Harbin Institute of Technology Fluid Mechanics Seminars

Initiated by Zijing Ding and edited by Zhen Ouyang

Upcoming Seminars

Speaker: Prof. Frederic Dias, University College Dublin, Ireland


Title: Agreed to talk.

Abstract: Agreed to talk.

Prof. Dias's homepage:

Past Seminars

Speaker: Prof. Michele Guala, University of Minnesota, USA

Date/Time:  Friday, 30th July 2021, 10:00 am (GMT+8)

Title:  In-stream hydropower inspired by wind energy research: new challenges for sustainable energy conversion

Abstract:  Energy production from renewable sources as wind, rivers or tidal streams poses new challenges as compared to conventional hydro-power or fossil-fuel plants. Not only the flow impinging on the energy extracting device is varying in time but also the boundary conditions may be subject to slow variations. One example is the scour-depositional patterns occurring around instream horizontal axis turbines in rivers, the effect of migrating sediment waves approaching the turbine rotor plane, and the morphodynamic equilibrium of the river bed around turbine arrays.  However, such an interaction is not necessarily problematic and could actually be functional for a better management of fluvial systems subject to excessive erosion.  In the course of this seminar I will present some of my latest research using basic, fundamental fluid mechanics and laboratory experiments on wind and fluvial turbines to envision and model sustainable and renewable energy systems.

The work of Craig Hill, Mirko Musa, Michael Heisel, Marco Redolfi and Bingzheng Dou is gratefully acknowledged.

Prof. Guala's homepage:

Speaker: Prof. Kang Luo, Harbin Institute of Technology, China.

Date/Time: Tuesday, 27th July 2021, 4:00 pm (GMT+8)

Title: Flow instability and heat transfer enhancement in electroconvection

Abstract: The flow motion driven by the Coulomb force exerted by the electric field on free space charges is fundamental problems in Electro-Hydro-Dynamics (EHD). Such flow plays an important role in a wide range of applications in industrial processes, such as EHD pumps, EHD turbulent mixer and electrostatic precipitators. In general, flow control and heat transfer enhancement with electricity-based techniques has some unique advantages, such as no moving mechanical parts, rapid and smart control, and low power consumption and noise.

   In this talk, I will review the last five years works on EHD of our group, including the theoretical analysis of rich linear and nonlinear instabilities in EHD, lattice Boltzmann modeling of EHD, Cellular flow patterns and their subcritical bifurcation phenomena of EHD, solid-liquid and solid-gas two phase EHD problems, electro-thermo-convection in non-Newtonian dielectric liquid.

Prof. Luo's homepage:

Speaker: Prof. Peter Haynes, University of Cambridge, U.K.

Date/Time: Thursday, 22nd July 2021, 4:00 pm (GMT+8)

Title: Eddy-driven beta-plane jets -- a fundamental atmosphere-ocean phenomenon

Abstract: The phenomenon that turbulence/forced eddying motion in a single-layer or multi-layer stratified system on a beta-plane leads to the formation of persistent jets in the longitudinal direction has attracted great attention over the last 40 years. (A beta-plane is a simple model device to represent the latitudinal variation in the vertical component of the planetary rotation.) It is relevant to midlatitude jets in the atmosphere, multiple jets in the Antarctic Circumpolar Current and to flows on outer planets in the Solar System.

I will review some of the ideas and models that have been formulated to explain the formation of the jets and to account for their dynamical and transport properties. I will then focus on the particular topic of time variability -- the jets are not steady but exhibit a rich range of time variability which depends on the external parameters -- and then discuss the phemonenology of the variability and some of the physical ingredients that seem important in determining its characteristics.

Prof. Haynes's homepage:

Speaker: Prof. Charles Chun Yang, Nanyang Technological University, Singapore

Date/Time: Tuesday, 20th July 2021, 4:00 pm (GMT+8)

Title: Electrokinetic Flows in Microchannels: Modeling, Characterizations and Microfluidic Applications

Abstract: Microfluidic devices consist of microchannels and microstructures. The past two decades have seen academic frenzy for microfluidics research that involves multidisciplinary fields such as engineering, physics, chemistry, biology, life science, etc. The fast development of microfluidics mainly lies in that microfluidic devices promise to offer a viable micro-fluidic platform for miniature medical, environmental and national security diagnostic kits. Compared to existing laboratory-scale instruments, microfluidics has numerous advantages, including inexpensive, portable, disposable, multi-functional, less sample consumption and waste generation, ease of operation, fast processing, and full automation. Scaling analysis shows the conventional pressure driven flows do not scale well with miniaturization, and often require complicated off-chip components such as pumps, connectors, tubings, etc. In contrast, electrokinetic driven flows that employ DC or AC electric fields to pump, mixing, split liquid buffers based on electroosmosis, enjoy numerous advantages such as no moving parts, ease of control, well integration with standard microelectronics and fabrication methods. In this talk, I will present the fundamental aspects of both linear and nonlinear electrokinetic flows, including  modeling, analyses, and characterizations as well as their microfluidic applications.

