Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session H04: Flow Instability: General (5:45pm  6:30pm CST)Interactive On Demand

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H04.00001: A wavepacketbased optimization method for resolvent analysis Barbara LopezDoriga, Scott T. M. Dawson We report on the development of a semianalytic method to approximate resolvent (pseudospectral) mode shapes and amplification levels. The method assumes that mode shapes can be accurately approximated by a sum of suitablydefined wavepackets. The small number of parameters prescribing the shape of these wavepackets may be found by solving a lowdimensional optimization problem, thus eliminating the need to form and decompose discretized linear operators. We demonstrate the applicability and assess the performance of this method on the Squire operator in laminar Couette and plane Poiseuille flow. In particular, we show that the method can be applied to cases where leading resolvent modes are affected by boundary conditions and/or multiple critical layers. We additionally explore the capabilities of this method to compute suboptimal mode shapes and amplification levels, and discuss prospects for applying this method to more complex systems. [Preview Abstract] 

H04.00002: ViscosityStratified Nonlinear Optimal Perturbation and its Evolution in a 3D Channel Ritabrata Thakur, Arjun Sharma, Rama Govindarajan We show that the early stages of nonlinear optimal perturbation growth in a viscositystratified flow are different from those in a constantviscosity flow. We use a numerical technique of directadjoint looping and nonlinear optimisation to obtain the nonlinear optimal perturbation which maximises the timeintgrated perturbation kinetic energy of the system. The geometry of flow is a 3dimensional channel. The two walls of the channel are kept at different temperatures and the viscosity varies as an exponential function of temperature. The Orr and modified liftup mechanisms are in operation at low (linear) and high (nonlinear) perturbation amplitudes, respectively, at our subcritical Reynolds number of 500 and Prandtl number 7. The nonlinear optimal perturbation contains more energy on the hot (lessviscous) side, with a stronger initial liftup. However, as the flow evolves, the important dynamics shifts to the cold (moreviscous) side, where wide highspeed streaks of low viscosity grow and persist. This strengthens the inflectional quality of the velocity profile. We show why the linear optimal misses this physics by describing the mechanism behind this energy growth. The Prandtl number does not qualitatively change the findings with the current viscosity model. [Preview Abstract] 

H04.00003: Experimental study of capillary jets of viscoelastic liquids Louise Cottier, Christophe Dumouchel, MarieCharlotte Renoult The development of capillary instability on lowvelocity jets manifest itself by surface deformations, whose evolution depends on the injection conditions, namely the nozzle geometry, the injection velocity and the liquid properties. When the liquid is viscoelastic, some of its properties depend on the other injection conditions. Also, under some conditions, the jet exhibit structures called ``beadsonastring'' that might be subject to coalescence phenomenon. Statistical analyses of experimental data are conducted to study the dynamics of free lowvelocity viscoelastic liquid jets. The data set is made up of jet images taken at successive positions downstream from the nozzle exit. The images have been treated to detect the liquid/gas interfaces. The main features of these interfaces are captured by carrying two different Proper Orthogonal Decompositions (POD) within each ROI. The one considers each pixel value of the raster images, and the other is carried on the measured volumebased scale distributions. The variation of the injection conditions brings important results about their impacts on the onset of the capillary instability, on its evolution and also on the coalescence and degradation mechanisms. [Preview Abstract] 

