompressible Navier–Stokes equations based on high‐order dual splitting scheme. In order to stay stable, the time step size of this method has been reported that is strictly limited. The upper bound of time step size is restricted by Courant–Friedrichs–Lewy (CFL) condition (Hesthaven and Warburton, 2007) and lower bound is required to be larger than the critical value which depends on Reynolds number and spatial resolution (Ferrer et al., 2014). For high‐Reynolds‐number flow problems, if the spatial resolution is low, the critical value may be larger than CFL condition, then instability will occur for any time step size. Therefore, sufficiently high spatial resolution is indispensable in order to maintain stability, which increases the computational cost. To overcome these difficulties and develop a robust solver for high‐Reynolds‐number flow problem, it is necessary to further study the instability problem at small time steps. We numerically investigate the effect of the pressure gradient term in projection step and the velocity divergence term in pressure Poisson equation on the stability for small time step size, respectively, and conclude that the DG formulation of the pressure gradient term has a more significant effect on the stability of the scheme than that of the velocity divergence term. Integration by parts of these terms is essential in order to improve the stability of the scheme. Based on this discretization format, an appropriate penalty parameter for pressure Poisson equation is utilized so as to provide the scheme with an inf‐sup stabilization. Moreover, the lid‐driven cavity flow is considered to verify that this numerical algorithm enhances the stability without additional stabilization term at small time step size and high‐Reynolds number for equal‐order polynomial approximations.
This article presents a method for performing CAD‐based aerodynamic shape optimization by manipulating the standard geometry. The method addresses the continuity issues that emerge during the update of the boundary representation (BRep) of the shape by imposing up to C1 constraints between neighboring patches and defines a parameterization scheme which inherently satisfies them. The proposed method is demonstrated in an academic case and in industrial‐like cases such as the S‐section of a duct and the tail surface of a car.
This article presents a method for performing adjoint‐based aerodynamic shape optimization by manipulating the standard CAD geometry of the shape to be optimized. A standard CAD file gives access to the boundary representation (BRep) of the shape and consequently its boundary surfaces which are usually trimmed patches. This is a sensible choice as the open format of such files is a requirement for the computation of the shape derivatives. The method addresses the continuity issues that emerge during the update of the shape by imposing up to C _{1} constraints between different CAD patches. A parameterization scheme based on NURBS surfaces is then defined, in which the aforementioned constraints are inherently satisfied. The proposed method is firstly demonstrated in a simple geometric case and then in the full‐scale optimization of industrial‐like cases such as the S‐section of a cooling duct and the tail surface of a passenger car.
We develop and implement a hybrid Reynolds averaged Navier–Stokes/large‐eddy simulations improved delayed detached eddy simulation model for flow and noise predictions of tandem cylinder experiment. The aeroacoustic simulations were conducted via modified acoustic analogies, namely the Curle's and Ffowcs‐Williams and Hawkings analogies. The results from the implemented computational methodologies were in good agreement with experimental acoustic power spectral density data as measured at NASA's Quiet Flow Facility.
This study employs a numerical approach to investigate noise mechanisms in tandem cylinders. The tandem cylinder configuration is an excellent model for aircraft landing gear. The study is therefore primarily motivated by the need to understand the aircraft landing gear as a primary contributor to airframe noise during approach and landing. Fluctuations in the flow properties induced by turbulent flow around the tandem cylinders are computed and analyzed. A hybrid improved delayed detached eddy simulation turbulence model is employed to compute the boundary layer flow as well as to compute the fluctuations in the flow properties. The numerical methodologies for the turbulent flow computations are implemented on the OpenFOAM software platform. The study also considers the impact of neglecting the volume sources and employs two modified versions of Curle's and Ffowcs‐Williams and Hawkings analogies. The results are in good agreement with published numerical and experimental data in the existing literature.