Prof. Yang's homepage:

Speaker: Prof. Victor Steinberg, Weizmann Institute of Science, Israel

Date/Time: Thursday, 15th July 2021, 3:00 pm (GMT+8)

Title: New direction in elastic instability and turbulence in straight channel viscoelastic flow

Abstract: After short introduction into polymer solution hydrodynamics, I shortly describe the main results on elastically driven instabilities and elastic turbulence in flow geometries with curvilinear streamlines, about prediction of elastic waves and absence of such waves in these flows. Then I switch to the main subject of the talk, namely recent development in parallel shear flows of polymer solutions proved to be linearly stable for the last about 50 years. We discovered in a straight channel flow elastically driven instability, elastic turbulence, elastic waves, and re-laminarization. In this regard, a short discussion of normal versus non-normal instabilities in such flows I give on the end.

Prof. Steinberg's homepage:

Speaker: Prof. Matthias Heil, University of Manchester, U.K.

Date/Time: Tuesday, 13th July 2021, 4:00 pm (GMT+8)

Title: Flows past cylinders: Are the transitions between different flow regimes caused by a continuous evolution or by bifurcations?

Abstract: Solutions to the Navier-Stokes equations often go through a sequence of distinct regimes, with the flow field becoming more 'complicated' as the Reynolds number increases. These changes may occur via (i) bifurcations of the underlying solutions of the Navier-Stokes equations, or (ii) a continuous evolution of the 'complicated' flow field (with quantifiable, discrete changes to its topology).

We analyse the interplay between these two, in principle distinct, mechanisms in the context of flows past circular cylinders. If the cylinder is stationary the flow undergoes a Hopf bifurcation at a Reynolds number of approximately 46, resulting in the formation of the famous von Kármán vortex street -- a time-periodic flow in which vortices are shed downstream. While this suggests that the change to the flow topology arises via mechanism (i) we show that the transition from steady to time-periodic flow (through the Hopf bifurcation) and the formation of individual vortices are in fact distinct events that occur at slightly different Reynolds numbers.

When the cylinder performs forced oscillations transverse to the flow direction, the vortex-shedding pattern becomes significantly more complex, leading to the formation of so-called 'exotic wakes' whose character is controlled by the Reynolds number as well as the period and amplitude of the cylinder's motion. While it has generally been assumed that the transition between different wake patterns in response to changes in the amplitude occurs via mechanism (ii) we show that they are actually associated with a spatio-temporal symmetry-breaking bifurcation of the time-periodic flow.

Prof. Heil's homepage:

Speaker: Prof. Vladimir S. Ajaev, Southern Methodist University, USA

Date/Time: Thursday, 8th July 2021, 10:00 am (GMT+8)

Title: Levitation and self-organization of microscale droplets 

Abstract: Levitating droplets of liquid condensate are known to organize themselves into highly ordered arrays over hot liquid-gas interfaces.  Our recent experimental observations show similar behavior of droplets over a dry heated solid surface at temperatures far below the Leidenfrost point.  Mathematical models are developed that predict the mechanisms of both droplet levitation and inter-droplet interaction leading to pattern formation over the dry surface; the models are shown to be in good agreement with the experimental data. Using the insights from the new experiments, we are able to resolve some long-standing controversies pertaining to the mechanism of levitation of droplets over liquid-gas interfaces and find the levitation height as a function of droplet size. Finally, by studying trajectories of levitating droplets near the contact line region we are able to obtain velocity profiles for local gas flow there. 

Speaker: Dr. Ashley P. Willis, University of Sheffield, U.K.

Date/Time: Tuesday, 6th July 2021, 4:00 pm (GMT+8)

Title: Nonlinear optimisation of transition in pipe flow.

