Vorticity Perturbations Research Articles

Towards a momentum potential theory for reacting flows

Mutual coupling of (thermofluiddynamic) modes of perturbations can affect the thermo-acoustic stability of combustors and contribute to combustion noise. For example, vortical or entropic perturbations can be transferred to acoustic perturbations if accelerated by the mean flow. The decomposition of perturbation fields into the respective modes and a linear description of their interactions in terms of fluctuating primitive variables is challenging. In contrast, Doak’s momentum potential theory promises an unambiguous decomposition in terms of momentum fluctuations, which is not limited to the linear regime. Whereas classical momentum potential theory takes into account hydrodynamic, acoustic and entropic modes in unconfined flows, the investigation of noise generation in combustion chambers requires the extension of the momentum potential theory to capture modes linked to the fluctuation of species mass fractions (“species mode”) arising from the change in chemical composition due to the reaction. Furthermore, a rigorous treatment of boundary conditions due to the confinement of the flow inside the combustor is required. The herein presented extension to reactive flows consists of two steps, (i) the formulation of a potential for momentum fluctuations related to species modes and (ii) identification of the total fluctuating enthalpy related to species modes. The extended theory is applied to post-process computational fluid dynamic simulation data of the propagation of entropy and species perturbations through one-dimensional ducts, nozzles and premixed flames. We find that although momentum potential theory offers a complete decomposition of momentum perturbations for reactive flows, the meaningful interpretation of this decomposition is rather challenging, even for non-reactive flows.

Signatures of Dipolarizing Flux Bundles in the Nightside Auroral Zone

AbstractDipolarizing flux bundles (DFBs) have been suggested to transport energy and momentum from regions of reconnection in the magnetotail to the high latitude ionosphere, where they can generate localized ionospheric currents that can produce large nighttime geomagnetic disturbances (GMDs). In this study we identified DFBs observed in the midnight sector from ∼7 to ∼10 RE by THEMIS A, D, and E during days in 2015–2017 whose northern hemisphere magnetic footpoints mapped to regions near Hudson Bay, Canada, and have compared them to isolated GMDs observed by ground magnetometers. We found 6 days during which one or more of these DFBs coincided to within ±3 min with ≥6 nT/s GMDs observed by latitudinally closely spaced ground‐based magnetometers located near those footpoints. Spherical elementary current systems (SECS) maps and all‐sky imager data provided further characterization of two events, showing short‐lived localized intense upward currents, auroral intensifications and/or streamers, and vortical perturbations of a westward electrojet. On all but one of these days the coincident DFB—GMD pairs occurred during intervals of high‐speed solar wind streams but low values of SYM/H. The observations reported here indicate that isolated DFBs generated under these conditions influence only limited spatial regions nearer Earth. In some events, in which the DFBs were observed closer to Earth and with lower Earthward velocities, the GMDs occurred slightly earlier than the DFBs, suggesting that braking had begun before the time of the DFB observation.

The cosmic web from perturbation theory

Context. Analysing the large-scale structure (LSS) in the Universe with galaxy surveys demands accurate structure formation models. Such models should ideally be fast and have a clear theoretical framework in order to rapidly scan a variety of cosmological parameter spaces without requiring large training data sets. Aims. This study aims to extend Lagrangian perturbation theory (LPT), including viscosity and vorticity, to reproduce the cosmic evolution from dark matter N-body calculations at the field level. Methods. We extend LPT to a Eulerian framework, which we dub eALPT. An ultraviolet regularisation through the spherical collapse model provided by Augmented LPT turns out to be crucial at low redshifts. This iterative method enables modelling of the stress tensor and introduces vorticity. The eALPT model has two free parameters apart from the choice of cosmology, redshift snapshots, cosmic volume, and the number of particles. Results. We find that compared to N-body solvers, the cross-correlation of the dark matter distribution increases at k = 1 h Mpc−1 and z = 0 from ∼55% with the Zel’dovich approximation (∼70% with ALPT), to ∼95% with the three-timestep eALPT, and the power spectra show percentage accuracy up to k ≃ 0.3 h Mpc−1.

