Vorticity Perturbations Research Articles

Origin of the pre-tropical storm Debby (2006) African easterly wave-mesoscale convective system

The origins of the pre-Debby (2006) mesoscale convective system (MCS) and African easterly wave (AEW) and their precursors were traced back to the southwest Arabian Peninsula, Asir Mountains (AS), and Ethiopian Highlands (EH) in the vicinity of the ITCZ using satellite imagery, GFS analysis data and ARW model. The sources of the convective cloud clusters and vorticity perturbations were attributed to the cyclonic convergence of northeasterly Shamal wind and the Somali jet, especially when the Mediterranean High shifted toward east and the Indian Ocean high strengthened and its associated Somali jet penetrated farther to the north. The cyclonic vorticity perturbations were strengthened by the vorticity stretching associated with convective cloud clusters in the genesis region—southwest Arabian Peninsula. A conceptual model was proposed to explain the genesis of convective cloud clusters and cyclonic vorticity perturbations preceding the pre-Debby (2006) AEW–MCS system.

Self-limiting and regenerative dynamics of perturbation growth on a vortex column

AbstractWe study the mechanisms of centrifugal instability and its eventual self-limitation, as well as regenerative instability on a vortex column with a circulation overshoot (potentially unstable) via direct numerical simulations of the incompressible Navier–Stokes equations. The perturbation vorticity (${\boldsymbol{\omega} }^{\prime } $) dynamics are analysed in cylindrical ($r, \theta , z$) coordinates in the computationally accessible vortex Reynolds number, $\mathit{Re}({\equiv }\mathrm{circulation/viscosity} )$, range of 500–12 500, mostly for the axisymmetric mode (azimuthal wavenumber $m= 0$). Mean strain generates azimuthally oriented vorticity filaments (i.e. filaments with azimuthal vorticity, ${ \omega }_{\theta }^{\prime } $), producing positive Reynolds stress necessary for energy growth. This ${ \omega }_{\theta }^{\prime } $ in turn tilts negative mean axial vorticity, $- {\Omega }_{z} $ (associated with the overshoot), to amplify the filament, thus causing instability. (The initial energy growth rate (${\sigma }_{r} $), peak energy (${G}_{\mathit{max}} $) and time of peak energy (${T}_{p} $) are found to vary algebraically with $\mathit{Re}$.) Limitation of vorticity growth, also energy production, occurs as the filament moves the overshoot outward, hence lessening and shifting $\vert {- }{\Omega }_{z} \vert $, while also transporting the core $+ {\Omega }_{z} $, to the location of the filament. We discover that a basic change in overshoot decay behaviour from viscous to inviscid occurs at $Re\sim 5000$. We also find that the overshoot decay time has an asymptotic limit of 45 turnover times with increasing $\mathit{Re}$. After the limitation, the filament generates negative Reynolds stress, concomitant energy decay and hence self-limitation of growth; these inviscid effects are enhanced further by viscosity. In addition, the filament transports angular momentum radially inward, which can produce a new circulation overshoot and renewed instability. Energy decays at the $\mathit{Re}$ studied, but, at higher $\mathit{Re}$, regenerative growth of energy is likely due to the renewed mean shearing. New generation of overshoot and Reynolds stress is examined using a helical ($m= 1$) perturbation. Regenerative energy growth, possibly resulting in even vortex breakup, can be triggered by this new overshoot at practical $\mathit{Re}$ (${\sim }1{0}^{6} $ for trailing vortices), which are currently beyond the computational capability.