Abstract:The transition to turbulence in pipe, Couette and channel flows is particularly interesting, as it is possible to have either laminar flow or turbulence at the same flow rate:  If the laminar flow is given a (sufficiently small) perturbation, then it will return to the laminar state; similarly, turbulence is likely to remain if perturbed.  

Two related questions naturally arise: 'What is the minimal perturbation to laminar flow that causes transition to turbulence?' and 'What is the minimal perturbation to turbulence [here via a body force] that can cause the flow to laminarise?'

These questions are closely related to control problems, where we might want to enhance turbulence to encourage mixing, or weaken turbulence to reduce drag.  They can be formulated as similar nonlinear variational problems, in principle.  Several issues arise in practice, but optimal perturbations and forces of consistent structure can nevertheless be determined.

 Dr. Willis's homepage:

Speaker: Prof. Jens G. Eggers, University of Bristol, U.K.

Date/Time: Friday, 2nd July 2021, 4:00 pm (GMT+8)

Title: Theory of bubble tips in strong viscous flows

Abstract:A free surface, placed in a strong viscous flow (such that viscous forces overwhelm surface tension), often develops ends with very sharp tips. We shown that the axisymmetric shape of the ends, non-dimensionalized by the tip curvature, is governed by a universal similarity solution. The shape of the similarity solution is close to a cone, but whose slope varies with the square root of the logarithmic distance from the tip.

Pursuing the calculation of the tip similarity solution to next order, we demonstrate matching to previous slender-body analyses, which fail near the tip. This allows us to resolve the long-standing problem, first raised by G.I. Taylor, of finding the global solution of a bubble in a strong hyperbolic flow. Our results are shown to agree in detail with experiment as well as full numerical simulations of the Stokes equation.

 Prof. Eggers's homepage:

Speaker: Prof. Tim Colonius, California Institute of Technology, USA

Date/Time: Tuesday, 29th June 2021, 10:00 am (GMT+8)

Title: Turbulence structure and modeling in the frequency domain

Abstract: Amongst many available data-driven modal decompositions of utility in fluid mechanics, the frequency-domain (spectral) version of the proper orthogonal decomposition (SPOD) plays a special role in the analysis of stationary turbulence.  SPOD modes are optimal in expressing structures that evolve coherently in both space and time, and they can be regarded as optimally-averaged DMD modes.  Importantly, the SPOD spectrum is also related to the resolvent spectrum of the linearized dynamics and examination of the relationships between the SPOD and resolvent modes yields information about how coherent structures are forced by nonlinear interactions amongst coherent and incoherent turbulence.  We discuss the application of these tools to analyze and model turbulence in high-speed jets and boundary layers.  We highlight recent developments including (a) utilizing eddy-viscosity models in resolvent analysis to enable RANS-based prediction of coherent structures, and (b) nonlinear extensions of resolvent analysis to discover worst-case disturbances for laminar-turbulent transition, and (c) the development fast spatial marching methods for large-scale resolvent problems.

Prof. Colonius's homepage:

Speaker: Dr. Baole Wen, University of Michigan, Ann Arbor, USA

Date/Time: Tuesday, 15th June 2021, 10:30 am (GMT+8)

Title: Asymptotic Transport in Strongly Nonlinear Rayleigh–Bénard Convection

Abstract: Rayleigh–Bénard convection plays a significant role in important applications ranging from microfluidics engineering to climate science and astrophysics, and has been studied extensively to gain insights into the development of turbulence.  A key feature of Rayleigh–Bénard convection is heat transport, and predicting transport for large applied temperature gradients in the strongly nonlinear regime remains a major challenge for the field.  Since the 1960s two distinct scaling theories, i.e., the classical scaling theory and the ultimate scaling theory, have contended to quantitatively characterize the strongly nonlinear regime, yet no clear winner has emerged.

The computations reported here offer new evidence for one of these theories and suggest a novel way to resolve the conundrum.  Our tactic is to study relatively simple time-independent states called rolls and compare heat transport by these rolls with that of turbulent convection.  These steady rolls are not typically seen in large-Rayleigh-number simulations or experiments because they are dynamically unstable.  Nonetheless, they are part of the global attractor for the infinite-dimensional dynamical system defined by Rayleigh’s model, and recent results suggest that steady rolls may be one of the key coherent states comprising the ‘backbone’ of turbulent convection.  The new numerical technique proposed here pushes the computations of steady solutions much further up to Rayleigh number 1014, yielding clear asymptotic scalings for Rayleigh–Bénard convection between no-slip boundaries.  We observe that rolls of the horizontal periods that maximize the heat flux at each Rayleigh number display classical scaling asymptotically.  Moreover – and perhaps somewhat surprisingly – aspect ratio optimized steady convection rolls transport more heat than turbulent experiments or simulations at similar parameters.

