Investigation of Stability of a Suspension of Motile Microorganisms Subjected to a High-Frequency Vibration

This paper investigates the effect of vertical vibration on the stability of a dilute suspension of negatively geotactic microorganisms in a fluid layer of finite depth. The case of high-frequency vibration is considered. Solutions of governing equations are decomposed into two components: one which varies slowly with time and a second which varies rapidly with time. An averaging method is utilized to derive the equations describing the mean flow. Linear stability analysis is used to investigate stability of the obtained averaged equations.

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

10.1017/jfm.2014.95 ◽

2014 ◽

Vol 745 ◽

pp. 647-681 ◽

Cited By ~ 5

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 ◽

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.

On strongly nonlinear gravity waves in a vertically sheared atmosphere

Mathematics of Climate and Weather Forecasting ◽

10.1515/mcwf-2020-0103 ◽

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 ◽

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.

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

10.1017/s0022112091001696 ◽

1991 ◽

Vol 224 ◽

pp. 159-175 ◽

Cited By ~ 19

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 ◽

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

10.1017/s0022112067002538 ◽

1967 ◽

Vol 27 (4) ◽

pp. 657-689 ◽

Cited By ~ 137

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 ◽

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.

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

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4048693 ◽

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 ◽

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.

Mean flow structure in horizontal convection

10.1017/jfm.2016.866 ◽

2017 ◽

Vol 812 ◽

pp. 525-540 ◽

Cited By ~ 7

Author(s):

Olga Shishkina

Keyword(s):

Aspect Ratio ◽

Heat Supply ◽

Fluid Layer ◽

Flow Structures ◽

Convection Cell ◽

Spatial Distributions ◽

Global Flow ◽

Mean Flow ◽

Horizontal Convection ◽

The Mean

We analyse the global flow structures in horizontal convection systems, where the heat supply and removal takes place through separated parts of a lower horizontal surface of a fluid layer. The results are based on direct numerical simulations for the length-to-height aspect ratio of the convection cell $\unicode[STIX]{x1D6E4}=10$, Rayleigh number $\mathit{Ra}$ from $3\times 10^{8}$ to $3\times 10^{11}$ and Prandtl number $\mathit{Pr}$ from 0.05 to 50. The structure of the mean flows in horizontal convection is described in terms of time-averaged spatial distributions of the temperature, velocity, kinetic energy, thermal and kinetic dissipation rates. A possible scenario of transition to turbulent horizontal convection in the whole convection cell of a large aspect ratio is discussed.

The Response of an Idealized Atmosphere to Localized Tropical Heating: Superrotation and the Breakdown of Linear Theory

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-17-0192.1 ◽

2018 ◽

Vol 75 (1) ◽

pp. 3-20 ◽

Cited By ~ 8

Author(s):

Nicholas J. Lutsko

Keyword(s):

Temperature Gradient ◽

General Circulation ◽

Circulation Model ◽

Mean Flow ◽

Heating Rates ◽

Momentum Fluxes ◽

The Mean ◽

The Stability ◽

The Waves ◽

Large Heating

An equatorial heat source mimicking the strong diabatic heating above the west Pacific is added to an idealized, dry general circulation model. For small (<0.5 K day−1) heating rates the responses closely match the expectations from linear Matsuno–Gill theory, though the amplitudes of the responses increase sublinearly. This “linear” regime breaks down for larger heating rates and it is found that this is because the stability of the tropical atmosphere increases. At the same time, the equatorial winds increasingly superrotate. This superrotation is driven by stationary eddy momentum fluxes by the waves excited by the heating and is damped by the vertical advection of low-momentum air by the mean flow and, at large heating rates, by the divergence of momentum by transient eddies. These dynamics are explored in additional experiments in which the equator-to-pole temperature gradient is varied. Very strong superrotation is produced when a large heating rate is applied to a setup with a relatively weak equator-to-pole temperature gradient, though there is no evidence that this is a case of “runaway” superrotation.