Warm Conveyor Belts in Idealized Moist Baroclinic Wave Simulations

AbstractThis idealized modeling study of moist baroclinic waves addresses the formation of moist ascending airstreams, so-called warm conveyor belts (WCBs), their characteristics, and their significance for the downstream flow evolution. Baroclinic wave simulations are performed on the f plane, growing from a finite-amplitude upper-level potential vorticity (PV) perturbation on a zonally uniform jet stream. This nonmodal approach allows for dispersive upstream and downstream development and for studying WCBs in the primary cyclone and the downstream cyclone. A saturation adjustment scheme is used as the only difference between the dry and moist simulations, which are systematically compared using a cyclone-tracking algorithm, with an eddy kinetic energy budget analysis, and from a PV perspective. Using trajectories and a selection criterion of maximum ascent, forward- and rearward-sloping WCBs in the moist simulation are identified. No WCB is identified in the dry simulation. Forward-sloping WCBs originate in the warm sector, move into the frontal fracture region, and ascend over the bent-back front, where maximum latent heating occurs in this simulation. The outflow of these WCBs is located at altitudes with prevailing zonal winds; they hence flow anticyclonically (“forward”) into the downstream ridge. In case of a slightly weaker ascent, WCBs curve cyclonically (“rearward”) above the cyclone center. A detailed analysis of the PV evolution along the WCBs reveals PV production in the lower troposphere and destruction in the upper troposphere. Consequently, WCBs transport low-PV air into their outflow region, which contributes to the formation of distinct negative PV anomalies. They, in turn, affect the downstream flow and enhance downstream cyclogenesis.

Jet formation in shock-heavy gas bubble interaction

The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analysis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pressure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.

Nonlinear Dynamics of Two Western Boundary Currents Colliding at a Gap

Abstract The nonlinear collision of two western boundary currents (WBCs) of equal transport at a gap of the western boundary is studied using a 1.5-layer reduced-gravity quasigeostrophic ocean model. It is found that, when the gap (of width 2a) is narrow, a ≤ 7.3LM (LM the Munk thickness), neither of the WBCs can penetrate into the western basin because of the restriction of the viscous force. When 7.3LM < a < 9.0LM, both WBCs penetrate into the western basin for small transport and choke for large transport. When 9.0LM ≤ a ≤ 9.6LM, the two WBCs penetrate for small transport, choke for intermediate transport, and shed eddies periodically for large transport. When a > 9.6LM, no steady choking state is found. Instead, the WBCs have only two equilibrium states: the penetrating and the periodic eddy shedding states. A Hopf bifurcation is found for a > 9.0LM. The Reynolds number (Re) of the Hopf bifurcation is sensitive to the magnitude of γ(a/LM) and the baroclinic deformation radius, being small for larger γ or deformation radius. In addition, a reverse Hopf bifurcations is identified in the decreased Re experiments, occurring at a smaller Re than that of the Hopf bifurcation. The Re of the reverse Hopf bifurcation is not sensitive to the magnitude of the baroclinic deformation radius. Hysteresis behavior of the WBCs is found for a > 9.0LM, because of the existence of the Hopf and reverse Hopf bifurcations. In between them, steady penetrating or choking states coexist with eddy-shedding states. The steady states are found to be sensitive to perturbations of relative vorticity and can transit to periodic eddy-shedding states at the forcing of a mesoscale eddy.

The Importance of the Nontraditional Coriolis Terms in Large-Scale Motions in the Tropics Forced by Prescribed Cumulus Heating

AbstractIn meteorological dynamics, the shallow-atmosphere approximation is generally used in the momentum equation, together with the “traditional approximation.” In the traditional approximation, two cosine Coriolis terms [hereafter called nontraditional Coriolis terms (NCTs)] and some metric terms are omitted. However, some studies have suggested that the omission of the NCTs may not be appropriate for conditions near the equator. Therefore, this paper investigates the effect of the NCTs on large-scale motions forced by local positive-only heating mimicking cumulus convection.The authors use the linearized quasihydrostatic equation system on an equatorial β plane. Prescribed heating is assumed to move eastward with the slow phase speed of an intraseasonal period. Results of scale analysis and numerical calculations show that differences with and without the NCTs (hereafter, contributions) exhibit the following four features. (i) Whereas contributions to horizontal divergence and vertical velocity are small, the NCTs have large effects on horizontal velocity (vertical vorticity) and perturbations of pressure, potential temperature, and density. (ii) Contributions to horizontal velocity and pressure perturbation have equivalent barotropic structure. (iii) Contributions show east–west asymmetric patterns, with large contributions appearing at the western side of the forcing. (iv) Contributions to vertical vorticity and pressure perturbation are extremely large when the meridional gradient of heating is large. These features can be comprehensively explained by the tilting of the meridional component of the planetary vorticity, which is caused by the meridional gradient of heating.

Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities

AbstractWe present an analytical model that describes the linear interaction of two successive shocks launched into a non-uniform density field. The re-shock problem is important in different fields, inertial confinement fusion among them, where several shocks are needed to compress the non-uniform target. At first, we present a linear theory model that studies the interaction of two successive shocks with a single-mode density perturbation field ahead of the first shock. The second shock is launched after the sonic waves emitted by the first shock wave have vanished. Therefore, in the case considered in this work, the second shock only interacts with the entropic and vortical perturbations left by the first shock front. The velocity, vorticity and density fields are later obtained in the space behind the second shock. With the results of the single-mode theory, the interaction with a full spectrum of random-isotropic density perturbations is considered by decomposing it into Fourier modes. The model describes in detail how the second shock wave modifies the turbulent field generated by the first shock wave. Averages of the downstream quantities (kinetic energy, vorticity, acoustic flux and density) are easily obtained either for two-dimensional or three-dimensional upstream isotropic spectra. The asymptotic limits of very strong shocks are discussed. The study shown here is an extension of previous works, where the interaction of a planar shock wave with random isotropic vorticity/entropy/acoustic spectra were studied independently. It is also a preliminary step towards the understanding of the re-shock of a fully turbulent flow, where all three of the modes, vortical, entropic and acoustic, might be present.

The 2010 Pakistan Flood and Russian Heat Wave: Teleconnection of Hydrometeorological Extremes

AbstractIn this paper, preliminary results are presented showing that the two record-setting extreme events during 2010 summer (i.e., the Russian heat wave–wildfires and Pakistan flood) were physically connected. It is found that the Russian heat wave was associated with the development of an extraordinarily strong and prolonged extratropical atmospheric blocking event in association with the excitation of a large-scale atmospheric Rossby wave train spanning western Russia, Kazakhstan, and the northwestern China–Tibetan Plateau region. The southward penetration of upper-level vorticity perturbations in the leading trough of the Rossby wave was instrumental in triggering anomalously heavy rain events over northern Pakistan and vicinity in mid- to late July. Also shown are evidences that the Russian heat wave was amplified by a positive feedback through changes in surface energy fluxes between the atmospheric blocking pattern and an underlying extensive land region with below-normal soil moisture. The Pakistan heavy rain events were amplified and sustained by strong anomalous southeasterly flow along the Himalayan foothills and abundant moisture transport from the Bay of Bengal in connection with the northward propagation of the monsoonal intraseasonal oscillation.

Three-dimensional hydrodynamic instabilities in stellar core collapses

A spherically symmetric hydrodynamic stellar core collapse under gravity is time-dependent and may become unstable once disturbed. Specifically for a homologously collapse of stellar core characterized by a polytropic exponent \Gamma=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index \gamma of perturbations can differ from \Gamma=4/3 of the general polytropic hydrodynamic background flow. Our model formulation here is more general and allows the existence of internal gravity g(-)-modes and/or g(+)-modes. Eigenvalues and eigen-functions of various oscillatory and unstable perturbation modes are computed. As studied in several specialized cases of Goldreich & Weber and of Cao & Lou, we further confirm that acoustic p-modes and surface f-modes remain stable in the current more general situations. In comparison, g(-)-modes and sufficiently high radial order g(+)-modes are unstable, leading to inevitable convective motions within the collapsing stellar interior. Unstable growths of 3D g-mode disturbances are governed dominantly by the angular momentum conservation and modified by the gas pressure restoring force. We note in particular that unstable temporal growths of 3D vortical perturbations exist even when the specific entropy distribution becomes uniform and \gamma=\Gamma=4/3. Conceptually, unstable g-modes might bear conceivable physical consequences on supernova explosions, the initial kicks of nascent proto-neutron stars (PNSs) and break-ups of the collapsing core, while unstable growths of vortical perturbations can lead to fast spins of compact objects and other relevant results.