Joint work with Charles R. Doering (University of Michigan, USA) and David Goluskin (University of Victoria, Canada).

Prof. Doering's homepage:

Dr. Wen's homepage:

Speaker: Prof. Xuerui Mao, Beijing Institute of Technology, Beijing, China

Date/Time: Friday, 11th June 2021

Title: Assimilation of fluid flow data.

Abstract: Data assimilation has grown to be a significant branch of fluid mechanics. In model based assimilation, considering the measured wall shear stress in a flat plate flow as the input, the incoming free-stream turbulence can be traced. Subsequently, a large part of the overall flow over the plate can be recovered and the development to the laminar-turbulence transition stage can be predicted. In data based assimilation, flow fields from various sources with various accuracy can be merged in a Gaussian Regression scheme to combine the merit of each individual set of data and mitigate their drawbacks. Here we consider the experimental data, commonly regarded as accurate but sparse, and the simulation data, which is dense but (sometimes!) inaccurate. By merging spatially and temporally discontinuous experimental data and continuous simulation one, we obtain a continuous high-fidelity set of data, shedding lights to a new relationship between experiments and simulations: rather than using one to validate the other, they can be combined! The same idea is then applied to merge DNS, LES and RANS data in an airfoil flow, aiming at using a small set of expensive and accurate data to tune the cheap and dirty one.

Speaker: Prof. Jan Kleissl, University of California, San Diego, USA

Date/Time: Thursday, 10th June 2021, 9:00 am (GMT+8)

Title: Urban Microclimatology: Implications of Realistic Urban Heating on Wind Flow and Dispersion

Abstract:As urbanization progresses, microclimate modifications are also aggravated, and more comprehensive and advanced methods are required to analyze the increasing environmental concerns. Among various factors that alter urban environments from undisturbed climates, street level air pollution due to vehicular exhausts is of major concern and is significantly affected by atmospheric motion and stability. Thermal forcing is shown to play an important role in determining flow patterns and pollutant dispersion in built environments, yet numerical studies of dispersion at microscale in urban areas are limited to simplified and uniform thermal conditions and the analyses on the effect of realistic surface heating are scarce.

To address this shortcoming, a detailed indoor-outdoor building energy model is employed to compute heat fluxes from street and building surfaces, which are then used as boundary conditiion for a Large-Eddy Simulation model. In comparison with previous studies, our model considers the transient non-uniform surface heating caused by solar insolation and inter-building shadowing, while coupling the indoor-outdoor heat transfer, flow field and passive pollution dispersion. Series of fluid flow and thermal field simulations are then performed for an idealized, compact mid-rise urban environment, and the pollution dispersion as well as turbulent exchange behavior in and above buildings are investigated. Additionally, a potentially universal characterization method of the flow field under realistic surface heating is evaluated, which aims to expand the results into a wider range of scenarios and investigate the potential correlations for various parameters of interest.

Prof. Kleissl's homepage:

Speaker: Prof. Demetrios Papageorgiou, Imperial College London, U.K.

Date/Time: Tuesday, 8th June 2021, 6:30 pm (GMT+8)

Title: Waves on the Microscale: Order, Chaos and its Control

Abstract:I will give an overview of the type of mathematics that needs to be invoked to study nonlinear waves in small scale geometries. Applied mathematicians are very familiar with large scale waves, such as water waves, and the activities that emanate from familiar models like the celebrated Kortweg de-Vries equation (a google search of “Kortweg de-Vries” comes up with 650,000 hits!). At large scales things are gravity driven and viscosity plays a secondary role and can be ignored. On the microscale, however, gravity’s gravity is typically diminished and viscosity rules. Interfaces between immiscible fluids (i.e. waves)  are quite happy to stay uniform and trundle along in their viscous morass. To do engineering on the microscope we need to drive them out of their equilibrium. One way to do this is by using external electric or magnetic fields, and I will begin with an overview of the mathematical models that emerge from such interventions - they involve a crucial coupling between the Navier-Stokes equations and the Maxwell equations in the right limit. The result is a host of PDEs that are derived asymptotically. Interestingly, these PDEs can produce chaotic solutions (we have rigorous proofs of this) even at zero Reynolds numbers. After deriving some of the models I will present computations of their solutions (mostly in the form of movies) and also address theoretically the problem of control and optimal control of such systems showing that this is possible and opens a gateway to useful physical exploitations.

