scholarly journals Stability and energy budget of pressure-driven collapsible channel flows

2011 ◽  
Vol 705 ◽  
pp. 348-370 ◽  
Author(s):  
H. F. Liu ◽  
X. Y. Luo ◽  
Z. X. Cai
Keyword(s):  
Pressure Drop ◽  
Kinetic Energy ◽  
Energy Budget ◽  
Neutral Curve ◽  
Channel Flows ◽  
Mean Flow ◽  
Mode 2 ◽  
The Mean ◽  
The Stability ◽  
Pressure Driven

AbstractAlthough self-excited oscillations in collapsible channel flows have been extensively studied, our understanding of their origins and mechanisms is still far from complete. In the present paper, we focus on the stability and energy budget of collapsible channel flows using a fluid–beam model with the pressure-driven (inlet pressure specified) condition, and highlight its differences to the flow-driven (i.e. inlet flow specified) system. The numerical finite element scheme used is a spine-based arbitrary Lagrangian–Eulerian method, which is shown to satisfy the geometric conservation law exactly. We find that the stability structure for the pressure-driven system is not a cascade as in the flow-driven case, and the mode-2 instability is no longer the primary onset of the self-excited oscillations. Instead, mode-1 instability becomes the dominating unstable mode. The mode-2 neutral curve is found to be completely enclosed by the mode-1 neutral curve in the pressure drop and wall stiffness space; hence no purely mode-2 unstable solutions exist in the parameter space investigated. By analysing the energy budgets at the neutrally stable points, we can confirm that in the high-wall-tension region (on the upper branch of the mode-1 neutral curve), the stability mechanism is the same as proposed by Jensen & Heil. Namely, self-excited oscillations can grow by extracting kinetic energy from the mean flow, with exactly two-thirds of the net kinetic energy flux dissipated by the oscillations and the remainder balanced by increased dissipation in the mean flow. However, this mechanism cannot explain the energy budget for solutions along the lower branch of the mode-1 neutral curve where greater wall deformation occurs. Nor can it explain the energy budget for the mode-2 neutral oscillations, where the unsteady pressure drop is strongly influenced by the severely collapsed wall, with stronger Bernoulli effects and flow separations. It is clear that more work is required to understand the physical mechanisms operating in different regions of the parameter space, and for different boundary conditions.

scholarly journals Characteristics, Energetics, and Origins of Agulhas Current Meanders and Their Limited Influence on Ring Shedding

2015 ◽  
Vol 45 (9) ◽  
pp. 2294-2314 ◽  
Author(s):  
Shane Elipot ◽  
Lisa M. Beal
Keyword(s):  
Kinetic Energy ◽  
Single Mode ◽  
Cyclonic Circulation ◽  
Recent Analysis ◽  
Altimeter Data ◽  
Western Boundary ◽  
Mean Flow ◽  
Current Time ◽  
Agulhas Current ◽  
The Mean

AbstractThe Agulhas Current intermittently undergoes dramatic offshore excursions from its mean path because of the downstream passage of mesoscale solitary meanders or Natal pulses. New observations and analyses are presented of the variability of the current and its meanders using mooring observations from the Agulhas Current Time-Series Experiment (ACT) near 34°S. Using a new rotary EOF method, mesoscale meanders and smaller-scale meanders are differentiated and each captured in a single mode of variance. During mesoscale meanders, an onshore cyclonic circulation and an offshore anticyclonic circulation act together to displace the jet offshore, leading to sudden and strong positive conversion of kinetic energy from the mean flow to the meander via nonlinear interactions. Smaller meanders are principally represented by a single cyclonic circulation spanning the entire jet that acts to displace the jet without extracting kinetic energy from the mean flow. Synthesizing in situ observations with altimeter data leads to an account of the number of mesoscale meanders at 34°S: 1.6 yr−1 on average, in agreement with a recent analysis by Rouault and Penven (2011) and significantly less than previously understood. The links between meanders and the arrival of Mozambique Channel eddies or Madagascar dipoles at the western boundary upstream are found to be robust in the 20-yr altimeter record. Yet, only a small fraction of anomalies arriving at the western boundary result in meanders, and of those, two-thirds can be related to ring shedding. Most Agulhas rings are shed independently of meanders.

