Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session A28: Flow Instability: Nonlinear Dynamics and Global Modes I 
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Chair: Alexander Mikishev, Sam Houston State University Room: Georgia World Congress Center B316 
Sunday, November 18, 2018 8:00AM  8:13AM 
A28.00001: Linear three dimensional stability of twosided nonfacing lid driven cavity flows Jun Hu The twosided nonfacing lid driven cavity flow for which the upper wall is moved to the right and the left wall to the bottom with equal speeds are investigated numerically for its linear three dimensional stability. The twodimensional basic steadystate is first obtained by the TaylorHood finite element method through Newton iteration process. The triangulation of finite element mesh is based on a transformed Chebyshev GaussLobatto collocation nodes, which is also used for the spatial discretization of the linear stability equations with a highorder finitedifference scheme. The resulting generalized eigenvalue problem in a matrix form is then solved by the implicitly restarted Arnoldi method with the shiftandinvert algorithm. Through the eigenvalue computation of linear stability equations, the most unstable stationary mode for long wave instability and two pairs of symmetrical travelling modes for short wave instability are found. The critical Reynolds number of the most unstable stationary mode occurs at Reynolds number Re_{c}=261.5 which is far smaller than that of the twodimensional instability . 
Sunday, November 18, 2018 8:13AM  8:26AM 
A28.00002: A new approach for the stability analysis in hydromagnetic Couette flow Jean Bio Chabi Orou This paper analyses the effects of small injection/suction Reynolds number, Hartmann parameter, permeability parameter and wave number on a viscous incompressible electrically conducting fluid flow in a parallel porous plates forming a channel. The plates of the channel are parallel with the same constant temperature and subjected to a small injection/suction. The upper plate is allowed to move in flow direction and the lower plate is kept at rest. A uniform magnetic field is applied perpendicularly to the plates. The main objective of the paper is to study the effect of the above parameters on temporal linear stability analysis of the flow with a new approach based on modified OrrSommerfeld equation. It is obtained that the permeability parameter, the Hartmann parameter and the wave number contribute to the linear temporal stability while the small injection/suction Reynolds number has a negligible effect on the stability.

Sunday, November 18, 2018 8:26AM  8:39AM 
A28.00003: On the stability of wake flows past porous bluff bodies Lorenzo Siconolfi, Pier Giuseppe Ledda, Francesco Viola, Simone Camarri, Francois Gallaire Inspired by nature and motivated by engineering applications, the study of the flow past and through porous media has received a growing interest in our community over the years. In this work, we present results from a numerical study aimed to investigate the effect of the porosity and permeability on the transition scenario of the wakes of porous bluff bodies at lowmoderate Reynolds numbers. This work is developed in the framework of direct numerical simulation and linear stability analysis. First, the twodimensional flow past porous rectangular cylinders is investigated, considering thicknesstoheight ratios ranging from 0.01 (flat plate) to 1.0 (square cylinder). Then, the cases of the flow past a porous sphere and a disk are studied. The results show that the permeability of the bodies has a strong effect in modifying the characteristics of the flow instabilities, while the porosity weakly affects the flow patterns. In particular, since the fluid can flow through the porous obstacles, the recirculation regions detach from the body first and then disappear in the near wakes when the permeability is increased. Lastly, for all the configurations here presented, critical values of the permeability are furthermore identified above which any flow instabilities are prevented. 
Sunday, November 18, 2018 8:39AM  8:52AM 
A28.00004: Global Stability Analysis of bluff bodies using spectral collocation technique Aswathy Nair K., A Sameen We discuss the development of a high accuracy and low computational complexity global stability solver for bluff body geometries based on Chebyshev Spectral collocation method. We propose and validate a series of coordinate transformations for the generation of a Chebyshev spectral collocated orthogonal grid from the bodyconformed grid of bluff body geometries. The inverse KarmanTrefftz and the Joukowsky transformations are used in conjunction with algebraic transformations to transform the bodyconformed grid of circular cylinders and airfoils into the orthogonal grid. The global stability equation is solved as an Eigen Value problem on the Chebyshev spectral collocated grid obtained after the transformations. The solver was validated by analysing the stability of the Blasius profile at Reynolds number (based on displacement thickness), $Re_{\delta^*} = 580$ and wave number, $\alpha = 0.179$ to successfully reproduce the local stability results. The validation of the technique was done by analysing stability of circular cylinders, symmetric and cambered airfoils in addition to square cylinder and wedge flows and will be presented at the time of conference. 