H04.00004: Centrifugal Instability of Coand\u{a} Flows Lev Dunaevich, David Greenblatt The first observations of stationary streamwise vortices within a centrifugally unstable laminar walljet flowing over a circular (Coand\u{a}) cylinder are presented. Flow visualization was used to analyze streamwise vortices and shear layer development, while PIV was used to determine the vortices' size and strength. Exponential growth of the shear layer was characterized by a linear dependence of the growthrate parameter exponent on the Goertler number (G). Extrapolation of the growthrate parameter to zero produced the firstever experimental estimate of the critical Goertler number, namely 3.1, which compared remarkably well with stability theory (3.5). Increases in G resulted in a second timedependent wavy instability whose median frequency increased linearly. Transition occurred at G$=$28, and was accompanied by multiple vortex wavenumbers and a large range of frequencies. Furthermore, transition corresponded to a minimum separation angle as a function of G for the following reasons. With increasing G, the relatively thick vortexdriven shear layer was more susceptible to separation and thus the separation angle, relative to the slot, decreased. However, following transition to turbulence, the highmomentum fluid near the wall that resulted from turbulent mixing, produced a subsequent increase in the separation angle. [Preview Abstract] 

H04.00005: Viscous stabilisation of RayleighPlateau modes on a cylindrical filament through radial oscillatory forcing Sagar Patankar, Saswata Basak, Palas Kumar Farsoiya, Ratul Dasgupta Faraday waves are standing wave patterns appearing on a liquid surface subject to an oscillatory body force and have been observed in base states of Cartesian, spherical or cylindrical coordinate systems (Benjamin et. al., Proc. Roy. Soc. Lond., 1954; Adou et. al., J. Fluid Mech., 2016; Patankar et. al., J. Fluid Mech. 2018). In these geometries, under inviscid irrotational approximation, smallamplitude standing waves are governed by the Mathieu equation. Taking viscosity into account produces a memory term leading to an integrodifferential, damped, Mathieu equation. In Cartesian geometry such an equation was derived by Beyer et. al., Phys. Rev. E, 1995. Here, we derive an analogous integrodifferential equation governing Faraday waves on a cylindrical filament of a viscous liquid utilising the toroidalpoloidal decomposition (Boronski et. al., J. Comput. Phys. 2007). We demonstrate perpetual stabilisation of an unstable axisymmetric Rayleigh$$Plateau mode $(kR_0<1)$ perturbation in the viscous case by choosing the strength of forcing appropriately. Linearised theory is compared with Direct Numerical Simulations using the opensource code Gerris showing good agreement. We also show the possibility of generating droplets in a controlled manner by fragmenting the filament. [Preview Abstract] 

H04.00006: Modified oneway NavierStokes equations with PSElike cost. Min Zhu, Aaron Towne Spatial marching methods offer a lowcost alternative to global linear methods and direct numerical simulation for studying the linear and nonlinear stability of slowly varying flows, e.g., boundary layers and jets. The widely used parabolized stability equations (PSE) provide adequate accuracy in some cases, but tend to fail, due to regularization required to overcome the illposedness of the spatial march, for flows involving multiply instability mechanisms, transient growth, and acoustics. An alternative method called the OneWay NavierStokes equations (OWNS) uses a recursive filter to yield a formally wellposed spatial march that can accurately capture the entire downstream solution, but at one to two ordersofmagnitude higher computational cost than PSE. In this presentation, we introduce a modified OWNS method with cost approaching that of PSE. The speedup is achieved by modifying the OWNS recursion equations to achieve better cost scaling and by borrowing ideas from PSE while still avoiding its limitations. The accuracy and efficiency of the method are demonstrated using a hypersonic boundary layer and a turbulent jet.. [Preview Abstract] 

H04.00007: Periodic fluctuations of streamwise vortices in inertiadominated intersecting flows Noa Burshtein, Konstantinos Zografos, Amy Q. Shen, Robert J. Poole, Simon J. Haward In the proximity of stagnation points, flow instabilities arise at relatively low Reynolds number, $Re\sim O~(10100)$, resulting in the formation of vortices that can evolve timeperiodic patterns. These flows are well studied where the stagnation point is downstream of a bluff body and the resulting vortices are in the spanwise direction (e.g. the von K\'{a}rm\'{a}n vortex street). However, they are less understood in intersecting flows, where the resulting vortices are stretched in the streamwise direction. In this work, quantitative flow velocimetry measurements and 3D numerical simulations, are used to characterize steady vortical flow fields at two intersecting rectangular channels with different degrees of confinement, determined by the channel aspect ratio (depth: width), $\alpha$. By tuning the parameters $\alpha$ and $Re$, we control the number of vortices in the steady flow field, their relative rotation direction and vortex core structure. These features will determine the onset parameters and dynamics of timeperiodic fluctuations. The dimensionless description of our findings can be applied in various scales, for control over vortexinduced vibrations that harm structures such as bridges, buildings, wind turbines and pipes in terrestrial and marine environments. [Preview Abstract] 

