A. K. M. F. Hussain

Coherent structures—reality and myth

The nature and significance of large‐scale coherent structures in turblent shear flows are addressed. A definition for the coherent structure is proposed and its implications discussed. The characteristic coherent structure properties are identified and the analytical and experimental constraints in the eduction of coherent structures are examined. Following a few comments on coherent motions in wall layers, the accumulated knowledge from a number of recent and ongoing coherent structure investigations in excited and unexcited free shear flows in the author’s laboratory is reviewed. Also briefly addressed are effects of initial conditions, the role of coherent structures in jet noise production and broadband noise amplification, the feedback effect of coherent structures, the use of the Taylor hypothesis in coherent structure description, negative production, turbulence suppression via excitation, validity of the Reynolds number similarity hypothesis, etc. From the detailed quantitative results, a picture...

Effects of the initial condition on the axisymmetric free shear layer: Effects of the initial momentum thickness

Spurred by large discrepancies among previous data on the free shear layer, effects of the initial condition on the characteristic measures of an axisymmetric air free shear layer were investigated experimentally. The initial, boundary layer state (i.e., laminar or turbulent), momentum thickness Reynolds number Rϑe, and fluctuation intensity u″pe/Ue have been taken as three characteristic identifiers of the initial condition. The discrepancies among published data are reviewed, and data showing the effects of variations in Rϑe (at constant u″pe/Ue) for both initially laminar and tripped (turbulent) boundary layers are reported. It is found that the spread rate, similarity parameter, and peak turbulent intensity in the self‐preserving region are essentially independent of Rϑe, but dependent on whether the initial boundary layer is laminar or tripped (turbulent). Initially, tripped shear layers manifest two stages of linear growth. The virtual origin as well as the distance required for attainment of self‐p...

Upstream influence on the near field of a plane turbulent jet

The effects of the mean and turbulence characteristics of the upstream (initial) boundary layer on the evolution of the flow in the near field of a plane jet have been experimentally investigated for four initial conditions. Rates of jet widening and centerline mean velocity decay as well as the kinematic and geometric virtual origins show evidence of systematic dependence on initial conditions. The growth rate of longitudinal turbulence intensity, and the mass flux are higher when the initial boundary layer is laminar than when turbulent. Immediately downstream of the exit, the nondimensional entrainment rates for the laminar initial boundary layer cases reach peak values which are about twice the delayed peak values for the fully turbulent initial boundary layer cases. Within the first 40 slit widths, increases in total average streamwise momentum flux range from 20% to 56%, the larger increases occurring for the laminar initial boundary layers; about 10% of each increase is due to the turbulence field. While such increases violate the traditionally accepted momentum flux invariance, they are consistent with the negative mean static pressure data.

Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets

The mean rate of dissipation e is measured along the axes of a plane jet and three circular jets, covering good ranges of the jet Reynolds number Ujd/ν and the downstream distance x. The data confirm the universal relations, derived from requirements of self‐preservation, between e and x, for both the circular jet and the plane jet. For either type of jet, the turbulence Reynolds number Rλ and the local Reynolds number Rc (based on local velocity and length scales) are found to be related as Rλ∼2.3Rc1/2.

Controlled excitation of elliptic jets

Studies of unexcited and excited elliptic jets reveal their characteristics to be noticeably different from circular jets, suggesting applications of excited elliptic jets for enhanced mixing and chemical reaction, and control of aerodynamic noise. The near‐field turbulence characteristics, jet spread, and locations of switching of major and minor axes of the jet cross section can be drastically altered by forcing. The preferred mode and the stable pairing mode of an elliptic jet scale with the exit equivalent diameter.

