The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise

1975 ◽  
Vol 70 (3) ◽  
pp. 595-604 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Closed Form Solution ◽  
Low Frequency ◽  
Form Solution ◽  
Point Sources ◽  
Mean Flow ◽  
Doppler Factor ◽  
The Mean ◽  
Axisymmetric Shear ◽  
Arbitrary Velocity ◽  
Multipole Sources

We have obtained a closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponentnof the Doppler factor (1 -Mcosθ)−nmultiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

The low frequency sound from multipole sources in axisymmetric shear flows. Part 2

1976 ◽  
Vol 75 (1) ◽  
pp. 17-28 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Shear Flows ◽  
Acoustic Radiation ◽  
Previous Analysis ◽  
Low Frequency ◽  
Frequency Sound ◽  
Doppler Factor ◽  
Axisymmetric Shear ◽  
Multipole Sources

A previous analysis of the acoustic radiation from multipole sources is extended to include additional components of the dipole and quadrupole sources. It is found that, unlike the components of the sources considered in the previous paper, the exponent of the Doppler factor now depends on the location of the sources within the jet.

Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets

2012 ◽  
Vol 695 ◽  
pp. 199-234 ◽  
Author(s):  
M. E. Goldstein ◽  
Adrian Sescu ◽  
M. Z. Afsar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Low Frequency ◽  
Source Location ◽  
Parallel Flow ◽  
Numerical Calculations ◽  
Mean Flow ◽  
Frequency Sound ◽  
The Mean ◽  
Radiated Sound

AbstractIt is now well-known that there is an exact formula relating the far-field jet noise spectrum to the convolution product of a propagator (that accounts for the mean flow interactions) and a generalized Reynolds stress autocovariance tensor (that accounts for the turbulence fluctuations). The propagator depends only on the mean flow and an adjoint vector Green’s function for a particular form of the linearized Euler equations. Recent numerical calculations of Karabasov, Bogey & Hynes (AIAA Paper 2011-2929) for a Mach 0.9 jet show use of the true non-parallel flow Green’s function rather than the more conventional locally parallel flow result leads to a significant increase in the predicted low-frequency sound radiation at observation angles close to the downstream jet axis. But the non-parallel flow appears to have little effect on the sound radiated at $9{0}^{\ensuremath{\circ} } $ to the downstream axis. The present paper is concerned with the effects of non-parallel mean flows on the adjoint vector Green’s function. We obtain a low-frequency asymptotic solution for that function by solving a very simple second-order hyperbolic equation for a composite dependent variable (which is directly proportional to a pressure-like component of this Green’s function and roughly corresponds to the strength of a monopole source within the jet). Our numerical calculations show that this quantity remains fairly close to the corresponding parallel flow result at low Mach numbers and that, as expected, it converges to that result when an appropriately scaled frequency parameter is increased. But the convergence occurs at progressively higher frequencies as the Mach number increases and the supersonic solution never actually converges to the parallel flow result in the vicinity of a critical- layer singularity that occurs in that solution. The dominant contribution to the propagator comes from the radial derivative of a certain component of the adjoint vector Green’s function. The non-parallel flow has a large effect on this quantity, causing it (and, therefore, the radiated sound) to increase at subsonic speeds and decrease at supersonic speeds. The effects of acoustic source location can be visualized by plotting the magnitude of this quantity, as function of position. These ‘altitude plots’ (which represent the intensity of the radiated sound as a function of source location) show that while the parallel flow solutions exhibit a single peak at subsonic speeds (when the source point is centred on the initial shear layer), the non-parallel solutions exhibit a double peak structure, with the second peak occurring about two potential core lengths downstream of the nozzle. These results are qualitatively consistent with the numerical calculations reported in Karabasov et al. (2011).