Modeling the stability of thin liquid film flows on a uniformly heated slippery inclined substrate: A realistic approach

We investigate the stability of gravity-driven, Newtonian, thin liquid film falling down a uniformly heated slippery rigid inclined wall. The authors of previous research works considered specified temperature (ST) boundary condition to study the effects of slip length. However, the ST boundary condition does not include the effects of heat fluxes at wall–air and wall–liquid interfaces and so fails to incorporate the real situation. Consequently, we consider heat flux/mixed-type boundary condition as the thermal boundary condition on the rigid plate. This boundary condition involves the heat flux from the rigid plate to the surrounding liquid and the heat losses from the wall to the ambient air. Using long-wave expansion method, we construct a highly nonlinear evolution equation in terms of the film thickness at any instant. Using normal mode approach, the linear study reveals the stabilizing (destabilizing) behavior of the wall film Biot number (dimensionless slip length). It is found that the destabilizing tendency of the slip length is more in the absence of thermocapillary stress. The linear study reveals that the destabilizing role of MB may be controlled to some extent by increasing the wall film Biot number Bw. Using asymptotic expansions of the flow variables in terms of the small wave number k, the Orr–Sommerfeld boundary value problem gives an onset of instability in terms of critical Reynolds number. It slightly differs from that of the same as obtained by Benney's long-wave expansion method, due to the consideration of small free surface Biot number [B=O(ϵ)]. For arbitrary wave numbers, using Chebyshev spectral collocation method, the effect of Marangoni number (Ma), slip length (δ), and wall film Biot number (Bw) on the H, S, P, and shear modes of instability are discussed in detail. Near the threshold, both Ma and δ show the destabilizing effect on H mode of instability, whereas Bw gives the stabilizing effect. Interestingly, their roles on H mode of instability becomes diametrically opposite far from the onset of instability. For S mode, both Ma and Bw display the destabilizing effect, whereas δ plays the dual role. For P mode, both Ma and δ show the destabilizing effect, whereas Bw plays the stabilizing role. The slip length (δ) plays the stabilizing role, in the case of shear mode. In the absence of thermocapillary effect, the vorticity balance at the liquid–air interface explains that the amplitude of the vorticity perturbation amplifies the surface deformation due to the presence of inertia and the slip length. In the absence of the slip length, a weakly nonlinear study transforms the evolution equation to the famous Kuramoto–Sivashinsky (KS) equation.

Effect of different vortex models on the linear instability characteristics of wingtip vortex

Different analytical vortex models have been developed to characterize the evolution of wingtip vortex. However, their effect on the instability characteristics has not been well recognized. In this paper, the wingtip vortex generated by an elliptical wing was first experimentally measured in the near-wake and far-wake regions by particle image velocimetry. Then, it was fitted to different one-scale and multiscale vortex models as the base flow for linear stability analysis. The results show that though the eigenvalue spectra by different vortex models exhibit a unified topology with an isolated point around ωi=0 and three continuous branches, the multiscale vortex models tend to overestimate the instability of the wingtip vortex nonphysically. Furthermore, structures of the most unstable eigenmodes (Mode C) also differ between one-scale and multiscale vortex models. On this basis, a meaningful parameter, penetration depth (dp), is defined to predict the instability behavior of one perturbation mode. It is found that the most unstable streamwise wavenumber coincides with the streamwise wavenumber, where 1−dp is the local minimum, regardless of vortex models. The negative correlation between ωi and 1−dp of Mode C indicates that the closer the perturbation vorticity to the vortex boundary, the larger the growth rate. This reminds us that the penetration length might be a candidate measure of the instability behavior of perturbation modes, which deserves to be further studied in a broader parameter space.