Prof. Papageorgiou's homepage:

Speaker: Dr. Louis-Alexandre Couston, Université de Lyon, France

Date/Time: Friday, 4th June 2021, 3:30 pm (GMT+8)

Title: Subglacial hydrodynamics. Topography of ice-water interfaces.

Abstract:This talk will discuss two research topics related to ice-ocean interactions. The first topic will focus on the 400 subglacial lakes trapped beneath the Antarctic ice sheet, which are extreme, isolated, yet viable habitats for microbial life. The physical conditions within subglacial lakes are critical to evaluating how and where life may best exist. In this talk, I will demonstrate that Earth’s geothermal flux provides efficient stirring of Antarctic subglacial lake water. I will show that most lakes are in a regime of vigorous turbulent vertical convection, enabling suspension of spherical particulates with diameters up to 36 micrometers, which is essential for biome support within the water column. The second part of the talk will discuss our recent effort to model ice-ocean interactions explicitly. We have derived a phase-field model, which can be used to simulate the turbulent dynamics of water and the diffusion of heat in ice layers simultaneously, enabling to track the movement of the ice-ocean interface due to phase changes. I will show that a turbulent shear flow promotes the spontaneous generation of channels and keels in the ice aligned with the direction of the mean flow and discuss some of the implications of our work for polar ocean modelling.

Speaker: Prof. George Haller, ETH Zurich, Switzerland

Date/Time: Thursday, 3rd June 2021, 4:00 pm (GMT+8)

Title: Material Barriers to the Transport of Momentum and Vorticity in Turbulence

Abstract:I will give an overview of the type of mathematics that needs to be invoked to study nonlinear waves in small scale geometries. Applied mathematicians are very familiar with large scale waves, such as water waves, and the activities that emanate from familiar models like the celebrated Kortweg de-Vries equation (a google search of “Kortweg de-Vries” comes up with 650,000 hits!). At large scales things are gravity driven and viscosity plays a secondary role and can be ignored. On the microscale, however, gravity is typically diminished and viscosity rules. Interfaces between immiscible fluids (i.e. waves) are quite happy to stay uniform and trundle along in their viscous morass. To do engineering on the microscope we need to drive them out of their equilibrium. One way to do this is by using external electric or magnetic fields, and I will begin with an overview of the mathematical models that emerge from such interventions - they involve a crucial coupling between the Navier-Stokes equations and the Maxwell equations in the right limit. The result is a host of PDEs that are derived asymptotically. Interestingly, these PDEs can produce chaotic solutions (we have rigorous proofs of this) even at zero Reynolds numbers. After deriving some of the models I will present computations of their solutions (mostly in the form of movies) and also address theoretically the problem of control and optimal control of such systems showing that this is possible and opens a gateway to useful physical exploitations.

Prof. Haller's homepage:

Speaker: Prof. Carlo L. Bottasso, TUM, Germany

Date/Time: Wednesday, 2nd June 2021, 4:00 pm (GMT+8)

Title: Understanding and controlling wind farm flows

Abstract:Wakes produced by upstream wind turbines have a profound influence on the performance of downstream machines. In fact, compared to clean isolated conditions, waked turbines experience a lower power output and increased loading, which in turn create cascading effects on operation & maintenance (O&M) and lifetime. Understanding and affecting wakes are extremely challenging scientific problems with very practical and concrete implications clearly felt by industry. Probably one of the most direct indications of the impact of wakes outside of the scientific literature is given by the press announcement issued in October 2019 by Ørsted (formerly DONG), the largest energy company in Denmark. In this striking announcement, Ørsted warned investors that it was not able to meet its long-term financial targets because “... of the negative impact … across our asset portfolio of … wake effects”. In addition, Ørsted stated that “… wake effects is likely to be an industry-wide issue”. This announcement had a major impact on the scientific and technical community, and sounds as a wake-up call: wake effects are one of the main priorities that need to be faced in the field of wind energy.

However, the effects of wakes go well beyond power capture and loading. In fact, with an increased penetration of wind in the energy mix, it has become necessary for wind energy systems to provide increased flexibility and services to the grid, including active power control, the provision of reserves, and the integration with storage and other power generation units. Here again, understanding and controlling wakes plays a central role in the ability to deliver such services, which build on complex behaviors such as maintaining enough reserves to hedge against wind fluctuations, or distributing fatigue damage and/or actuator duty cycle according to the status of the individual assets and their components.

