Showing papers on "Vortex published in 1994"

Vortical structure in the wake of a transverse jet

Abstract: Structural features resulting from the interaction of a turbulent jet issuing transversely into a uniform stream are described with the help of flow visualization and hot-wire anemometry. Jet-to-crossflow velocity ratios from 2 to 10 were investigated at crossflow Reynolds numbers from 3800 to 11400. In particular, the origin and formation of the vortices in the wake are described and shown to be fundamentally different from the well-known phenomenon of vortex shedding from solid bluff bodies. The flow around a transverse jet does not separate from the jet and does not shed vorticity into the wake. Instead, the wake vortices have their origins in the laminar boundary layer of the wall from which the jet issues. It is argued that the closed flow around the jet imposes an adverse pressure gradient on the wall, on the downstream lateral sides of the jet, provoking 'separation events’ in the wall boundary layer on each side. These result in eruptions of boundary-layer fluid and formation of wake vortices that are convected downstream. The measured wake Strouhal frequencies, which depend on the jet-crossflow velocity ratio, match the measured frequencies of the separation events. The wake structure is most orderly and the corresponding wake Strouhal number (0.13) is most sharply defined for velocity ratios near the value 4. Measured wake profiles show deficits of both momentum and total pressure.

Vorticity and turbulence

Abstract: This is an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The first three chapters of the book constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; and a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible.

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Abstract: Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack

Abstract: Mathematical modeling of unsteady aerodynamic forces and moments plays an important role in aircraft dynamics investigation and stability analysis at high angles of attack. In this article the state-space representation of aerodynamic forces and moments for unsteady aircraft motion is proposed. Consideration of separated flow about an airfoil and flow with vortex breakdown about a slender delta wing gives the base for mathematical modeling using internal variables describing the flow state. Coordinates of separation points or vortex breakdown can be taken, e.g., as internal state-space variables. These variables are governed by some differential equations. Within the framework of the proposed mathematical model it is possible to achieve good agreement with different experimental data obtained in water and wind tunnels. These high angle-of-attack experimental results demonstrate considerable dependence of aerodynamic loads on motion time history.

Control of an axisymmetric jet using vortex generators

Abstract: The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter‐rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular‐shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180° apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four ‘‘fingers,’’ resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream ‘‘pressure hill,’’ generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.

Geometrical barriers in high-temperature superconductors.

Abstract: A theoretical description of vortex dynamics in thin flat samples is derived and is found to compare favorably with experimental results. In perpendicular applied magnetic field the vortex penetration is delayed significantly due to the presence of a potential barrier of geometrical origin. This novel geometrical barrier effect results in hysteretic magnetization and in the existence of an irreversibility line in the absence of bulk pinning. Among the unique characteristics of the barrier are a vortex concentration in the center of the sample and a zero-field peak in the magnetization loops.

Electrical turbulence in three-dimensional heart muscle

Abstract: Rotors or vortex action potentials with a diameter of about 1 centimeter and a rotation period of about 0.1 second occur in normal myocardium just before transition to fibrillation, a disorderly pattern of action potential propagation. Numerical models and corresponding mathematical analysis have recently suggested candidate mechanisms, all two-dimensional, for this transition from periodic electrical activity to something resembling turbulence. However, comparably recent experiments unanimously show that rotors, and the spiral waves they radiate, remain stably periodic in two-dimensional myocardium. This seeming paradox suggests a transition mediated through disorderly dynamics of the electrical vortex in three dimensions, as a "vortex filament."

Vortex Interactions with Walls

Abstract: Situations where an effectively irrotational freest ream contains regions of concentrated vorticity are common in external aerodynamics, where vortices are known to play an important role in the flight of modern helicopters (Carr 1988) and aircraft (Cunningham 1989, Mabey 1989). Vortices may arise as a consequence of shedding from some upstream surface or near certain three-dimensional boundary geometries that act to promote vortex formation. Examples of the former type of vortex gen­ eration include: 1. vortices that trail from the tips of airfoils (Harvey & Perry 1971) and control surfaces on submarines (Lugt 1983), 2. transverse vortices shed from maneuvering airfoil surfaces and helicopter blades in a process known as dynamic stall (McCroskey 1982, Francis & Keesee 1985, Carr 1988), and 3. shedding from stationary obstacles. Geometry-induced creation can occur in any situation where a flow along a wall approaches a surface-mounted obstacle; examples include: 1. airframe features such as wing/body junctions, 2. conning towers on submarines, and 3 . computer chips mounted on electrical circuit boards. Similar geometries are en-