Nonlinear interaction of two non-uniform vortex sheets and large vorticity amplification in Richtmyer–Meshkov instability

Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and plasma physics. Regarding vortex interactions, only limited problems, such as point vortex interactions, have been studied. Here, the nonlinear interaction of two non-uniform vortex sheets with density stratification is investigated using the vortex sheet model. These non-uniform vortex sheets appear, for example, in the Richtmyer–Meshkov instability that occurs when a shock wave crosses a layer with two corrugated interfaces. When a strong vortex sheet approaches a weaker vortex sheet with opposite-signed vorticity, a locally peaked secondary vorticity is induced on the latter sheet. This emerging secondary vorticity results in a remarkable vorticity amplification on the stronger sheet, and a strong vortex core is formed involving the weak vortex sheet. The amplified vortices with opposite signs on the two vortex sheets form pseudo-vortex pairs, which cause an intense rolling-up of the two sheets. We also investigated the dependence of distance and initial phase difference of vorticity perturbations between two vortex sheets on the vorticity amplification and vortex sheet dynamics.

MHD flow of submerged jets behind the inlet disturbance

AbstractIn a broad variety of configurations in technology and industrial applications, the properties of liquid metal flows subjected to strong magnetic fields, are largely governed by the dynamics of coherent structures, known to settle several basic types, such as thin shear layers, forming near the walls or within the fluid domain, vortices extended along the field, or planar and round jets. In some cases, these structures are created by the design, like a submerged jet formed by a sudden expansion from the nozzle into a blanket channel, or jets formed behind some flow obstruction. In the other cases this may be due to instability and evolution of secondary structures, for example, descending and ascending jets appearing as a result of convective instability in blanket channels. In this study, we undertake an attempt to affect liquid metal flow via inlet disturbance formed by a simple rod placed along the magnetic induction lines. The disturbance can generate flat jets behind the rod and, furthermore, a sustainable flow of anisotropic vortical perturbations further downstream the flow. We seek to analyze the most important mechanisms of the flow dynamics and effects of magnetic field on the integral system properties of enhancing mixing, mass and heat transport for such flow. The most optimal regimes of vortex generation are found to be governed by the magnetic interaction parameter (Stuart number). The exact ratio of the optimal Stuart number is found to be in a range between 20 and 40, based on the channel double width as a characteristic size. The observed vortices attain quasi‐2D shape and exist at a length of dozens of duct calibers, being the strongest at higher flow rates. The obtained flow regimes and their turbulent properties are also found to resemble significant similarity to the results on quasi‐2D turbulence found in prior studies of channel and duct flows under spanwise magnetic field.

Nonlinear dynamical features of vortex-acoustic lock-on in a backward-facing step combustor

Unstable shear layers characteristic of step combustors display strong vortex shedding and play a dominant role in combustion instability. Past non-premixed flame experiments with Reynolds number (Re) as the bifurcation parameter showed that during instability, the frequency of acoustic oscillations locks-on to the natural vortex shedding mode for a range of Re. In the present work, we study the dynamical features of this type of lock-on. We employ a vortex model to bring out the nonlinearity in the flame response to vortical perturbations. This is coupled with a Galerkin model for the acoustic field. Regimes of aperiodic oscillations, low-amplitude lock-on and high-amplitude lock-on are predicted in agreement with experimental trends. Phase portraits show a transition to instability during lock-on via a supercritical Hopf bifurcation with an increase in limit cycle amplitudes. Synchronisation between the acoustic pressure and vortex-driven heat release perturbation is studied using recurrence analysis. The system transitions from asynchronous to phase synchronisation in the low-amplitude lock-on regime, characterised by an increasing degree of phase correlation. In the high-amplitude lock-on regime, a state of generalised synchronisation exists, where in addition to the phase, the amplitudes also show strong correlation.