Potential vorticity diagnosis of rapid intensification of very severe cyclone GIRI (2010) over the Bay of Bengal

The life cycle of Bay of Bengal cyclone GIRI, characterized by a rapid intensification during 36-h interval, is investigated. The cyclone under study underwent a period of explosive cyclogenesis from 0000 UTC 21 October to 1200 UTC 22 October 2010. During this period, the sea level pressure minimum at the center of cyclone dropped by 52 hPa. European Centre for Medium Range Weather Forecasts (ECMWF) model data is used to perform the analysis of Q-vectors, K-Index and potential vorticity (PV) perturbation in order to diagnose the life cycle of this unusual cyclone. The analysis reveals that during the period of explosive development, the 500–700 hPa column-averaged Q-vector convergence (regions of quasi-geostrophic forcing for ascent) directly above the surface cyclone had strengthened, which in turn affected the lower to middle-tropospheric ascent and associated surface cyclogenesis. The analysis also reveals that the presence of lower-tropospheric cyclogenetic forcing in the environment, characterized by reduced static stability as measured by very high values of the K-Index produced a burst of heavy precipitation during the development stage of the cyclone. The associated latent heat release produced a substantial diabatic positive PV anomaly in the middle and lower troposphere that caused lower-tropospheric height falls associated with the explosive cyclogenesis. Thus, diabatic consequence of the latent heat release fueled the explosive development of the cyclone. The intensification mechanism of the cyclone occurred in two stages. A diabatically generated lower-tropospheric positive PV anomaly dominated the rapid intensification stage after initial triggering by a positive upper-level PV anomaly. A limited verification of ECMWF model shows that the model could predict the rapid intensification of the cyclone to a large extent and landfall near observed landfall point and time. It predicted lowest central pressure of 970.5 hPa 24-h in advance with landfall near 19.7°N and 93.7°E around 1400 UTC 22 October 2010 against the lowest estimated central pressure of 950 hPa and observed landfall near 20.0°N and 93.5°E around 1400 UTC 22 October 2010.

Ensemble prediction of Mediterranean high-impact events using potential vorticity perturbations. Part II: Adjoint-derived sensitivity zones

In Part I of this work, an ensemble prediction system (EPS) based on different combinations of model physical parameterizations was compared against another ensemble based on perturbing initial and boundary conditions through the Potential Vorticity (PV) field. This comparison was done for western Mediterranean cyclonic situations associated with high-impact weather phenomena such as heavy rain and showed a better performance of the PV-perturbed ensemble over the more traditional multiphysics approach. The current study extends the comparison to another ensemble based on perturbing initial and boundary conditions through the PV field but guided by the MM5 adjoint derived sensitivity zones (PV-adjoint) instead of by the three-dimensional PV features showing intense values and gradients as was done in Part I (PV-gradient).The PV-adjoint and PV-gradient EPSs perturb specific areas of the cyclonic development using a PV error climatology that typifies PV errors in the initial and boundary conditions to provide the appropriate error range. The non-hydrostatic MM5 mesoscale model nested in the ECMWF forecast fields is used to provide all predictions.For the studied cases, 19 cyclonic events associated with heavy rain, the verification results show that both PV-perturbed are skillful, the PV-gradient being the best. Therefore, for our testbed, the extra computational cost of running the MM5 adjoint model does not provide a significant ensemble skill improvement.

Ensemble prediction of Mediterranean high-impact events using potential vorticity perturbations. Part I: Comparison against the multiphysics approach

The western Mediterranean is a very cyclogenetic area and many of the cyclones developed over this region are associated with high-impact weather phenomena that affect the society of the coastal countries. Two ensemble prediction systems (EPSs) based on multiphysics and perturbed initial and boundary conditions (IBC) are designed in order to improve the forecast of these heavy rain episodes. The MM5 mesoscale model nested in the ECMWF forecast fields provides the simulations, run at 22.5 km resolution for a two-day period. The multiphysics ensemble combines different model physical parameterization schemes while the other ensemble perturbs the initial state and boundary forcing of the model with the aid of a PV inversion scheme. A PV error climatology derived from the large-scale fields allows to perturb the ECMWF PV fields using the appropriate error range. The verification procedure indicates that even though both EPSs are skillful, the perturbed IBC ensemble is more proficient than the multiphysics EPS for the 19 Mediterranean cyclonic events with heavy rain considered in the study. Therefore the results show a more dominant role of the uncertainties in the initial and boundary conditions than the model error, although both of them contribute significantly to improve the predictability of Western Mediterranean high impact weather situations.