On the motion of air through the stratospheric polar vortex

Abstract: Trajectory calculations using horizontal winds from the U.K. Meteorological Office data assimilation system and vertical velocities from a radiation calculation are used to simulate the three-dimensional motion of air through the stratospheric polar vortex for Northern Hemisphere (NH) and Southern Hemisphere (SH) winters since the launch of the Upper Atmosphere Research Satellite. Throughout the winter, air from the upper stratosphere moves poleward and descends into the middle stratosphere. In the SH lower to middle stratosphere, strongest descent occurs near the edge of the polar vortex, with that edge defined by mixing characteristics. The NH shows a similar pattern in late winter, but in early winter strongest descent is near the center of the vortex, except when wave activity is particularly strong. Strong barriers to latitudinal mixing exist above about 420 K throughout the winter. Below this, the polar night jet is weak in early winter, so air descending below that level mixes between pola...

Stretched vortices - the sinews of turbulence; large-Reynolds-number asymptotics

Abstract: A large-Reynolds-number asymptotic theory is presented for the problem of a vortex tube of finite circulation [Gcy ] subjected to uniform non-axisymmetric irrotational strain, and aligned along an axis of positive rate of strain. It is shown that at leading order the vorticity field is determined by a solvability condition at first-order in e = 1/R[Gcy ] where R[gcy ] = [gcy ]/ν. The first-order problem is solved completely, and contours of constant rate of energy dissipation are obtained and compared with the family of contour maps obtained in a previous numerical study of the problem. It is found that the region of large dissipation does not overlap the region of large enstrophy; in fact, the dissipation rate is maximal at a distance from the vortex axis at which the enstrophy has fallen to only 2.8% of its maximum value. The correlation between enstrophy and dissipation fields is found to be 0.19 + O(e2). The solution reveals that the stretched vortex can survive for a long time even when two of the principal rates of strain are positive, provided R[gcy ] is large enough. The manner in which the theory may be extended to higher orders in e is indicated. The results are discussed in relation to the high-vorticity regions (here described as ‘sinews’) observed in many direct numerical simulations of turbulence.

Active vorticity control in a shear flow using a flapping foil

Abstract: It is shown experimentally that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow.First, flow-visualization experiments are conducted in Kalliroscope fluid at Reynolds number 550. A foil is placed in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process. The foil performs a heaving and pitching oscillation at a frequency close to the Strouhal frequency of the cylinder, while cylinder and foil also move forward at constant speed. By varying the phase of the foil oscillation, three basic interaction modes are identified. (i) Formation of a street of pairs of counter-rotating vortices, each pair consisting of one vortex from the initial street of the cylinder and one vortex shed by the foil. The width of the wake is then substantially increased. (ii) Formation of a street of vortices with reduced or even reverse circulation compared to that of oncoming cylinder vortices, through repositioning of cylinder vortices by the foil and interaction with vorticity of the opposite sign shed from the trailing edge of the foil. (iii) Formation of a street of vortices with circulation increased through merging of cylinder vortices with vortices of the same sign shed by the foil. In modes (ii) and (iii) considerable repositioning of the cylinder vortices takes place immediately behind the foil, resulting in a regular or reverse Karman street. The formation of these three interaction patterns is achieved only for specific parametric values; for different values of the parameters no dominant stable pattern emerges.Subsequently, the experiments are repeated in a different facility at larger scale, resulting in Reynolds number 20000, in order to obtain force and torque measurements. The purpose of the second set of experiments is to assess the impact of flow control on the efficiency of the oscillating foil, and hence investigate the possibility of energy extraction. It is found that the efficiency of the foil depends strongly on the phase difference between the oscillation of the foil and the arrival of cylinder vortices. Peaks in foil efficiency are associated with the formation of a street of weakened vortices and energy extraction by the foil from the vortices of the vortex street.

Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability

Abstract: Nonlinear stability of a model swept-wing boundary layer, subject to crossflow instability, is investigated by numerically solving the governing partial differential equations The three-dimensional boundary layer is unstable to both stationary and travelling crossflow disturbances Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble quite well the surface oil-flow visualizations in swept-wing experiments Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc) are also captured in these calculations Nonlinear interaction of the stationary and travelling waves is also studied When initial amplitude of the stationary vortex is larger than the travelling mode, the stationary vortex dominates most of the downstream development When the two modes have the same initial amplitude, the travelling mode dominates the downstream development owing to its higher growth rate It is also found that, prior to laminar/turbulent transition, the three-dimensional boundary layer is subject to a high-frequency secondary instability, which is in agreement with the experiments of Poll (1985) and Kohama, Saric & Hoos (1991) The frequency of this secondary instability, which resides on top of the stationary crossflow vortex, is an order of magnitude higher than the frequency of the most-amplified travelling crossflow mode