The Role of Turbine Operating Conditions on Combustor–Turbine Interaction—Part I: Change in Expansion Ratio

Abstract Aeroengine lean-burn combustors release vorticity and temperature perturbations that, interacting with the first turbine stage, impact the stage aerodynamics, the blade cooling, and noise production. The first of these issues is addressed in this paper that is Part I of a two-fold contribution. A detailed experimental analysis is carried out to study the impact on the combustor–turbine interaction of the off-design conditions experienced by aero-engines in their duty. Engine-representative disturbances are generated by a combustor simulator able to produce swirling entropy waves. Two injection positions and four injection cases are studied. Experimental measurements are carried out at three traverses: upstream of the stator, at the interstage, and downstream of the rotor. This paper analyses the effect of the stage expansion ratio: two values are studied, namely 1.4 and 1.76, representative of subsonic and transonic flow conditions. They are chosen imposing similar velocity triangles at the rotor inlet. Results show that the swirl profile considerably impacts the stage aerodynamics. The aerothermal flow field downstream of the stator is modified significantly by the combustor disturbances. Conversely, downstream of the rotor, the differences in aerodynamics lessen. However, the entropy wave persists at the stage outlet and its transport depends on both the operating point and the injection position.

The Role of Turbine Operating Conditions on Combustor–Turbine Interaction—Part II: Loading Effects

Abstract Aero-engine combustors burn a lean and premixed blend releasing vorticity and temperature perturbations. Interacting with the first turbine stage, these disturbances impact the cascade aerodynamics, add criticality to the blade cooling, and are sources of noise. The first of these issues is addressed in this paper, focusing on off-design turbine conditions, as experienced by aero-engines in their duty. This paper, Part II of a two-fold contribution, analyses the effect of the stage loading obtained by changing the rpm (three different values) at the same expansion ratio of 1.4, representative of subsonic flow conditions. Engine-representative disturbances are generated by a combustor simulator able to produce a swirling entropy wave. Two injection positions and four injection patterns are considered. Experimental measurements are carried out through the stage, measuring the injected disturbance and the aerothermal flow field downstream of the stator and the rotor. Results show that the swirl profile mostly impacts the stage aerodynamics. The different work extraction and the interaction with secondary flow structures change the entropy wave transport, diffusion, and decay through the rotor. Furthermore, the increased angle of the incidence caused by the injected disturbance can make the blade stall under the most loaded operating condition.

Evolution Characteristics of the Flows Around the Tibetan Plateau and the Relationship with the Climate in China in Winter

During the winter half-year (previous October–April), the mid-latitude westerlies flows around the Tibetan Plateau (TP) and generate a dynamic low-pressure trough on its south side and a high-pressure ridge on its north side. In this study, we define the vorticity perturbation as the difference between local vorticity and the meridionally-averaged vorticity. Then, the difference of averaged vorticity perturbation at 600 hPa in the two key areas where the trough and ridge are located is used to represent the intensity of the flows around the Tibetan Plateau (FAT). The evolution characteristics of FAT in the winter half-year, as well as in autumn, winter and spring, are analyzed. Moreover, under global warming, in winter the relationship of FAT to the precipitation and temperature in China are discussed. The results show that FAT steadily exists on both sides of TP during the winter half-year. With the north-south migration of the mid-latitude westerlies, the FAT gradually strengthens in autumn, with the strongest intensity and the widest range in winter, and begins to weaken in spring. The intensity of FAT (IFAT) has a decreasing trend and a quasi-4a period variation on the interannual scale in all the time, both of which are closely related to the mid-latitude westerlies upstream of TP. Represented by the winter when IFAT is strongest, the IFAT is significantly correlated to the change of precipitation and temperature in most parts of China under global warming, especially in the convergence area over central-eastern China. There is also a significant correlation between IFAT and the precipitation and temperature anomalies in Northwest China, TP, and Northeast China. This relationship between the FAT anomaly and the climate anomaly in China in winter can be well explained by analyzing the anomalies of large-scale circulation, outgoing longwave radiation and water vapor flux divergence. The FAT anomaly maybe one of the reasons for the climate extreme events in China in winter.