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

scholarly journals The influence of idealized surface heterogeneity on virtual turbulent flux measurements

2018 ◽  
Vol 18 (7) ◽  
pp. 5059-5074 ◽  
Author(s):  
Frederik De Roo ◽  
Matthias Mauder
Keyword(s):  
Energy Budget ◽  
Turbulent Flux ◽  
Surface Heterogeneity ◽  
Surface Fluxes ◽  
Convective Conditions ◽  
Mean Flow ◽  
Flux Divergence ◽  
Length Scales ◽  
Flux Measurements ◽  
The Mean

Abstract. The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity, which affects the boundary-layer turbulence. To investigate the impact of surface variables on the partitioning of the energy budget of flux measurements in the surface layer under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on surface heterogeneity of the kilometer scale, and one order of magnitude smaller. For these two length scales, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g., downdraft region, updraft region, at border between domains, etc.). As the storage term is always small, the non-closure is given by the sum of the advection by the mean flow and the flux-divergence. Remarkably, the missing flux can be described by either the advection by the mean flow or the flux-divergence separately, because the latter two have a high correlation with each other. For kilometer scale heterogeneity, we notice a clear dependence of the updrafts and downdrafts on the surface heterogeneity and likewise we also see a dependence of the energy partitioning on the tower location. For the hectometer scale, we do not notice such a clear dependence. Finally, we seek correlators for the energy balance ratio in the simulations. The correlation with the friction velocity is less pronounced than previously found, but this is likely due to our concentration on effectively strongly to freely convective conditions.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

scholarly journals Energy-consistent entrainment relations for jets and plumes

2015 ◽  
Vol 782 ◽  
pp. 333-355 ◽  
Author(s):  
Maarten van Reeuwijk ◽  
John Craske
Keyword(s):  
Kinetic Energy ◽  
Richardson Number ◽  
Turbulence Kinetic Energy ◽  
Mean Flow ◽  
Unified Framework ◽  
First Order ◽  
Entrainment Coefficient ◽  
The Mean ◽  
Flow Turbulence ◽  
Pure Plume

We discuss energetic restrictions on the entrainment coefficient${\it\alpha}$for axisymmetric jets and plumes. The resulting entrainment relation includes contributions from the mean flow, turbulence and pressure, fundamentally linking${\it\alpha}$to the production of turbulence kinetic energy, the plume Richardson number$\mathit{Ri}$and the profile coefficients associated with the shape of the buoyancy and velocity profiles. This entrainment relation generalises the work by Kaminskiet al. (J. Fluid Mech., vol. 526, 2005, pp. 361–376) and Fox (J. Geophys. Res., vol. 75, 1970, pp. 6818–6835). The energetic viewpoint provides a unified framework with which to analyse the classical entrainment models implied by the plume theories of Mortonet al.(Proc. R. Soc. Lond.A, vol. 234, 1955, pp. 1–23) and Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1954, pp. 144–157). Data for pure jets and plumes in unstratified environments indicate that to first order the physics is captured by the Priestley and Ball entrainment model, implying that (1) the profile coefficient associated with the production of turbulence kinetic energy has approximately the same value for pure plumes and jets, (2) the value of${\it\alpha}$for a pure plume is roughly a factor of$5/3$larger than for a jet and (3) the enhanced entrainment coefficient in plumes is primarily associated with the behaviour of the mean flow and not with buoyancy-enhanced turbulence. Theoretical suggestions are made on how entrainment can be systematically studied by creating constant-$\mathit{Ri}$flows in a numerical simulation or laboratory experiment.

On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

2009 ◽  
Vol 638 ◽  
pp. 423-452 ◽  
Author(s):  
EMMANUEL MIGNOT ◽  
D. HURTHER ◽  
E. BARTHELEMY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Mean Flow ◽  
Local Flow ◽  
Gravel Bed ◽  
Wall Flows ◽  
The Mean ◽  
Conditional Statistics

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).

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