A Mechanism for Oblique Wave Resornance in the Far Wake

In this paper, we investigate to what extent the far-wake ‘signature’ of the near-wake vortex dynamics of a nominally two-dimensional bluff body is affected by the character of the free-stream noise. We confirm the existence of an oblique wave resonance (at frequency, fK–fT), which is caused by nonlinear ‘quadratic’ interactions between primary oblique shedding waves (fK) and secondary two-dimensional waves (fT), which are amplified from free-stream disturbances. In this work, oblique wave resonance is induced by acoustic forcing of two-dimensional waves. The use of acoustic forcing reveals a set of higher-order oblique wave resonances corresponding to frequencies (fK–nfT), where n is an integer. We find from visualization that, even when the secondary two-dimensional waves have the same frequency as the oblique waves, it is the oblique waves that are preferentially amplified. Oblique wave angles up to 74° have been observed. The response of the wake to a large range of forcing frequencies shows a broad region of peak response, centred around F = (fT/fK) = 0.55, and is in reasonable agreement with predictions from linear stability analysis. A similar broad response is found for each of the higher-order oblique wave modes. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = 1/2n = 1/2, 1/4, 1/6,…, and an oblique wave angle given by θmax = 2θK, where θK is the angle of oblique vortex shedding. An increase in forcing amplitude has the effect of bringing the nonlinear wave interactions, leading to oblique wave resonance, further upstream. Paradoxically, the effect of an increase in amplitude (A) of the two-dimensional wave forcing is to further amplify the oblique waves in preference to the two-dimensional waves and, under some conditions, to inhibit the appearance of prominent two-dimensional waves where they would otherwise appear. With a variation in forcing amplitude, the amplitude of oblique wave response is found to be closely proportional to A½. In summary, this investigation confirms the surprising result that it is only through the existence of noise in the free stream that the far wake is ‘connected’ to the near wake.

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Oblique Wave Resonance in the Far Wake

Fluid Mechanics and Its Applications - Advances in Turbulence V ◽

10.1007/978-94-011-0457-9_102 ◽

1995 ◽

pp. 559-564

Author(s):

C. H. K. Williamson ◽

A. Prasad

Keyword(s):

Oblique Wave ◽

Wave Resonance ◽

Far Wake

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A new mechanism for oblique wave resonance in the ‘natural’ far wake

Journal of Fluid Mechanics ◽

10.1017/s0022112093002794 ◽

1993 ◽

Vol 256 ◽

pp. 269-313 ◽

Cited By ~ 46

Author(s):

C. H. K. Williamson ◽

A. Prasad

Keyword(s):

Wave Energy ◽

Free Stream ◽

Three Dimensional ◽

Spectral Peak ◽

Two Dimensional ◽

Near Wake ◽

Wake Structure ◽

Oblique Wave ◽

Wave Resonance ◽

Far Wake

There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.

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Quadrant analysis in the turbulent far-wake of a cylinder

Fluid Dynamics Research ◽

10.1016/0169-5983(87)90013-x ◽

1987 ◽

Vol 2 (1) ◽

pp. 3-14 ◽

Cited By ~ 7

Author(s):

R A Antonia ◽

L W B Browne

Keyword(s):

Quadrant Analysis ◽

Far Wake

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A Double Birkhoff Wake Oscillator for the Modeling of Vortex-Induced Vibration

Volume 7: CFD and VIV; Offshore Geotechnics ◽

10.1115/omae2011-49435 ◽

2011 ◽

Author(s):

R. H. M. Ogink

Keyword(s):

Free Vibration ◽

Added Mass ◽

Mass Force ◽

Near Wake ◽

Vibration Measurements ◽

Vortex Induced Vibration ◽

Fluid Forces ◽

Wake Oscillator ◽

Model Equations ◽

Far Wake

A double Birkhoff wake oscillator for the modeling of vortex-induced vibration is presented in which the oscillating variables are assumed to be associated with the boundary layer/near wake and the far wake. The fluid forces are assumed to consist of a potential added mass force and a force due to vortex shedding. In the limit of vanishing incoming flow velocity, the model equations reduce to a form similar to the Morison equation. The results of the double wake oscillator have been compared with forced vibration measurements and free vibration measurements over a range of mass and damping ratios. The model is capable of describing the most important trends in both the forced and free vibration experiments. Specifically, the double wake oscillator is able to model both the upper and lower branch of free vibration.

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Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers

Journal of Fluid Mechanics ◽

10.1017/s0022112009993703 ◽

2010 ◽

Vol 650 ◽

pp. 181-214 ◽

Cited By ~ 75

Author(s):

ANTONIOS MONOKROUSOS ◽

ESPEN ÅKERVIK ◽

LUCA BRANDT ◽

DAN S. HENNINGSON

Keyword(s):

Boundary Layer ◽

Boundary Layer Flow ◽

Wave Packets ◽

Three Dimensional ◽

Computational Domain ◽

Initial Condition ◽

Oblique Wave ◽

Layer Flow ◽

Optimal Disturbances ◽

Matrix Free

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier–Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien–Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

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