Adjoint‐based shape optimization using unsteady solvers is costly and/or memory demanding. When mild unsteadiness is present or the flow in/around the optimized shape is not expected to be time‐varying, steady primal and adjoint solvers can be used instead. However, in such a case, convergence difficulties caused by flow unsteadiness must properly be treated. In this article, the steady primal and the corresponding (continuous) adjoint solvers are both stabilized by implementing the Recursive Projection Method (RPM). This is carried out in the adjointOptimisation library of OpenFOAM, developed and made publicly available by the group of authors. Upon completion of the optimization using steady solvers, unsteady reevaluations of the optimized solutions confirm a reduction in the time‐averaged objective function. In complex cases, in which the RPM may not necessarily ensure convergence of the adjoint solver on its own, the controlled damping of the adjoint transposed‐convection (ATC) term is additionally implemented. This is demonstrated in the shape optimization of a motorbike fairing where averaged primal fields over a number of iterations of the steady flow solver are used for the solution of the adjoint equations. Cases in which the RPM is, on its own, sufficient in ensuring convergence of the adjoint solver are additionally studied by using a controlled ATC damping, to assess its impact on the computed sensitivity derivatives. Comparisons show that controlled/mild ATC damping is harmless and greatly contributes to robustness.
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Francesco De Vita, Filippo De Lillo, Roberto Verzicco, Miguel Onorato
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Anton G. Artemov, Emanuel H. Rubensson
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Xiaofeng Yang
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Dong An, Sara Y. Cheng, Teresa HeadGordon, Lin Lin, Jianfeng Lu
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Maria Han Veiga, David A. VelascoRomero, Quentin Wenger, Romain Teyssier
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Christopher J. Arthurs, Andrew P. King
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Shaozhong Deng, Zhilin Li, Kejia Pan
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Xuhui Meng, Hessam Babaee, George Em Karniadakis
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): H. Carrillo, E. Macca, C. Parés, G. Russo, D. Zorío
Publication date: 1 August 2021
Source: Journal of Computational Physics, Volume 438
Author(s): Zhen Chen, Dongbin Xiu
The blood flow in a normal aorta is simulated directly based on patientspecific data for boundary conditions. This study provides insight into the implications of using two different outlet boundary conditions in accurate modeling of the blood flow based on using pressure or flow rate outlet boundary conditions. Both boundary conditions at the outlet provided similar blood flow characteristics through the main aortic pathway with a reasonable accuracy of 4% relative to the laboratory measurements. Compared to the pressure outlet boundary condition, however, specifying the flow rate at the outlet underestimates pressure in the aortic arch and the flow rates through the outlets of the aortic arch. Additionally, using the flow rate boundary condition leads to an overestimation of peak local Reynolds Number in the aortic arch, and an inaccurate prediction of transition to turbulence.
The present paper reports an investigation of the statistical properties of pressure fluctuations in the near field of subsonic compressible jets. The database analyzed has been obtained numerically by DNS and LES of two singlestream circular jets, having diameterbased Reynolds numbers of 3125 and 100,000 and Mach number 0.9, respectively, initially laminar and highly disturbed. Pressure fluctuations are extracted from several virtual probes positioned in the near field of the jets and covering a region from 0 to 20 diameters in the axial direction and from 0.5 to 3 diameters in the radial. An azimuthal decomposition of the pressure fluctuations is performed, and the statistical analysis is applied to the axisymmetric 0mode component and compared to the results obtained from the full original signals. The intermittent behavior is investigated by the estimation of standard statistical indicators, such as probability distribution functions and flatness factor, as well as through conditional statistics based on the application of the wavelet transform. It is shown that downstream of the potential core, intermittency estimated through the traditional indicators is relevant even at the lowest Re for the full signals, whereas it is apparently not significant for the 0mode component. The wavelet analysis provides an estimation of intermittency scalebyscale and allows for the calculation of a frequencydependent FF. This approach reveals that the 0mode component has a relevant degree of intermittency around the frequencies associated with the Kelvin–Helmholtz instability. The statistics of the intermittent events, in terms of their temporal appearance and energy content, are shown to be weakly sensitive to the jet Reynolds number and the universal behavior can be reproduced by simple stochastic models.