Vorticity amplification in wavy viscoelastic channel flow

Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. In Newtonian fluids, the vorticity induced by small surface undulations on the lower wall is advected by the background flow and diffuses into the fluid. When the fluid is viscoelastic, we identify new mechanisms by which significant vorticity perturbations can be generated in both inertialess and elasto-inertial channel flows. We focus on the case where the lengthscale of the surface distortion is much longer than the channel depth, where we find significant departure from plane shear (Page & Zaki, J. Fluid Mech., vol. 901, 2016, pp. 392–429) due to the non-monotonic base-flow streamwise-normal elastic stress. In inertialess flows, a purely elastic response results in streamlines deforming to match the bottom topography in the lower half the channel. However, the vanishing stress at the centreline introduces a blocking effect, and the associated $O(1)$ jump in normal velocity is balanced by a large-amplitude streamwise-oscillating ‘jet’ in a boundary layer, resulting in a localised, chevron-shaped vorticity perturbation field. In elasto-inertial flows, resonance between the frequency of elasto-inertial ‘Alfvén’ waves and the frequency apparent to an observer moving with the fluid results in vorticity amplification in a pair of critical layers on either side of the channel. The vorticity in both layers is equal in magnitude, to leading order in Weissenberg number, and as such the perturbation vorticity field penetrates the full channel depth even when inertia is dominant. The results demonstrate that long-wave distortions, which are relatively innocuous in Newtonian fluids, can drive a significant flow distortion in viscoelastic fluids for a wide range of parameter values.

Modeling of indirect combustion noise through a stator

In gas turbines, flow fluctuations generated by the flame are accelerated through the turbine and produce sound that may trigger combustion instabilities when propagating back to the combustor and contributes to community noise when leaving the engine. The development of safe and quiet engines requires fast and reliable models to predict these noise sources. Following the recent theoretical developments of Brind and Pullan (2021), a frequency-dependent analytical model is developed to predict noise scattering as well as entropy- and vorticity-noise production through a 2D stator cascade. The flow is inviscid and subsonic and perturbations are one-dimensional (planar waves). Validations are provided with comparisons to numerical simulations and the sensitivity of the results to input parameters is highlighted. Noise scattering is correctly captured by the model for all the frequencies considered, whereas the agreement is limited to a few hundred Hertz for entropy forcing when shear dispersion is not accounted for analytically. When shear dispersion of the entropy waves is included in the model, entropy-based transfer functions collapse with the numerical results for all the frequencies considered. The model also qualitatively predicts vorticity noise production. This noise comes from the acceleration and deviation of vorticity perturbations by the mean flow upstream of the blade leading edge and its contribution to the global indirect noise is negligible.

波状壁の上を通過する粘弾性流体のせん断流れの数値解析

A two-dimensional shear flow of a viscoelastic fluid over a wavy wall was numerically analyzed by the finite difference method. The upper convected Maxwell (UCM) model was used as the constitutive equation, and the unsteady flow problem was solved numerically using the stream function-vorticity method. Variables are discretized using a staggered grid with uniform mesh width. The volume penalization method was used to represent the moving upper wall and the fixed lower wavy wall that induces a vorticity perturbation. The flow in an infinitely long channel is computed using periodic boundary conditions in the flow direction. The results show that the vorticity intensifies over the wavy surface with positive and negative vorticity stripes, at which extreme wall-normal velocity fluctuations are also observed. At relatively high Deborah numbers, the lower ends of these extreme fluctuation regions are close to the critical line associated with a change of type of the governing partial differential equations in a Couette flow. In contrast, the upper ends of the extreme fluctuation region are close to the critical layer of the shear flow, where the flow velocity coincides with the viscoelastic Alfvén wave speed.