Transport out of the lower stratospheric Arctic vortex by Rossby wave breaking

Abstract: The fine-scale structure in lower stratospheric tracer transport during the period of the two Arctic Airborne Stratospheric Expeditions (January and February 1989; December 1991 to March 1992) is investigated using contour advection with surgery calculations These calculations show that Rossby wave breaking is an ongoing occurrence during these periods and that air is ejected from the polar vortex in the form of long filamentary structures There is good qualitative agreement between these filaments and measurements of chemical tracers taken aboard the NASA ER-2 aircraft The ejected air generally remains filamentary and is stretched and mixed with midlatitude air as it is wrapped around the vortex This process transfers vortex air into midlatitudes and also produces a narrow region of fine-scale filaments surrounding the polar vortex Among other things, this makes it difficult to define a vortex edge The calculations also show that strong stirring can occur inside as well as outside the vortex

On particle adhesion and removal mechanisms in turbulent flows

Abstract: Particle removal mechanisms in a turbulent flow are examined and two models which are based on the structure of turbulence near wall flow are described. The theory of critical moment, along with the sliding detachment models, is used, and the effects of the near-wall coherent vortices, as well as turbulence burst/inrush phenomena, are included. The down sweep flow patterns are modeled as viscous stagnation point flows. The hydrodynamic force and torque acting on a spherical particle attached to a wall are used in the model developments. For different adhesion models, the minimum critical shear velocities for removing particles of different sizes are evaluated. The model predictions are compared with the available data and discussed.

An Alternative Form for Potential Vorticity

Abstract: A form of potential vorticity is described that has conservation properties similar to those of Ertel's potential vorticity (EPV) but removes the exponential variation with height displayed by EPV. This form is thus more suitable for inspecting vertical cross sections of potential vorticity and for use (with potential temperature) as a quasi-conserved coordinate in the analysis of chemical constituent data.

Coherent structures in rotating three-dimensional turbulence

Abstract: Numerical simulations investigating the formation and stability of quasi-twodimensional coherent vortices in rotating homogeneous three-dimensional flow are described. In a numerical study of shear flows Lesieur, Yanase & Metais (1991) found that cyclones (respectively anticyclones) with 1~02~1 - 0(2R), where (02D is the vorticity and Q is the rotation rate, are stabilized (respectively destabilized) by the rotation. A study of triply periodic pseudo-spectral simulations (64’) was undertaken in order to investigate the vorticity asymmetry in homogeneous turbulence. Specifically, we examine (i) the possible three-dimensionalization of initially two-dimensional vortices and (ii) the emergence of quasi-two-dimensional structures in initially-isotropic threedimensional turbulence. Direct numerical simulations of the Navier-Stokes equations are compared with large-eddy simulations employing a subgridscale model based on the second-order velocity structure function evaluated at the grid separation and with simulations employing hyperviscosity. Isolated coherent two-dimensional vortices, obtained from a two-dimensional decay simulation, were superposed with a low-amplitude three-dimensional perturbation, and used to initialize the first set of simulations. With R = 0, a threedimensionalization of all vortices was observed. This occurred first in the small scales in conjunction with the formation of longitudinal hairpin vortices with vorticity perpendicular to that of the initial quasi-two-dimensional flow. In agreement with centrifugal stability arguments, when 2R = [cuZD],,,,, a rapid destabilization of anticyclones was observed to occur, whereas the initial two-dimensional cyclonic vortices persisted throughout the simulation. At larger Q, both cyclones and anticyclones remained two-dimensional, consistent with the Taylor-Proudman theorem. A second set of simulations starting from isotropic three-dimensional fields was initialized by allowing a random velocity field to evolve (52 = 0) until maximum energy dissipation. When the simulations were continued with 252 = [o . n],,,,, /Q, the three-dimensional flow was observed to organize into two-dimensional cyclonic vortices. At larger Q, two-dimensional anticyclones also emerged from the initially-isotropic flow. The consequences for a variety of industrial and geophysical applications are clear. For quasi-two-dimensional eddies whose characteristic circulation times are of the order of Q-’, rotation induces a complete disruption of anticyclonic vortices, while stabilizing cyclonic ones.