The problem of the boundary condition setting is considered for creeping flows over cylindrical and spherical obstacles. The interaction of Newtonian and micropolar liquid with the solid surface is discussed in the context of the Stokes paradox and the cell model technique. Mathematical and mechanical aspects of various types of boundary conditions at the hypothetical liquid surface are considered in the framework of the spherical cell model used for the simulation of membrane flows. New properties of the flow pattern in a spherical cell are found, and their independence of the boundary conditions is rigorously proved. The criteria of the boundary conditions equivalence are derived in terms of the membrane porosity and hydrodynamic permeability.
Highfrequency ventilation is a type of mechanical ventilation therapy applied on patients with damaged or delicate lungs. However, the transport of oxygen down, and carbon dioxide up, the airway is governed by subtle transport processes which hitherto have been difficult to quantify. We investigate one of these mechanisms in detail, nonlinear mean streaming, and the impact of the onset of turbulence on this streaming, via direct numerical simulations of a model 1:2 bifurcating pipe. This geometry is investigated as a minimal unit of the fractal structure of the airway. We first quantify the amount of gas recirculated via mean streaming by measuring the recirculating flux in both the upper and lower branches of the bifurcation. For conditions modeling the tracheatobronchi bifurcation of an infant, we find the recirculating flux is of the order of 3–5% of the peak flux . We also show that for conditions modeling the upper generations, the mean recirculation regions extend a significant distance away from the bifurcation, certainly far enough to recirculate gas between generations. We show that this mean streaming flow is driven by the formation of longitudinal vortices in the flow leaving the bifurcation. Second, we show that conditional turbulence arises in the upper generations of the airway. This turbulence appears only in the flow leaving the bifurcation, and at a point in the cycle centered around the maximum instantaneous flow rate. We hypothesize that its appearance is due to an instability of the longitudinalvortices structure.
A coupled level set and volume–of–fraction method is applied to investigate hollow oil droplet impacts on heated walls. Results show that given the increase in impact velocity, three evolutionary processes of spreading, transition, and central jet occur after the hollow oil droplet impact on a heated wall. The variation in the spreading length of hollow oil droplets is similar in different evolutionary processes, but the variation in the center height of hollow oil droplets is relatively different. The wall heat flux and the position of the maximum heat flux increase with impact velocity. In addition, the wall temperature influences the flow and heat transfer characteristics of the hollow oil droplet impingement. Considering the viscosity–temperature characteristics of the lubricating oil, the spreading length of the hollow oil droplet increases with the wall temperature, but the central height of the hollow oil droplet is unaffected by the wall surface temperature. The wall heat flux and the position of the maximum heat flux also increase with the impact velocity. Pressure and velocity distribution indicate that the bubble rupture at the central jet originates from the combined effect of inertial force and surface tension. The results of this study provide a basis for an improved understanding of the flow and heat transfer characteristics of hollow oil droplet impact on a heated wall and serve as a theoretical reference for investigating the effect of bubbles on oil–gas lubrication processes.
In this work, the breakup of a droplet passing through an obstacle in an orthogonal cross section is numerically investigated. The relevant boundary data of the velocity field is numerically computed by solving the depthaveraged Brinkman equation via a selfconsistent integral equation using the boundary element method. To study the dependence of the droplet breakup on the obstacle shape, two different shapes of obstacle, circular and elliptical, are considered in the present work. We investigate the effect of obstacle size, obstacle position, and capillary number on the breakup treatment of the droplet. Numerical results indicate that the critical capillary number depends on the obstacle shape, obstacle position and droplet size. In the elliptical obstacle, in addition, the results also show that the area ratio of daughter droplets depends on the capillary number. Results show that the area ratio of daughter droplets depends on the capillary number, obstacle shape, and obstacle position. Our results is in a good agreement with the previous studies.
Purpose: We present a constructive procedure for the calculation of 2D potential flows in periodic domains with multiple boundaries per period window.