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

Wall friction and velocity measurements in a double-frequency pulsating turbulent flow

2016 ◽  
Vol 788 ◽  
pp. 521-548 ◽  
Author(s):  
L. R. Joel Sundstrom ◽  
Berhanu G. Mulu ◽  
Michel J. Cervantes
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Low Frequency ◽  
Turbulent Pipe Flow ◽  
Oscillating Flow ◽  
Base Case ◽  
Mean Flow ◽  
Double Frequency ◽  
The Mean ◽  
Wall Shear

Wall shear stress measurements employing a hot-film sensor along with laser Doppler velocimetry measurements of the axial and tangential velocity and turbulence profiles in a pulsating turbulent pipe flow are presented. Time-mean and phase-averaged results are derived from measurements performed at pulsation frequencies ${\it\omega}^{+}={\it\omega}{\it\nu}/\bar{u}_{{\it\tau}}^{2}$ over the range of 0.003–0.03, covering the low-frequency, intermediate and quasi-laminar regimes. In addition to the base case of a single pulsation imposed on the mean flow, the study also investigates the flow response when two pulsations are superimposed simultaneously. The measurements from the base case show that, when the pulsation belongs to the quasi-laminar regime, the oscillating flow tends towards a laminar state in which the velocity approaches the purely viscous Stokes solution with a low level of turbulence. For ${\it\omega}^{+}<0.006$, the oscillating flow is turbulent and exhibits a region with a logarithmic velocity distribution and a collapse of the turbulence intensities, similar to the time-averaged counterparts. In the low-frequency regime, the oscillating wall shear stress is shown to be directly proportional to the Stokes length normalized in wall units $l_{s}^{+}~(=\sqrt{2/{\it\omega}^{+}})$, as predicted by quasi-steady theory. The base case measurements are used as a reference when evaluating the data from the double-frequency case and the oscillating quantities are shown to be close to superpositions from the base case. The previously established view that the time-averaged quantities are unaffected by the imposition of small-amplitude pulsed unsteadiness is shown to hold also when two pulsations are superposed on the mean flow.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

scholarly journals The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

2015 ◽  
Vol 45 (8) ◽  
pp. 2095-2113 ◽  
Author(s):  
Ru Chen ◽  
Glenn R. Flierl
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Ocean Model ◽  
Invariance Property ◽  
Mean Flow ◽  
Eddy Diffusivities ◽  
Energy Cascades ◽  
The Mean ◽  
Flow Theories ◽  
Noise Forcing

AbstractLow-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

Topographic Form Drag on Tides and Low-Frequency Flow: Observations of Nonlinear Lee Waves over a Tall Submarine Ridge near Palau

2020 ◽  
Vol 50 (5) ◽  
pp. 1489-1507 ◽  
Author(s):  
Gunnar Voet ◽  
Matthew H. Alford ◽  
Jennifer A. MacKinnon ◽  
Jonathan D. Nash
Keyword(s):  
Ocean Circulation ◽  
Neap Tide ◽  
Spring Tide ◽  
Tidal Flow ◽  
Low Frequency ◽  
Buoyancy Frequency ◽  
Mean Flow ◽  
Submarine Ridge ◽  
The Mean ◽  
The Waves

AbstractTowed shipboard and moored observations show internal gravity waves over a tall, supercritical submarine ridge that reaches to 1000 m below the ocean surface in the tropical western Pacific north of Palau. The lee-wave or topographic Froude number, Nh0/U0 (where N is the buoyancy frequency, h0 the ridge height, and U0 the farfield velocity), ranged between 25 and 140. The waves were generated by a superposition of tidal and low-frequency flows and thus had two distinct energy sources with combined amplitudes of up to 0.2 m s−1. Local breaking of the waves led to enhanced rates of dissipation of turbulent kinetic energy reaching above 10−6 W kg−1 in the lee of the ridge near topography. Turbulence observations showed a stark contrast between conditions at spring and neap tide. During spring tide, when the tidal flow dominated, turbulence was approximately equally distributed around both sides of the ridge. During neap tide, when the mean flow dominated over tidal oscillations, turbulence was mostly observed on the downstream side of the ridge relative to the mean flow. The drag exerted by the ridge on the flow, estimated to for individual ridge crossings, and the associated power loss, thus provide an energy sink both for the low-frequency ocean circulation and the tidal flow.

scholarly journals Interannual Variability of the Intraseasonal Oscillation and Its Impact on the Summertime Wave Patterns and Tropical Cyclones over the Western North Pacific