Unsteady, Turbulent Convection into a Homogeneous, Rotating Fluid,with Oceanographic Applications

Abstract: Turbulent convection into a homogeneous, rotating fluid has been generated in laboratory tanks, for both laterally confined and unconfined domains. When a given experiment was in a solid-body rotation, a source located at the top surface of the water column was activated to release denser saltwater into the underlying, less-dense fluid of total depth H. As a result, a downward propagating 3D turbulent front was formed. Eventually, at a transition depth zc, rotational effects dominated the turbulence and many quasi-2D vortices were generated, which then penetrated downward beneath the upper 3D turbulent layer. Measurements in the confined experiments gave zc ≈ (12.7 ± 1.5) (B0/f3)1/2; the mean diameter (Dv) of the quasi-2D vortices as Dv≈(15.0±1.5) (B0/f3)1/2, their downward speed of propagation (uc) as uc ≈ (1.0 ± 0.1) (B0/f)1/2, and the maximum swirl velocity (uv) of an individual vortex as uv ≈ (4.0 ± 0.4)(B0/f)1/2 (where B0 is the surface buoyancy flux and f the Coriolis parameter). All are in...

Modification of the Euler equations for ``vorticity confinement'': Application to the computation of interacting vortex rings

Abstract: A new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admit solutions that consist of Lagrangian‐like confined vortical regions, or covons, in the shape of two‐dimensional (2‐D) vortex ‘‘blobs’’ and three‐dimensional (3‐D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. The discretized Euler equations with the extra term ca...

On Chaplygin's investigations of two-dimensional vortex structures in an inviscid fluid

Abstract: This paper describes exact solutions of two-dimensional vortex structures that were published by Chaplygin (1899, 1903) at the turn of the last century, which seem to have escaped the attention of later investigators in this field. Chaplygin's solutions include that of an elliptical patch of uniform vorticity in an exterior field of pure shear and that of a (symmetric or non-symmetric) dipolar vortex with a continuous distribution of vorticity translating steadily along a straight path. In addition, a solution is presented for a non-symmetric vortex dipole moving along a circular trajectory. A concise account of Chaplygin's solutions is given, complemented by a more detailed analysis of some of their relevant properties.

Warm Core Vortex Amplification over Land

Abstract: A convectively generated mesoscale vortex that was instrumental in initiating and organizing five successive mesoscale convective systems over a period of three days is documented. Two of these convective systems were especially intense and resulted in widespread heavy rain with localized flooding. Based upon radar and satellite data, the detectable size of the vortex became much larger following the strong convective developments, nearly tripling its initial diameter over its three-day life cycle. During nighttime, when convection typically intensified within the vortex, movement of the system tended to slow. Following dissipation of the convection in the morning, the daytime movement accelerated. Cross sections of potential vorticity taken through the vortex center clearly show a maximum at midlevels and a well-defined minimum directly above. The vortex and the potential vorticity maximum were essentially colocated and the system was nearly axisymmetric in the vertical. Over the three-day life ...

Numerical investigations of transitional H2/N2 jet diffusion flames

Abstract: A numerical method for accurate simulation of the time and spatial characteristics of the inner and outer vortex structures in transitional H 2 /N 2 jet diffusion flames is presented. The direct numerical simulation, incorporating buoyancy, a simple one-step chemistry model, coefficients that depend on temperature and species concentration, is described in detail. The species and energy equations are simplified by introducing two conserved scalars β 1 and β 2 and by assuming that the Lewis number of the flow is equal to unity. An implicit, third-order-accurate, upwind numerical scheme having very low numerical diffusion is used to simulate the inner small-scale structures and the outer large-scale structures simultaneously

Annual Review of Fluid Mechanics

Abstract: This book covers the following topics: recent developments in three dimensional and unsteady turbulence boundary-layer computations; flows far from equilibrium via molecular dynamics; physics of convention-solidification interaction; the continental shelf bottom boundary layer; gravity currents in rotating systems; strange attractors in fluids: another view; eddies, waves, circulation, and mixing: statistical geofluid mechanics; regular and mach reflection of shock waves; ship propellers; coherent structures; the critical layer and stability; general circulation of the oceans; characteristic-based schemes for the euler equations; vortex flows in aerodynamics; steady and unsteady boundary-layer separation; and wind wave prediction.

Design of optimum propellers

Abstract: Improvements have been made in the equations and computational procedures for design of propellers and wind turbines of maximum efficiency. These eliminate the small angle approximation and some of the light loading approximations prevalent in the classical design theory. An iterative scheme is introduced for accurate calculation of the vortex displacement velocity and the flow angle distribution. Momentum losses due to radial flow can be estimated by either the Prandtl or Goldstein momentum loss function. The methods presented here bring into exact agreement the procedure for design and analysis. Furthermore, the exactness of this agreement makes possible an empirical verification of the Betz condition that a constant-displacement velocity across the wake provides a design of maximum propeller efficiency. A comparison with experimental results is also presented.