Sunday, November 18, 2018 8:52AM  9:05AM 
A28.00005: The role of parasitic modes in nonlinear closure via the resolvent feedback loop Sean Symon, Kevin Rosenberg, Beverley J McKeon Resolvent modes are compared to Dynamic Mode Decomposition (DMD) modes at the first and second harmonics of the shedding frequency for cylinder flow. Sharma et al. (2016) and Towne et al. (2018) have discussed when these modes are likely to agree. While there is a match between the modes at the first harmonic, the structure predicted by resolvent analysis bears no resemblance to the DMD mode at the second harmonic where there is no separation of the resolvent operator's singular values. We use the feedback loop of McKeon and Sharma (2010), where the nonlinear term is the intrinsic forcing of the resolvent operator, to educe the structure of fluctuations where linear mechanisms are not active. The selfinteraction of the resolvent mode at the shedding frequency is similar to the second harmonic's nonlinear forcing. When it is run through the resolvent operator, the `forced' resolvent mode agrees with the DMD mode. The role of parasitic modes, labeled as such since they are driven by the amplified frequencies, is important in terms of their contribution to the nonlinear forcing of the main amplification mechanisms. This is demonstrated for the shedding mode which has subtle discrepancies with its DMD counterpart. 
Sunday, November 18, 2018 9:05AM  9:18AM 
A28.00006: Oscillatory longwave Marangoni convection in a heated liquid layer covered by insoluble surfactant: Bifurcation analysis Alexander Mikishev, Alexander Nepomnyashchy A bifurcation analysis of the deformational mode of threedimensional longwave oscillatory Marangoni convection, which occurs in a heated layer of liquid covered by insoluble surfactant, is performed. The analysis is carried out in the framework of a set of nonlinear evolution equations derived in our previous work. The bifurcation analysis of monotonic mode has been done formerly. Here we consider the oscillatory instability mode. The weakly nonlinear expansions are applied near the instability threshold. We find stability regions for a variety of convective patterns including single traveling and standing waves, superpositions of two traveling and two standing waves, and superpositions of three traveling waves. It is found that stability of convective patterns strongly depends on the parameters related to the surfactant adsorbed on the free deformable surface of the layer. 
Sunday, November 18, 2018 9:18AM  9:31AM 
A28.00007: Nonlinear transient growth in compressible pipe flow Zhu Huang, Tim Flint, M. J. Philipp Hack A variational method for flow optimization based on the nonlinear compressible NavierStokes equations is presented. The framework allows the identification of finiteamplitude optimal perturbations which maximize the growth of perturbation kinetic energy via a seminorm formulation. The method is applied in the analysis of nonlinear effects on the transient amplification of disturbances in pipe flow at subsonic Mach numbers. We consider spatially localized perturbations that are restricted to the inflow of the simulation domain. As such, the approach allows direct comparisons to experiments and simulations which commonly introduce disturbances into the flow at a given downstream position. Time integration of the adjoint equations is facilitated via a checkpointing method. The spatial discretization is based on fourth order finite differences on a curvilinear cylindrical grid. The computed perturbations are compared to linearly optimal disturbances which generate streamwise streaks by means of the liftup mechanism. 
Sunday, November 18, 2018 9:31AM  9:44AM 
A28.00008: Numerical method for adjoint global stability analysis of compressible flows based on matrixfree approach Yuya Ohmichi, Kento Yamada A numerical method for threedimensional adjoint global linear stability analysis of compressible flows was developed. The compressible adjoint NavierStokes equations were derived. The developed method solves the adjoint stability problems using a timestepping method which is a matrixfree approach. Because of the low memory requirement of the matrixfree approach, the developed method can analyze threedimensional flows. The method was applied to a flow field around a twodimensional cylinder and a threedimensional cubic liddriven cavity flow. Sensitivity regions of the flow fields were calculated using the direct and adjoint global modes. We confirmed that numerical and experimental results reported by the previous studies were precisely reproduced by the developed method. 
Sunday, November 18, 2018 9:44AM  9:57AM 
A28.00009: Instabilities of swirling liquid film in cylindrical chamber Yanxing Wang, Vigor Yang A highfidelity numerical exploration is carried out for the stability of a gradually thickened swirling liquid film on the inner wall of a cylindrical chamber. A comprehensive mathematical method is developed to extract spatially evolving instabilities. By examining the time averaged flow field and the characteristics of instability waves, two dominant instabilities (i.e., centrifugal and shear instabilities) are identified, and the interaction and competition between the two instabilities are discovered. The wave behaviors are primarily determined by the combination of flow and geometric factors: the liquid film thickness, profiles of the axial and azimuthal velocities, thickness of the boundary layer on inner wall surface, and curvature of the solid wall. As flow travels downstream, viscus dissipation makes the film thickness increase and the velocity profiles in the film change, which then trigger the transition of dominant wave types from one to the other. A unified theory for the onset and transition of instabilities of a swirling liquid film is established based on a comprehensive analysis of the flow characteristics over a wide range of operating parameters. 
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