2017 ◽  
Vol 145 (9) ◽  
pp. 3465-3483 ◽  
Author(s):  
Ken-Chung Ko ◽  
Jyun-Hong Liu
Keyword(s):  
Tropical Cyclones ◽  
Large Scale ◽  
Intraseasonal Oscillation ◽  
Low Frequency ◽  
Mean Flow ◽  
Background Flow ◽  
Wave Patterns ◽  
Intraseasonal Oscillations ◽  
The Mean ◽  
Local Weather

In this study, intraseasonal oscillations (ISOs) and submonthly wave patterns were separated into maximal variance (MaxV) and minimal variance (MinV) years on the basis of ISO variance from July to October. The mean-state 850-hPa streamfunction for submonthly cases indicated that, in the MinV years, tropical cyclones (TCs) formed near areas southeast of those in the MaxV years. ISOs propagated northward in the MaxV years, whereas a weaker westward-propagating tendency was observed in the MinV years. Track analysis of the centers of the submonthly cyclonic anomalies suggested that the background flow dictated the propagation routes of the easterly cyclonic anomalies in the MaxV years. However, the propagation routes of the westerly cyclonic anomalies were barely affected by the background flow. Further analysis of the ISO mean flow patterns showed that in the MaxV years, the propagation routes of the westerly cyclonic anomalies were more likely controlled by the anomalous easterly flow generated by the ISO westerly cyclonic anomalies. Moreover, rainfall was heavier in Taiwan in the MaxV years because the background flow in the MinV years caused the submonthly cyclonic anomaly tracks to shift away from Taiwan. Therefore, low-frequency large-scale circulations can affect smaller-scale phenomena and local weather.

scholarly journals Temperature Distribution to Fluid Transport in a Vertical Porous Tube under the Action of Peristalsis

2019 ◽  
Vol 9 (1S5) ◽  
pp. 302-305
Keyword(s):  
Heat Transfer ◽  
Fluid Transport ◽  
Amplitude Ratio ◽  
Wave Length ◽  
Closed Form Solution ◽  
Form Solution ◽  
Boundary Wall ◽  
Long Wave ◽  
The Mean ◽  
Axisymmetric Tube

Peristaltic transport of a Newtonian fluid, with heat transfer, in a vertical porous axisymmetric tube under long wave length approximation is considered. Closed form solution is obtained as an asymptotic expansion in terms of porosity and free convection parameters. Expressions for temperature, coefficient of heat transfer and pressure -flow relationship at the boundary wall of the tube are derived. It is observed that pressure drop increases as amplitude ratio increases. Further, it has been observed that for some specific values of otherparameters under consideration the mean flux significantly increases by about 8 to 10 percent as Grashof number increasesfrom 1 to 2.

Finding Multiple Basin Modes in a Linear Ocean Model

2007 ◽  
Vol 24 (6) ◽  
pp. 1033-1049 ◽  
Author(s):  
Yury Vikhliaev ◽  
Paul Schopf ◽  
Tim DelSole ◽  
Ben Kirtman
Keyword(s):  
Linear Models ◽  
Low Frequency ◽  
Ocean Model ◽  
Water Model ◽  
Mean Flow ◽  
Breeding Method ◽  
Breeding Technique ◽  
Complex Eigenvalues ◽  
Basin Geometry ◽  
The Mean

A method for finding the most unstable eigenmodes in linear models using the breeding technique was developed. The breeding technique was extended to allow for the calculation of complex eigenvalues and eigenvectors of the linear model operator without involving computationally expensive matrix manipulations. While the breeding method finds the most unstable modes, multiple planetary basin modes may be found by removing the leading modes using the adjoint model. To test the sensitivity of basin modes to model formulation, the method was applied for the calculation of the gravest planetary basin modes in a reduced-gravity linear shallow water model with complex basin geometry and background circulation. It was found that the leading basin modes are not sensitive to the form of the dissipation or model resolution, suggesting that the decadal modes are robust. However, the properties of the low-frequency modes are strongly affected by the basin geometry and the mean flow.

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