Quasi-two-dimensional dynamics of plasmas and fluids.

Abstract: In the lowest order of approximation quasi‐two‐dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa–Mima (CHM) equation. In contrast to the two‐dimensional Navier–Stokes equation, the CHM equation admits ‘‘shielded vortex solutions’’ in a homogeneous limit and linear waves (‘‘Rossby waves’’ in the planetary atmosphere and ‘‘drift waves’’ in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in nonideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and non...

Experiments on the instabilities of a swirling jet

Abstract: Instabilities present in a swirling jet in the Reynolds number range from 20 000 to 60 000 and a nominal swirl number of 05 were studied experimentally, using smoke visualization, hot‐wire anemometry and acoustic excitation Flow visualization photographs of the natural jet show vortex breakdown at the core and rolling up of the shear layer around the jet into weak, irregular, large‐scale organized structures When forced by acoustic excitation these structures became energetic and periodic Axisymmetric and helical instability waves in the Strouhal number range 075 to 15 were excited and their evolution along the axial direction were measured from velocity spectra and ensemble averaged measurements Compared to a nonswirling jet, the overall growth of the instability waves is considerably smaller, and vortex pairing is suppressed in a swirling jet However, the overall spread and mass entrainment rates are higher in the latter Measurements of the mean velocity components and turbulence fluctuations show that the vortex breakdown affects the axial velocity distribution and rapidly replaces the potential core with a large amount of turbulence Upon interacting with the vortex breakdown, the shear layer along the jet periphery loses its organized structure and, in general, ‘‘random turbulence’’ follows

Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows

Abstract: A complex Stokes flow has several cells, is subject to bifurcation, and its velocity field is, with rare exceptions, only available from numerical computations. We present experimental and computational studies of two new complex Stokes flows: a vortex mixing flow and multicell flows in slender cavities. We develop topological relations between the geometry of the flow domain and the family of physically realizable flows; we study bifurcations and symmetries, in particular to reveal how the forcing protocol's phase hides or reveals symmetries. Using a variety of dynamical tools, comparisons of boundary integral equation numerical computations to dye advection experiments are made throughout. Several findings challenge commonly accepted wisdom. For example, we show that higher-order periodic points can be more important than period-one points in establishing the advection template and extended regions of large stretching. We demonstrate also that a broad class of forcing functions produces the same qualitative mixing patterns. We experimentally verify the existence of potential mixing zones for adiabatic forcing and investigate the crossover from adiabatic to non-adiabatic behaviour. Finally, we use the entire array of tools to address an optimization problem for a complex flow. We conclude that none of the dynamical tools alone can successfully fulfil the role of a merit function; however, the collection of tools can be applied successively as a dynamical sieve to uncover a global optimum.

Oblique-mode breakdown and secondary instability in supersonic boundary layers

Abstract: Laminar–turbulent transition mechanisms for a supersonic boundary layer are examined by numerically solving the governing partial differential equations. It is shown that the dominant mechanism for transition at low supersonic Mach numbers is associated with the breakdown of oblique first-mode waves. The first stage in this breakdown process involves nonlinear interaction of a pair of oblique waves with equal but opposite angles resulting in the evolution of a streamwise vortex. This stage can be described by a wave–vortex triad consisting of the oblique waves and a streamwise vortex whereby the oblique waves grow linearly while nonlinear forcing results in the rapid growth of the vortex mode. In the second stage, the mutual and self-interaction of the streamwise vortex and the oblique modes results in the rapid growth of other harmonic waves and transition soon follows. Our calculations are carried all the way into the transition region which is characterized by rapid spectrum broadening, localized (unsteady) flow separation and the emergence of small-scale streamwise structures. The r.m.s. amplitude of the streamwise velocity component is found to be on the order of 4–5 % at the transition onset location marked by the rise in mean wall shear. When the boundary-layer flow is initially forced with multiple (frequency) oblique modes, transition occurs earlier than for a single (frequency) pair of oblique modes. Depending upon the disturbance frequencies, the oblique mode breakdown can occur for very low initial disturbance amplitudes (on the order of 0.001% or even lower) near the lower branch. In contrast, the subharmonic secondary instability mechanism for a two-dimensional primary disturbance requires an initial amplitude on the order of about 0.5% for the primary wave. An in-depth discussion of the oblique-mode breakdown as well as the secondary instability mechanism (both subharmonic and fundamental) is given for a Mach 1.6 flat-plate boundary layer.