Turbulent Statistics of a Hot, Overexpanded Rectangular Jet

The near-field dynamics of a rectangular heated overexpanded jet of aspect ratio two is examined with an implicit large-eddy simulation using experimental data for validation purposes. The conical nozzle, representative of practical configurations, results in multiple shock trains from the throat region as well as the overexpanded operating condition. Each train introduces unsteadiness that influences the external shock cell and plume structure. A detailed analysis of the terms contributing to the turbulent kinetic energy (TKE) is performed to examine the evolution of the plume. The major-axis shear layer experiences significant amplification of the TKE compared with the minor axis, particularly near the core collapse region, and thus pressure fluctuations in the near acoustic field are correspondingly larger in that direction. The most prominent source of TKE in this region is associated with strong mean flow gradients across the major-axis shear layer, and larger corresponding cross-correlations of velocity fluctuations. These effects are shown to be consistent with protrusions of vortical perturbations arising in the minor-axis shear layer into the potential core. The evolution of pressure perturbations from asymmetric to axisymmetric occurs relatively quickly, to achieve agreement with far-field experimental data.

Unprecedented North American snowstorm and East Asian cold wave in January 2016: Critical role of the Arctic atmospheric circulation

AbstractDuring January 21–24, 2016, most land areas in the Northern Hemisphere experienced extreme low temperatures. In North America, a historic snowstorm hit the northern and eastern United States. In East Asia, an unprecedented cold wave occurred and led to record‐breaking low temperatures in many regions. In this study, observational analyses revealed that both extreme events were triggered by a remarkable change in atmospheric circulation in the Arctic region in early January 2016, which switched from a concentric ring pattern to a dipole pattern. The dipole pattern resulted in two inverted Ω‐shaped circulation patterns that dominated the North America and East Asia. The inverted Ω‐shaped circulation patterns induced remarkable tropopause folding, which conveyed high‐potential‐vorticity cold air downwards from the lower stratosphere of Arctic to the middle and lower troposphere of North America, which increased cyclonic vorticity and negative height perturbations, and converged with moist air from the western North Atlantic and Gulf Stream, resulting in a severe snowstorm in the northern and eastern United States from 22 to 24 January. In East Asia, the tropopause folding transported high‐potential‐vorticity cold air downwards to the middle and lower troposphere of East Asia, resulting in the outbreak of a severe cold wave in East Asia from 21 to 24 January.

Amplitude-Dependent Damping and Driving Rates of High-Frequency Thermoacoustic Oscillations in a Lab-Scale Lean-Premixed Gas Turbine Combustor

Abstract This paper presents the numerical investigations of amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, atmospheric, swirl-stabilized, lab-scale gas turbine combustor. A hybrid computational fluid dynamics/computational aeroacoustics (CFD/CAA) approach is applied to individually compute thermoacoustic damping and driving rates for various acoustic amplitude levels at the combustors' first transversal (T1) eigenfrequency. Harmonically forced CFD simulations with the unsteady Reynolds-averaged Navier–Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. A slow and monotonous increase of the forcing amplitude over time allows observation of the amplitude-dependent flow field and flame evolution. In accordance with measured OH*-chemiluminescence images, a pulsation amplitude-dependent flame contraction is reproduced in the CFD simulations, where acoustically induced backflow at the combustion chamber inlet is identified as the root cause of this phenomenon. At several amplitude levels, period-averaged flow fields are then denoted as reference states, which serve as inputs for the CAA part. There, eigenfrequency simulations with linearized flow equations are performed with the finite element method. The outcomes are damping and driving rates as a response to the amplitude dependency of the mean flow field, which combined give the net thermoacoustic growth rate. It is found that driving due to flame-acoustics interactions only governs a weak amplitude dependency, which agrees with prior, experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root cause for limit-cycle oscillations—at least in this high-frequency thermoacoustic system. Instead, significantly increased dissipation due to the interaction of acoustically induced vorticity perturbations with the mean flow is identified, which may explain the formation of a limit cycle.