Nonlinear transient growth in a vortex column

Growth of optimal transient perturbations to an Oseen vortex column into the nonlinear regime is studied via direct numerical simulation (DNS) for Reynolds number, Re (≡ circulation/viscosity), up to 10000. An optimal bending-wave transient mode is obtained from linear analysis and used as the initial condition. (DNS of a vortex column embedded in finer-scale turbulence reveals that optimal modes are preferentially excited during vortex–turbulence interaction.) Tilting of the optimal mode's radial vorticity perturbation into the azimuthal direction and its concomitant stretching by the column's strain field produces positive Reynolds stress, hence kinetic energy growth. Modes experiencing the largest growth are those with initial vorticity localized at a ‘critical radius’ outside the core, such that this perturbation vorticity resonantly induces core waves. Resonant forcing leads to growth of perturbation energy concentrated within the core. Moderate-amplitude (~5%) perturbations cause significant distortion of the core and generate secondary filament-like spiral structures (‘threads’) outside the core. As the mode evolves into the nonlinear regime, radially outward self-advection of thread dipoles accelerates growth arrest by removing the perturbation from the critical radius and disrupting resonant forcing. With increasing Re, the evolving vorticity patterns become more chaotic, more turbulent-like (finer scaled, contorted vorticity), and persist longer. This suggests that at typical Re (~106), nonlinear transient growth may indeed be able to break up, hence induce rapid decay of, column vortices – highly relevant for addressing the aircraft wake hazard crisis and the looming air traffic capacity crisis. In addition, we discover a regenerative transient growth scenario in which threads induce secondary perturbations closer to the vortex column. A parent–offspring regenerative mechanism is postulated and verified by DNS. There is a clear trend towards stronger regenerative growth with increasing Re. These results, showing an important role of transient growth in turbulent vortex decay, are highly relevant to the prediction and control of vortex-dominated flows.

Analysis and forecasting of heavy-rainfall event by strong convection

For the case of severe convection occurring in the southern region of North China on July 8, 2009, the three dynamical factors, namely, vertical component of convective vorticity vector, moist thermodynamic advection parameter and wave-activity density are diagnosed. The result shows that the anomalous-value regions of dynamical factors are located mainly in middle and lower troposphere over the strong precipitation area. Since the dynamical factors can effectively describe the synthetical characteristics of strong convective system, such as vertical shear of horizontal wind, advection of potential temperature, vorticity perturbation and baroclinicity of moist atmosphere, they correspond to the observation of 6-h accumulative rainfall in horizontal distribution patterns. Using the 6-h, 12-h, 18-h and 24-h forecasting dataset of U.S. NCEP/NCAR 0.5-Degree GFS, the dynamical factors are calculated to analyze their indications of precipitation forecasting during a longer period. The results show that during June 2 – Oct 1, 2009, the 6-h, 12-h, 18-h and 24-h forecasted dynamical factors each have an indication of strong precipitation. The moist thermodynamic advection parameter suggests that the precipitation is best among the three dynamical factors.

A high order finite-difference solver for investigation of disturbance development in turbulent boundary layers

This paper outlines a velocity–vorticity based numerical simulation method for modelling perturbation development in laminar and turbulent boundary layers at large Reynolds numbers. Particular attention is paid to the application of integral conditions for the vorticity. These provide constraints on the evolution of the vorticity that are fully equivalent to the usual no-slip conditions. The vorticity and velocity perturbation variables are divided into two distinct primary and secondary groups, allowing the number of governing equations and variables to be effectively halved. Compact finite differences are used to obtain a high-order spatial discretization of the equations. Some novel features of the discretization are highlighted: (i) the incorporation of the vorticity integral conditions and (ii) the related use of a co-ordinate transformation along the semi-infinite wall-normal direction. The viability of the numerical solution procedure is illustrated by a selection of test simulation results. We also indicate the intended application of the simulation code to parametric investigations of the effectiveness of spanwise-directed wall oscillations in inhibiting the growth of streaks within turbulent boundary layers.