H04.00008: Investigation of tipvortex instability in the nearwake region of a rotor Prabakaran Rajamanickam, Lokesh Silwal, Vrishank Raghav Most studies of stability of tip vortices generated from rotors have been focused in the farfield wake, where the vortices are usually modeled as interlaced, helical vortices. In the near wake, due to bladevortex interactions and a reduction in the crosssectional area of the slipstream, the tipvortex configuration deviates from the circular, helical structures found in the farfield wake. These nearwake effects are well captured by the Landgrebe's empricial model for the vortex trajectories. The dependence of nearwake characteristics on the stability of tip vortices becomes significant especially in hovering rotors, where the vortices are convected away from the blade slowly when compared with rotors in forward or, axial flight. The dependence of nearwake characteristics also increases with decreasing thrust coefficients. A linear stability analysis is carried out for the Landgrebe's vortices to predict the growth rate and the instability modes, following closely the classical work of Gupta and Loewy (1974). The predictable quantities from the linear theory are functions of the wake age, with its values approaching the farfield values for very large wake ages. The theoretical results are then compared with the experimental observations conducted in our experimental setup. [Preview Abstract] 

H04.00009: Resolvent Analysis Of Laminar Separated Flows Over Swept Wings Jean Helder Marques Ribeiro, ChiAn Yeh, Kai Zhang, Kunihiko Taira \sout{\textsc{WE STUDY LAMINAR SEPARATED FLOWS OVER SPANWISEPERIODIC SWEPT WINGS AT HIGH ANGLES OF ATTACK USING RESOLVENT ANALYSIS. THREEDIMENSIONAL POSTSTALL FLOW PHYSICS OF SWEPT WINGS REMAINS LARGELY UNEXPLORED. WE USE RESOLVENT ANALYSIS TO GAIN INSIGHTS ON THE BEHAVIOR OF COHERENT STRUCTURES AND AMPLIFICATION MECHANISMS AS WE VARY THE SWEEP ANGLE, STROUHAL NUMBER, SPANWISE WAVENUMBER, AND ANGLE OF ATTACK. ADJOINTBASED PARAMETRIC SENSITIVITY ANALYSIS IS LEVERAGED TO SPAN THE PARAMETER SPACE FOR DIFFERENT SPANWISE WAVENUMBERS AND STROUHAL NUMBERS. AT THE ZERO SPANWISE WAVENUMBER, THE RESOLVENT GAIN PEAK IS FOUND TO ALIGN WITH THE DOMINANT SHEDDING FREQUENCY. IN THIS CONFIGURATION, AN INCREASE IN SWEEP ANGLE IS SHOWN TO REDUCE THE RESOLVENT GAIN. AT THE NONZERO SPANWISE WAVENUMBERS, INCREASE IN SWEEP ANGLE SHIFTS DOMINANT GAIN TO HIGHER FREQUENCIES. FOR THE SWEEP ANGLE OF 45}}\sout{$^{\mathrm{O}}$\sout{\textsc{, 3D MODES ARE AMPLIFIED MORE THAN 2D MODES. THE PRESENT STUDY SERVES AS A FUNDAMENTAL BASIS TO REVEAL UNIQUE WAKE DYNAMICS SEEN FOR SWEPT WINGS.}} [Preview Abstract] 
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