Impact of Swirling Entropy Waves on a High Pressure Turbine

AbstractThe harsh environment exiting modern gas turbine combustion chamber is characterized by vorticity and temperature perturbations, the latter commonly referred as entropy waves. The interaction of these unsteadiness with the first turbine stage causes non-negligible effects on the aerodynamic performance, blade cooling, and noise production. The first of these drawbacks is addressed in this paper by means of an experimental campaign: entropy waves and swirl profile are injected upstream of an axial turbine stage through a novel combustor simulator. Two injection positions and different inlet conditions are considered. Steady and unsteady experimental measurements are carried out through the stage to address the combustor-turbine interaction characterizing the injected disturbance, the nozzle, and rotor outlet aerothermal field. The experimental outcomes show a severe reduction of the temperature perturbation already at stator outlet. The generated swirl profile influences significantly the aerodynamic, as it interacts with the stator and rotor secondary flows and wakes. Furthermore, the clocking position changes the region most affected by the disturbance, showing a potential modifying the injection position to minimize the entropy wave and swirl profile impact on the stage. Finally, this work shows that in order to proficiently study entropy waves, the unsteady aerodynamic flow field stator downstream has to be addressed.

Dynamical propagation and growth mechanisms for convectively coupled equatorial Kelvin waves over the Indian Ocean

AbstractConvectively coupled equatorial Kelvin waves (CCKWs) are high‐impact tropical weather systems that can lead to severe flooding over the Maritime Continent. Here, a vorticity budget for CCKWs over the Indian Ocean is constructed using reanalysis data, to identify the basic mechanisms of eastward propagation and growth. The budget is reasonably well closed, with a small residual/subgrid‐scale term. In the lower troposphere, CCKWs behave like strongly modified theoretical equatorial Kelvin waves. Vortex stretching, from the divergence of the Kelvin wave acting on planetary vorticity (the term), is the sole mechanism by which the vorticity structure of a theoretical Kelvin wave propagates eastward. In the lower and middle troposphere, this term is also the key mechanism for the eastward propagation of CCKWs but, due to subtleties in its structure and phasing linked to a combination of modal structures, it also contributes to growth. Unlike in the theoretical Kelvin wave, other vorticity source terms also play a role in the propagation and growth of CCKWs. In particular, vortex stretching from relative vorticity (the term) is the largest source term, and this leads strongly to growth, through interactions between the background and perturbation vorticity and divergence. Horizontal vorticity advection by the background flow contributes to propagation, and also acts to retard the growth of the CCKW. The sum of the source terms in this complex vorticity budget leads to eastward propagation and growth of CCKWs. The structure and vorticity budget of CCKWs in the upper troposphere is quite unlike that of a Kelvin wave, and appears to arise as a forced response to the lower‐tropospheric structure. The implications for numerical weather prediction and climate simulations are discussed.

Entrainment and growth of vortical disturbances in the channel-entrance region

The entrainment of free-stream unsteady three-dimensional vortical disturbances in the entry region of a channel is studied via matched asymptotic expansions and by numerical means. The interest is in flows at Reynolds numbers where experimental studies have documented the occurrence of intense transient growth, despite the flow being stable according to classical stability analysis. The analytical description of the vortical perturbations at the channel mouth reveals how the oncoming disturbances penetrate into the wall-attached shear layers and amplify downstream. The effects of the channel confinement, the streamwise pressure gradient and the viscous/inviscid interplay between the oncoming disturbances and the boundary-layer perturbations are discussed. The composite perturbation velocity profiles are employed as initial conditions for the unsteady boundary-region perturbation equations. At a short distance from the channel mouth, the disturbance flow is mostly confined within the shear layers and assumes the form of streamwise-elongated streaks, while farther downstream the viscous disturbances permeate the whole channel although the base flow is still mostly inviscid in the core. Symmetrical disturbances exhibit a more significant growth than anti-symmetrical disturbances, the latter maintaining a nearly constant amplitude for several channel heights downstream before growing transiently, a unique feature not reported in open boundary layers. The disturbances are more intense as the frequency decreases or the bulk Reynolds number increases. We compute the spanwise wavelengths that cause the most intense downstream growth and the threshold wall-normal wavelengths below which the perturbations are damped through viscous dissipation.