Effects of the initial condition on the axisymmetric free shear layer: Effect of the initial fluctuation level

An axisymmetric air free shear layer was experimentally investigated in order to determine the effect of the initial peak fluctuation level u′pe/Ue on the characteristic measures of the free shear layer. The shear layer width and the similarity parameter depend noticeably on u′pe/Ue. The asymptotic peak turbulence intensity u′p∞ increases with u′pe/Ue but appears to have a limiting value of about 0.18. The location for achievement of self‐preservation progressively moves upstream with increasing u′pe/Ue, suggesting that higher initial fluctuations hasten the spectral evolution of the velocity fluctuations and development of the shear layer. The results show that the initial fluctuation level has a much more dramatic effect on the evolution and the average characteristic measures of the free shear layer than the initial momentum thickness has, and may have been the primary reason for discrepancies among results from different previous inverstigations.

The coupling between scales in shear flows

In order to explore the relationship between the large‐ and small‐scale motions in turbulent shear flows, a number of flows have been studied based on short‐time correlation measurements. The shear flows investigated are boundary layers, plane and axisymmetric mixing layers, plane wakes and the far fields of plane and circular jets. The coupling between the scales has been obtained by correlating the low‐frequency component of the u‐velocity signal with a signal that is similar to the envelope of the high‐frequency part of the velocity signal. The coupling is found to be significant in all flows. Phase reversal across the shear region is found to occur in the boundary layers and the mixing layers only. This is interpreted to mean that in boundary layers and mixing layers, the streamwise extent of the large structure over which the small‐scale activity reaches a peak moves at one transverse end of the large structure over which its ensemble averaged u fluctuation is positive to another where it is negative. This phase shift (≂180°) of the location of the peak activity of the small scales with respect to the large structure takes place gradually resulting in a midlayer where the phase difference is about 90°. On the other hand, in the far field of the jets and wakes, all across the layer, the peak activity of the small scales always remains confined to that half of the streamwise extent of the large structure where its ensemble averaged u fluctuation is positive; in the remaining streamwise half of the large structure, the small scales remain dormant.

Errors in simultaneous measurements of temperature and velocity in the outer part of a heated jet

Simultaneous measurements of velocity and temperature fluctuations in the outer part of a heated circular jet discharged into still air may be in error as a result of reverse flow regions and the inevitable contamination of the cold (temperature) wire signal by the thermal wake of the hot wire. The error in mean and rms temperature is estimated for the case of two standard hot wire‐cold wire arrangements. At the half‐temperature radius, the mean and rms temperature are overestimated by about 16% and 46%, respectively. Conditional measurements of velocity fluctuations are also presented as a first attempt to obtain velocity statistics without the effect of reverse flow regions. Measured normalized moments of the velocity fluctuation are larger than the ’’corrected’’ values, the difference increasing with the order of the moment and with radial distance in the outer part of the jet.

Dynamics of entangled vortex filaments

The mechanics of two co‐rotating, entangled, slender vortex filaments are analyzed. An equation governing the motions of the vortices is derived on the assumption that their curvature is small. Particular solutions are obtained for two flow situations: one with and one without an external strain field.

A spectral theory for weakly nonlinear instabilities of slowly divergent shear flows

A general theory is proposed for the downstream evolution of nonlinearly interacting waves in a nonparallel shear flow. The waves are represented as Fourier integrals over the spectral range. A multiple scales expansion is employed to predict evolutions of the Fourier mode amplitudes A(x,ω)—where x is the streamwise coordinate and ω is the frequency—by assuming that both nonlinear and nonparallel effects can be expressed in terms of the same expansion parameter e. The theory produces in the leading order the Orr–Sommerfeld equation, and in the next order a Landau‐type integrodifferential equation for A. The linear part of the equation contains only the first‐order spatial derivative, and the nonlinear part consists of wave–wave interactions integrated over the entire spectral range of A. The approach is very general in that no Reynolds number (Re) scaling is involved as Re is retained independent of e throughout and that no Landau constant is involved so that each wave can grow or decay in space or time. The Landau‐type equation is too intricate for analytic solution but is suitable for numerical solution. An asymptotic analysis for large x via the method of stationary phase reveals that the subharmonic components provide the dominant contribution to the nonlinear terms, consistent with experimental observations.