In this talk we will review the recent progress in the understanding and modeling of wakes, and the latest achievements in the field of wind farm flow control. We will take the opportunity offered by some of these topics to present highlights from the work developed by the Wind Energy Institute at TUM, spanning from to digital technologies for smart operation of turbines and farms, to validation and testing.

Prof. Bottasso's homepage:

Speaker: Prof. Mohamed Farhat, EPFL, Switzerland

Date/Time: Thursday, 27th May 2021, 3:00 pm (GMT+8)

Title: On cavitation phenomenon: From single bubble dynamics in still liquid to cavitation in turbulent flows

Abstract:The cavitation phenomenon is an issue of a long-lasting interest because of the powerful phenomena associated with the collapse of vapor bubbles. In hydraulic machinery, cavitation is always associated with severe erosion and drop in hydrodynamic performances. However, if tuned properly, cavitation can be useful in a variety of application, such as cleaning, food processing and biomedicine. In the present lecture, I will give an overview of the research performed at EPFL on the cavitation phenomenon. I will show how the case of a single bubble dynamics reveals a rich physics and let us better understand the extraordinary power of collapsing bubbles. I will then present some results related to cavitation in flowing water around a hydrofoil. I will focus on the tip vortex cavitation and the role of the gas content on the inception and development of such cavitation. I will present some promising techniques for flow control that we have developed for the mitigation of tip vortex cavitation.

 Prof. Farhat's homepage:

Speaker: Prof. Genta Kawahara, Osaka University, Japan

Date/Time: Tuesday, 25th May 2021, 10:00 am (GMT+8)

Title: Ultimate heat transfer in convective and sheared turbulence

Abstract:Direct numerical simulations have been performed for turbulent heat transfer in thermal convection and shear flow between parallel permeable walls, on which the transpiration velocity is assumed to be proportional to the local pressure fluctuations (Jimenez et al. 2001 J. Fluid Mech. 442, 89-117). Turbulent heat transfer has been found to be substantially enhanced by the appearance of large-scale turbulence structures (large-scale thermal plumes in convection or large-scale spanwise rolls in shear flow) arising from the wall permeability. At high Rayleigh numbers or high Reynolds numbers we have achieved the ultimate heat transfer represented by a wall heat flux being independent of thermal conductivity, although the heat transfer on the wall is dominated by thermal conduction. The key to the achievement of the ultimate heat transfer is interpreted in terms of significant heat transfer enhancement by large-scale intense turbulence with the length scale of the order of the wall distance and with the velocity scale comparable to the buoyancy-induced terminal velocity in convection or the bulk-mean velocity in shear flow without flow separation from the permeable walls.

Papers in support of Prof. Kawahara's webinar:

Prof. Kawahara's homepage:

Speaker: Prof. Sjoerd W. Rienstra, Eindhoven University of Technology, Netherlands

Date/Time: Thursday, 20th May 2021, 3:00 pm (GMT+8)

Title: Sound Propagation in Shear Flow – Adiabatic Invariants of Slowly Varying Modes

Abstract:Adiabatic invariants are the holy grail in a WKB analysis of waves in a slowly varying medium. If one exists, it serves as an exact integral for the slowly varying mplitude of the wave. This is no exception for acoustic modes in a slowly varying duct with slowly varying mean flow.

Adiabatic invariants are invariants under slow variation, not any variation. Their existence ensues sometimes, but not only, from the more stringent conservation of energy. Acoustic energy in mean flow is not always conserved: it is conserved in potential flow, but not in vortical (i.e. shear) flow where the acoustic field exchanges energy with the mean flow. Adiabatic invariants are therefore common for modes in slowly varying potential flows, but so far unknown in sheared flows.

We found that: (i) in 2D shear flow the modes satisfy in general an incomplete adiabatic invariant; (ii) this reduces to a complete one for linear shear flow. This result makes the WKB approximation for a mode in a slowly varying duct almost as simple as the solution for a mode in a straight duct.

Papers in support of Prof. Rienstra's webinar:

Prof. Rienstra's homepage:

Speaker: Prof. Neil J. Balmforth, University of British Columbia, Canada.


Title: Declined.

Abstract: Declined.

Prof. Neil J. Balmforth: