scholarly journals Lateral Momentum Fluxes at the Confluence of the Negro and Solimões Rivers

Geosciences ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 7
Author(s):  
Adriano Coutinho de Lima
Keyword(s):  
Shear Layer ◽  
Reynolds Stress ◽  
Turbulent Mixing ◽  
Mean Flow ◽  
Long Distance ◽  
Momentum Fluxes ◽  
Hydrodynamic Processes ◽  
Lateral Mixing ◽  
River Confluences ◽  
The Mean

Hydrodynamic zones of river confluences are remarkable not only for the turbulent mixing induced by the shear layer at the center of the mixing interface but also for the lateral momentum fluxes associated with channel topography. Detailed characterizations of lateral momentum transfers in river confluences, however, are few. In this study, contributions to the lateral momentum fluxes in the confluence of the Negro and Solimões rivers in Brazil were calculated based on a comprehensive set of field data. Results show that the lateral fluxes by the mean flow exceed the turbulent fluxes by two orders of magnitude. Furthermore, the Reynolds stress along the far field of the Solimões side of the Amazon channel scales with or surpasses the Reynolds stress at the interface with the Negro side. The importance of the shear layer in the lateral mixing is thus overshadowed by the competing hydrodynamic processes. This configuration partially explains the long distance required to complete the mixing of the waters of the two tributary rivers.

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Axial Compressor ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo PIV measurements performed in a refractive index matched facility in a series of closely-spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy-viscosity is also evaluated by calculating it from the ratio between stress and strain components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strains do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Asymptotic properties of the overall sound pressure level of subsonic jet flows using isotropy as a paradigm

2010 ◽  
Vol 664 ◽  
pp. 510-539 ◽  
Author(s):  
M. Z. AFSAR
Keyword(s):  
Reynolds Stress ◽  
Sound Pressure Level ◽  
Small Angle ◽  
Sound Pressure ◽  
Asymptotic Properties ◽  
Jet Noise ◽  
Pressure Level ◽  
Mean Flow ◽  
The Mean ◽  
Jet Axis

Measurements of subsonic air jets show that the peak noise usually occurs when observations are made at small angles to the jet axis. In this paper, we develop further understanding of the mathematical properties of this peak noise by analysing the properties of the overall sound pressure level with an acoustic analogy using isotropy as a paradigm for the turbulence. The analogy is based upon the hyperbolic conservation form of the Euler equations derived by Goldstein (Intl J. Aeroacoust., vol. 1, 2002, p. 1). The mean flow and the turbulence properties are defined by a Reynolds-averaged Navier–Stokes calculation, and we use Green's function based upon a parallel mean flow approximation. Our analysis in this paper shows that the jet noise spectrum can, in fact, be thought of as being composed of two terms, one that is significant at large observation angles and a second term that is especially dominant at small observation angles to the jet axis. This second term can account for the experimentally observed peak jet noise (Lush, J. Fluid Mech., vol. 46, 1971, p. 477) and was first identified by Goldstein (J. Fluid Mech., vol. 70, 1975, p. 595). We discuss the low-frequency asymptotic properties of this second term in order to understand its directional behaviour; we show, for example, that the sound power of this term is proportional to the square of the mean velocity gradient. We also show that this small-angle shear term does not exist if the instantaneous Reynolds stress source strength in the momentum equation itself is assumed to be isotropic for any value of time (as was done previously by Morris & Farrasat, AIAA J., vol. 40, 2002, p. 356). However, it will be significant if the auto-covariance of the Reynolds stress source, when integrated over the vector separation, is taken to be isotropic in all of its tensor suffixes. Although the analysis shows that the sound pressure of this small-angle shear term is sensitive to the statistical properties of the turbulence, this work provides a foundation for a mathematical description of the two-source model of jet noise.

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.

Phase Averaging by Wavelet Transformation and the Application to Periodically Fluctuated Separation Flow

2002 ◽  
Author(s):  
Masaki Yamagishi ◽  
Tomoko Togano ◽  
Shinichi Tashiro
Keyword(s):  
Shear Layer ◽  
Wavelet Transformation ◽  
Dominant Frequency ◽  
Separation Flow ◽  
Mean Flow ◽  
Field Phase ◽  
Phase Averaging ◽  
Separated Shear Layer ◽  
The Mean ◽  
Almost All

The vortex structures in a separated region are generated by the motion of the separated shear layer caused by the introduction of periodic fluctuation. The main cause of the motion of the separated shear layer is the external fluctuation with the characteristic frequency. In order to investigate the principal motion of the velocity field, phase averaging was conducted to the velocity signals obtained by single hot-wire measurement. In phase averaging, wavelet analysis was applied to obtain the dominant frequency and the characteristic phase in the fluctuation. The profiles and the contours of the phase-averaged velocity could be found and discussed. The profiles vary dynamically at each phase and show the periodic motion of the shear layer. The separated shear layer flutters with the external fluctuation in the mean flow. If the suitable frequency is selected in the external fluctuation, the separated region disappears in almost all each phases owing to the depression of the shear layer near the wall.

A vortex-street model of the flow in the similarity region of a two-dimensional free turbulent jet

1982 ◽  
Vol 123 ◽  
pp. 523-535 ◽  
Author(s):  
J. W. Oler ◽  
V. W. Goldschmidt
Keyword(s):  
Experimental Data ◽  
Reynolds Stress ◽  
Turbulent Jet ◽  
Vortex Street ◽  
Two Dimensional ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Core ◽  
The Mean ◽  
Similarity Relationships

The mean-velocity profiles and entrainment rates in the similarity region of a two-dimensional jet are generated by a simple superposition of Rankine vortices arranged to represent a vortex street. The spacings between the vortex centres, their two-dimensional offsets from the centreline, as well as the core radii and circulation strengths, are all governed by similarity relationships and based upon experimental data.Major details of the mean flow field such as the axial and lateral mean-velocity components and the magnitude of the Reynolds stress are properly determined by the model. The sign of the Reynolds stress is, however, not properly predicted.

Turbulence characteristics of the boundary layer on a rotating disk

1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Structural Model ◽  
Rotating Disk ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Dimensional Boundary ◽  
The Mean

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

1976 ◽  
Vol 352 (1669) ◽  
pp. 213-247 ◽  
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Viscous Dissipation ◽  
Mean Flow ◽  
Fine Grained ◽  
Large Eddy ◽  
The Mean ◽  
Three Components

In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

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

2018 ◽  
Vol 75 (1) ◽  
pp. 3-20 ◽  
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.

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