Methods: The solution requires two steps: (i) a conformal mapping from a canonical circular domain to the physical target domain, and (ii) the construction of the complex potential inside the circular domain. All singly periodic domains may be classified into three distinct types: unbounded in two directions, unbounded in one direction, and bounded. In each case, we use conformal mappings to relate the target periodic domain to a canonical circular domain with an appropriate branch structure.
Results: We then present solutions for a range of potential flow phenomena including flow singularities, moving boundaries, uniform flows, straining flows and circulatory flows.
Conclusion: By using the transcendental SchottkyKlein prime function, the ensuing solutions are valid for an arbitrary number of obstacles per period window. Moreover, our solutions are exact and do not require any asymptotic approximations.
We present a comprehensive analysis of the cumulant lattice Boltzmann model with the threedimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourthorder convergent diffusion and fourthorder convergent advection with and without limiters. In addition, a cumulant model combined with a WALE subgrid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the nonfiltered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ( \({\hbox {Re}}=160{,}000\) ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourthorder convergent diffusion show much better results than single relaxation time methods.
The dynamics of a fully threedimensional liddriven cubical cavity (3DLDC) flow at several postcritical conditions, i.e., beyond the first bifurcation, are elucidated using both linear and nonlinear analyses. When the Reynolds number is increased beyond the critical value, symmetry breaks down intermittently with subsequent gradual growth in spanwise inhomogeneity. This results in crossflow as well as pronounced secondary flow due to enhanced imbalance between centrifugal and pressure forces. Thus, while a stable solution is obtained at \(\hbox {Re}=1900\) (Reynolds number based on lid velocity and cavity side length), nonlinear analysis identifies intermittent and nearly saturated regimes at \(\hbox {Re}=2100\) and \(\hbox {Re}=3000\) , respectively. These changes in the regime are examined by considering five basic states at different Reynolds numbers starting from \(\hbox {Re}=1900\) . At the lowest Reynolds number, linear analysis yields only symmetric modes, characterized by Taylor–Görtlerlike (TGL) vortices. However, at \(\hbox {Re}=2100\) , the intermittent breakdown of symmetry results in the emergence of an antisymmetric lowfrequency mode apart from primary highfrequency mode. The frequencies of both these modes are numerically close to those obtained from corresponding nonlinear simulations. When the Reynolds number is increased even further, the TGL structures drift under the influence of the crossflow to occupy the previously structureless region near the wall. The frequency of each mode decreases with increase in \(\hbox {Re}\) ; between 1900 and 3000, the frequency of the primary mode changes by more than 20%. Furthermore, the spatial support of each mode becomes larger within the cavity. Both primary and secondary modes are increasingly destabilized with \(\hbox {Re}\) ; however, the secondary antisymmetric mode is destabilized at a higher rate. The current study thus provides a comprehensive picture of the overall dynamics of 3DLDC flows in pre and postbifurcation regimes in an extended \(\hbox {Re}\) range not considered hitherto.
Hill’s vortex is a threedimensional vortex structure formpreserving solution of the Euler equations (Hill in Philos Trans R Soc Lond A 185:213–245, 1894). For small amplitude axisymmetric disturbances on the external surface, the linear stability analysis by Moffat and Moore (J Fluid Mech 87:749–760, 1978) predicted the formation of a tail. Successive linear and nonlinear investigations confirmed this fact and in addition observed that the shape of the tail was linked to number of small amplitude azimuthal disturbances of the surface. In this paper, the Navier–Stokes equations are solved, at high Reynolds number, by imposing large amplitude axisymmetric and threedimensional disturbances on the surface of the vortex. The axisymmetric disturbances are convected in the rear side, are dumped and form an axisymmetric wave increasing at the same rate as that in the linear stability analysis. The azimuthal disturbances produce a hierarchy of structures inside the vortex, and in a shorttime evolution, the shape of the vortex is maintained. For a longtime evolution, direct numerical simulations show that Hill’s vortex for azimuthal disturbances loses its original form for the formation of a wide range of energy containing scales characteristic of threedimensional flows. Although a true turbulent state has not been reached, the DNS of this simple vortex structure shows the passage from a vortex dominated to a turbulent state.