On the shape of flames under strong acoustic forcing: a mean flow controlled by an oscillating flow

10.1017/s0022112097006940 ◽

1997 ◽

Vol 350 ◽

pp. 295-310 ◽

Cited By ~ 39

Author(s):

D. DUROX ◽

F. BAILLOT ◽

G. SEARBY ◽

L. BOYER

Keyword(s):

High Frequency ◽

Combustion Velocity ◽

High Amplitude ◽

Acoustic Velocity ◽

Oscillating Flow ◽

Mean Flow ◽

Cellular Flames ◽

The Mean ◽

Acoustic Modulation ◽

Unusual Situation

A conical flame, in the presence of high-frequency (≈1000 Hz) and high-amplitude acoustic modulation of the cold gases, deforms to a shape which is approximately hemispherical. It is shown that the acoustic level required to produce a hemispherical flame is such that the ratio of acoustic velocity to laminar combustion velocity is about 3. This flame flattening is equivalent to the phenomenon of acoustic restabilization observed for cellular flames propagating in tubes. The transition between the conical flame and a hemispherical flame is described. The surface area of the reaction zone of the flame is found to be unmodified when the flame flattens. The velocity field at the burner outlet is examined with and without a flame. The mean flow lines are strongly deflected when the hemispherical flame is present. We show that the presence of the flame creates an unusual situation where the oscillating flow controls the geometry of the mean flow.

Seasonal Variations of High-Frequency Gravity Wave Momentum Fluxes and Their Forcing toward Zonal Winds in the Mesosphere and Lower Thermosphere over Langfang, China (39.4° N, 116.7° E)

Atmosphere ◽

10.3390/atmos11111253 ◽

2020 ◽

Vol 11 (11) ◽

pp. 1253

Author(s):

Caixia Tian ◽

Xiong Hu ◽

Yurong Liu ◽

Xuan Cheng ◽

Zhaoai Yan ◽

...

Keyword(s):

Seasonal Variations ◽

High Frequency ◽

Momentum Flux ◽

Lower Thermosphere ◽

Mean Flow ◽

Zonal Winds ◽

Short Period ◽

Momentum Fluxes ◽

The Mean ◽

Mesosphere And Lower Thermosphere

Meteor radar data collected over Langfang, China (39.4° N, 116.7° E) were used to estimate the momentum flux of short-period (less than 2 h) gravity waves (GWs) in the mesosphere and lower thermosphere (MLT), using the Hocking (2005) analysis technique. Seasonal variations in GW momentum flux exhibited annual oscillation (AO), semiannual oscillation (SAO), and quasi-4-month oscillation. Quantitative estimations of GW forcing toward the mean zonal flow were provided using the determined GW momentum flux. The mean flow acceleration estimated from the divergence of this flux was compared with the observed acceleration of zonal winds displaying SAO and quasi-4-month oscillations. These comparisons were used to analyze the contribution of zonal momentum fluxes of SAO and quasi-4-month oscillations to zonal winds. The estimated acceleration from high-frequency GWs was in the same direction as the observed acceleration of zonal winds for quasi-4-month oscillation winds, with GWs contributing more than 69%. The estimated acceleration due to Coriolis forces to the zonal wind was studied; the findings were opposite to the estimated acceleration of high-frequency GWs for quasi-4-month oscillation winds. The significance of this study lies in estimating and quantifying the contribution of the GW momentum fluxes to zonal winds with quasi-4-month periods over mid-latitude regions for the first time.

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

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4051990 ◽

2021 ◽

Author(s):

Thomas Hofmeister ◽

Thomas Sattelmayer

Keyword(s):

Flow Field ◽

Gas Turbine ◽

Limit Cycle ◽

High Frequency ◽

Mean Flow ◽

Gas Turbine Combustor ◽

Cfd Simulations ◽

The Mean ◽

Amplitude Dependency ◽

Thermoacoustic Oscillations

Abstract This paper presents numerical investigations of the amplitude-dependent stability behavior of thermoacoustic oscillations at screech level frequencies in a lean-premixed, 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. Forced CFD simulations with the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations mimic the real combustor's rotating T1 eigenmode. An 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. 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 (FEM). The outcomes are damping and driving rates as a response to the amplitude-dependency of the mean flow field. It is found that driving due to flame-acoustics interactions governs a weak amplitude-dependency, which agrees with experimentally based studies at the authors' institute. This disqualifies the perception of heat release saturation as the root-cause for limit-cycle oscillations 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.