scholarly journals The evolution of a thermocline effected by a turbulent stream

1995 ◽  
Vol 2 (1) ◽  
pp. 49-57 ◽  
Author(s):  
O. A. Druzhinin ◽  
V. I. Kazakov ◽  
P. A. Matusov ◽  
L. A. Ostrovsky
Keyword(s):  
Turbulent Energy ◽  
Quantitative Agreement ◽  
Marginal Stability ◽  
Mean Velocity ◽  
Induced Drag ◽  
The Mean ◽  
The Stability ◽  
Semi Empirical ◽  
Oceanic Currents ◽  
Small Disturbances

Abstract. The process of thermocline evolution under the action of turbulent stream in the upper layer is investigated in laboratory experiment in thermally stratified tank, the initial temperature profile with pronounced thermocline being similar to that observed in tropic seas. The mean velocity and turbulent energy spatial distributions have been shaped to model the hydrological conditions in strong oceanic currents or wind-induced drag currents. The experiment demonstrates the gradual deepening and transformation of thermocline in a case where no global instability took place (i.e., with Richardson numbers always exceeding 0.3-0.4). The process of thermocline evolution resulted also in recurring "bursts" of microstructure. A numerical experiment based on equations of semi-empirical theory of turbulence shows quantitative agreement with experimental data. Moreover, simple analytical solutions and numerical results show that a layer with marginal stability is formed with Richardson numbers being very close to the stability threshold, so that quite small disturbances in thermocline can result in appearance of internal waves and bursts of turbulence.

The stability of an incompressible two-dimensional wake

1972 ◽  
Vol 51 (2) ◽  
pp. 233-272 ◽  
Author(s):  
G. E. Mattingly ◽  
W. O. Criminale
Keyword(s):  
Reference Frames ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Spatial Reference ◽  
Spatial Reference Frames ◽  
The Mean ◽  
Temporal And Spatial ◽  
The Stability ◽  
Transverse Oscillations ◽  
Small Disturbances

The growth of small disturbances in a two-dimensional incompressible wake has been investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory wherein small disturbances are considered from both temporal and spatial reference frames. Through a combined stability analysis, in which small disturbances are permitted to amplify in both time and space, the relationship between the disturbance characteristics for the temporal and spatial reference frames is shown. In these analyses a quasi-uniform assumption is adopted to account for the continuously varying mean-velocity profiles that occur behind flat plates and thin airfoils. It is found that the most unstable disturbances in the wake produce transverse oscillations in the mean-velocity profile and correspond to growing waves that have a minimum group velocity.Experimentally, the downstream development of the wake of a thin airfoil and the wave characteristics of naturally amplifying small disturbances are investigated in a water tank. The disturbances that develop are found to produce transverse oscillations of the mean-velocity profile in agreement with the theoretical prediction. From the comparison of the experimental results with the predictions for the characteristics of the most unstable waves via the temporal and spatial analyses, it is concluded that the stability analysis for the wake is to be considered solely from the more realistic spatial viewpoint. Undoubtedly, this conclusion is also applicable to other highly unstable flows such as jets and free shear layers.In accordance with the disturbance vorticity distribution as determined from the spatial model, a description of the initial development of a vortex street is put forth that contrasts with the description given by Sato & Kuriki (1961).

Breakdown of the Laminar Flow Regime in Permeable-Walled Ducts

1973 ◽  
Vol 40 (2) ◽  
pp. 337-342 ◽  
Author(s):  
E. M. Sparrow ◽  
G. S. Beavers ◽  
T. S. Chen ◽  
J. R. Lloyd
Keyword(s):  
Laminar Flow ◽  
Velocity Slip ◽  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Laminar Regime ◽  
Permeable Material ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability ◽  
Plate Channel

The stability of laminar flow in a parallel-plate channel having one permeable bounding wall is investigated by means of linear theory. The analysis takes account of the coupling of the disturbance fields in the channel and in the permeable material and of velocity slip at the surface of the permeable wall. Complementary experiments are performed in which the breakdown of the laminar regime in flat rectangular ducts is identified from pressure-drop measurements and from flow visualization studies. The experiments cover the range of slip velocities from 15–30 percent of the mean velocity and, in addition, the case of zero slip (impermeable walls). In the slip range of the experiments, the instability Reynolds number results of both analysis and experiment lie below the corresponding values for the case of the impermeable-walled duct. Furthermore, in this range, the instability Reynolds numbers are rather insensitive to variations in the slip velocity. Quantitative agreement between analysis and experiment was found to be somewhat better in the slip range than for the impermeable-walled duct.

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.

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.

Spectral analogues of the law of the wall, the defect law and the log law

2014 ◽  
Vol 757 ◽  
pp. 498-513 ◽  
Author(s):  
Carlo Zúñiga Zamalloa ◽  
Henry Chi-Hin Ng ◽  
Pinaki Chakraborty ◽  
Gustavo Gioia
Keyword(s):  
Turbulent Energy ◽  
Wall Turbulence ◽  
Spectral Domain ◽  
Energy Spectra ◽  
Scaling Relations ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean ◽  
Log Law ◽  
The Law

AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defect law and the log law. By design, each spectral analogue applies in the same spatial domain as the attendant scaling relation for the mean-velocity profiles: the spectral analogue of the law of the wall in the inner layer, the spectral analogue of the defect law in the outer layer and the spectral analogue of the log law in the overlap layer. In addition, as we are able to show without invoking any model of wall turbulence, each spectral analogue applies in a specific spectral domain (the spectral analogue of the law of the wall in the high-wavenumber spectral domain, where viscosity is active, the spectral analogue of the defect law in the low-wavenumber spectral domain, where viscosity is negligible, and the spectral analogue of the log law in a transitional intermediate-wavenumber spectral domain, which may become sizable only at ultra-high$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }$), with the implication that there exist model-independent one-to-one links between the spatial domains and the spectral domains. We test the spectral analogues using experimental and computational data on pipe flow and channel flow.

Axisymmetric laminar wake behind a slender body of revolution

1976 ◽  
Vol 76 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Francis R. Hama ◽  
Leigh F. Peterson
Keyword(s):  
Experimental Information ◽  
The Body ◽  
Body Of Revolution ◽  
Empirical Theory ◽  
Mean Velocity ◽  
Laminar Wake ◽  
Flow Field Characteristics ◽  
The Mean ◽  
Semi Empirical ◽  
Slender Body Of Revolution

At the body-diameter Reynolds number 2000, the axisymmetric wake behind a slender streamlined body of revolution remained laminar without any indication of breakup far beyond the five-body-lengths test section. The mean-velocity profiles were measured with close spacings in order to obtain experimental information on the transient process from boundary layer to fully developed wake. A semi-empirical theory was developed to describe the flow-field characteristics.

The Response of a Developed Turbulent Boundary Layer to Local Transverse Surface Motion

1976 ◽  
Vol 98 (3) ◽  
pp. 354-363 ◽  
Author(s):  
R. P. Lohmann
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Turbulent Energy ◽  
Transverse Motion ◽  
Mean Velocity ◽  
Surface Motion ◽  
The Mean ◽  
Structure Lead

Measurements were obtained of the mean velocity, Reynolds stress tensor components and spectral distribution of turbulent energy in a boundary layer that was adjusting spatially from a collateral to a three-dimensional state because of transverse motion of the bounding wall. The results indicate that changes to the turbulent structure lead to a strong coupling between the axial and transverse components of mean velocity. The influence of the imposed motion was found to be confined to a discrete region near the wall over the first ten initial boundary layer thicknesses, after which it became more global in nature.

A Turbulent Energy Dissipation Model for Flows With Drag Reduction

1978 ◽  
Vol 100 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Samuel Hassid ◽  
Michael Poreh
Keyword(s):  
Energy Dissipation ◽  
Drag Reduction ◽  
Eddy Diffusivity ◽  
Turbulent Energy ◽  
Momentum Equation ◽  
Mean Velocity ◽  
Turbulent Length Scale ◽  
Dissipation Model ◽  
The Mean ◽  
Good Agreement

A turbulent-energy-dissipation model is proposed for flows with and without drag reduction. The model is based on an eddy diffusivity approximation in the momentum equation, and on transport equations for the turbulent energy and the turbulent energy dissipation. The model describes the mean velocity profile and the turbulent energy distribution as a function of the reduction in the friction coefficient. It also yields a turbulent length scale which is shown to grow with drag reduction. The predictions of the model are in good agreement with the available experimental data.

Particle dynamics in the channel flow of a turbulent particle–gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

2011 ◽  
Vol 687 ◽  
pp. 41-71 ◽  
Author(s):  
Partha S. Goswami ◽  
V. Kumaran
Keyword(s):  
Relaxation Time ◽  
Particle Velocity ◽  
Volume Fraction ◽  
Quantitative Agreement ◽  
Mean Square ◽  
Mass Loading ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Viscous Relaxation

AbstractThe particle and fluid velocity fluctuations in a turbulent gas–particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of $9. 15\ensuremath{\times} 1{0}^{\ensuremath{-} 5} $ (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall–particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by ${\ensuremath{\sim} }1$–2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20–30 % of the experimental values.

Similarity behaviour of momentumless turbulent wakes

1975 ◽  
Vol 71 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Michael L. Finson
Keyword(s):  
Initial Conditions ◽  
Turbulent Energy ◽  
Similarity Solutions ◽  
Decay Rates ◽  
Grid Turbulence ◽  
Mean Velocity ◽  
Radial Profiles ◽  
The Mean ◽  
Momentumless Wake ◽  
Far Wake

Similarity solutions are determined for the turbulent wake of a self-propelled body (thrust = drag). The momentumless wake is shown to behave in a manner intermediate to homogeneous grid turbulence and more familiar free-shear flows such as the drag wake or jet. In essence the decay of momentumless-wake turbulence is similar to that of grid turbulence, but proceeds at a somewhat greater rate owing to lateral diffusion. The mean velocity difference is coupled to the difference $\overline{u^2}-\overline{v^2}$ between the axial and radial components of the mean-square fluctuating velocity. It is necessary to consider governing relations for various second-order turbulence quantities. Previously developed closure approximations yield far-wake decay rates that agree well with available measurements. Production of turbulent energy is negligible asymptotically; thus there is no balance between production and dissipation, and the far-wake behaviour does not become independent of the initial (near-wake) conditions. Even the radial profiles depend on the initial conditions, and there is no natural length scale with which to characterize the far wake.

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