On the Use of Two-Dimensional Incompressible Flow to Study Secondary Eyewall Formation in Tropical Cyclones

Abstract Previous studies have offered hypotheses for the mechanisms that lead to secondary eyewall formation in tropical cyclones by using two-dimensional incompressible flow. Those studies represented the convection-induced vorticity field as either large but weak vortices that are the same sign as the tropical cyclone core or as purely asymmetric vorticity perturbations that are an order of magnitude weaker than the core. However, both observations and full-physics simulations of tropical cyclones indicate that the convection-induced vorticity field should also include clusters of small vorticity dipoles whose magnitude is comparable to that of the high-vorticity core. Results of numerical simulations indicate that the interaction between the tropical cyclone core vortex and the convection-induced small vorticity dipoles of considerable strength in two-dimensional flow does not lead to coherent concentric vorticity ring formation. The axisymmetrization process under the simplification of two-dimensional incompressible flow appears to be incomplete for describing secondary eyewall formation.

Large-eddy simulation of the compressible flow past a wavy cylinder

Numerical investigation of the compressible flow past a wavy cylinder was carried out using large-eddy simulation for a free-stream Mach numberM∞= 0.75 and a Reynolds number based on the mean diameterRe= 2 × 105. The flow past a corresponding circular cylinder was also calculated for comparison and validation against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including drag reduction and fluctuating force suppression, shock and shocklet elimination, and three-dimensional separation and separated shear-layer instability, have been studied systematically. Because of the passive control of the flow over a wavy cylinder, the mean drag coefficient of the wavy cylinder is less than that of the circular cylinder with a drag reduction up to 26%, and the fluctuating force coefficients are significantly suppressed to be nearly zero. The vortical structures near the base region of the wavy cylinder are much less vigorous than those of the circular cylinder. The three-dimensional shear-layer shed from the wavy cylinder is more stable than that from the circular cylinder. The vortex roll up of the shear layer from the wavy cylinder is delayed to a further downstream location, leading to a higher-base-pressure distribution. The spanwise pressure gradient and the baroclinic effect play an important role in generating an oblique vortical perturbation at the separated shear layer, which may moderate the increase of the fluctuations at the shear layer and reduce the growth rate of the shear layer. The analysis of the convective Mach number indicates that the instability processes in the shear-layer evolution are derived from oblique modes and bi-dimensional instability modes and their competition. The two-layer structures of the shear layer are captured using the instantaneous Lamb vector divergence, and the underlying dynamical processes associated with the drag reduction are clarified. Moreover, some phenomena relevant to the compressible effect, such as shock waves, shocklets and shock/turbulence interaction, are analysed. It is found that the shocks and shocklets which exist in the circular cylinder flow are eliminated for the wavy cylinder flow and the wavy surface provides an effective way of shock control. As the shock/turbulence interaction is avoided, a significant drop of the turbulent fluctuations around the wavy cylinder occurs. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the passive control of the compressible flow past a wavy surface.

Angular redistribution of nonlinear perturbations: A universal feature of nonuniform flows

Classically, the net action of nonlinear turbulent processes is interpreted as either a direct or inverse cascade. However, in nonuniform/shear flows the dominant process is a nonlinear redistribution over wave number angle of perturbation spatial Fourier harmonics. We call this process a nonlinear transverse redistribution (NTR). This phenomenon is demonstrated for a simple two-dimensional constant shear (non-normal) flow by numerically simulating the nonlinear dynamics of coherent and stochastic vortical perturbations in the flow. NTR is a general feature of nonlinear processes that should manifest itself in nonuniform engineering, environmental, and astrophysical flows. The conventional characterization of turbulence in terms of direct and inverse cascades, which ignores NTR, appears to be misleading for shear flow turbulence. We focus on the action of nonlinear processes on the spectral energy. NTR redistributes perturbations over different quadrants of the wave number plane and the interplay of this nonlinear redistribution with linear phenomena becomes intricate: it can realize either positive or negative feedback. In the case of positive feedback, it repopulates the quadrants in wave number space where the shear flow induces linear transient growth.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

The wake behind a cylinder rolling on a wall at varying rotation rates

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow.Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Rec of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Rec and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding.An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.