/pdf/evidence-of-very-long-meandering-features-in-the-logarithmic-2m2f4f0daq.pdf

Evidence of very long meandering features in the logarithmic region of turbulent boundary layers

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

/pdf/the-phenomenology-of-small-scale-turbulence-3a5uzrupts.pdf

The phenomenology of small-scale turbulence

Turbulence models for near-wall and low Reynolds number flows - A review

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

Additional experimental studies of the structure of Reynolds stress which supplement our previous work (Willmarth & Lu 1971) are reported. The velocity at the edge of the viscous sublayer is again used as a detector signal for bursts and sweeps. The signal uv obtained from an X-wire probe at various locations is conditionally sampled and sorted into four quadrants of the u, v plane. Using this method it is found that, when the velocity uw at the edge of the viscous sublayer becomes low and decreasing, a burst occurs. On the other hand, a sweep occurs when uw becomes large and increasing. The convection speeds of the bursts and the sweeps are found to be equal and are about 0·8 times the local mean velocity and 0·425 times the free-stream velocity at a distance y ≈ 0·15δ* from the wall (δ* is the displacement thickness). Throughout the turbulent boundary layer, the bursts are the largest contributors to from different events. Both mean time intervals are approximately equal and constant for most of the turbulent boundary layer. The scaling of the mean time interval between bursts with outer flow variables is confirmed. It is suggested that many of the features of the fluctuating flow revealed by the measurements may be explained by convection past the measuring station of an evolving deterministic flow pattern such as the hairpin vorticity model of Willmarth & Tu (1967).

Measurements of the structure of the Reynolds stress in a turbulent boundary layer

Using a hot wire in a turbulent boundary layer in air, an experimental study has been made of the frequent periods of activity (to be called ‘bursts’) noticed in a turbulent signal that has been passed through a narrow band-pass filter. Although definitive identification of bursts presents difficulties, it is found that a reasonable characteristic value for the mean interval between such bursts is consistent, at the same Reynolds number, with the mean burst periods measured by Kline et al. (1967), using hydrogen-bubble techniques in water. However, data over the wider Reynolds number range covered here show that, even in the wall or inner layer, the mean burst period scales with outer rather than inner variables; and that the intervals are distributed according to the log normal law. It is suggested that these ‘bursts’ are to be identified with the ‘spottiness’ of Landau & Kolmogorov, and the high-frequency intermittency observed by Batchelor & Townsend. It is also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and outer layers.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112071001605

The ‘bursting’ phenomenon in a turbulent boundary layer

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter
 \[
 \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02,
 \]
 where U* is the friction velocity. Downstream of this region the decay of fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

On the criteria for reverse transition in a two-dimensional boundary layer flow

Static pressures have been measured in the separated flow region behind backward-facing steps in a wind tunnel, suitable corrections being applied for the model blockage. The results indicate a reasonably well defined similarity in the pressure distribution.

Similarities in Pressure Distribution in Separated Flow Behind Backward-Facing Steps

Investigations have been carried out of some aspects of the fine-scale structure of turbulence in grid flows, in boundary layers in a zero pressure gradient and in a boundary layer in a strong favourable pressure gradient leading to relaminarization. Using a narrow-band filter with suitable mid-band frequencies, the properties of the fine-scale structure (appearing as high frequency pulses in the filtered signal) were analysed using the variable discriminator level technique employed earlier by Rao, Narasimha & Badri Narayanan (1971). It was found that, irrespective of the type of flow, the characteristic pulse frequency (say Np) defined by Rao et al. was about 0·6 times the frequency of the zero crossings.
It was also found that, over the small range of Reynolds numbers tested, the ratio of the width of the fine-scale regions to the Kolmogorov scale increased linearly with Reynolds number in grid turbulence as well as in flat-plate boundarylayer flow. Nearly lognormal distributions were exhibited by this ratio as well as by the interval between successive zero crossings.
The values of Np and of the zero-crossing rate were found to be nearly constant across the boundary layer, except towards its outer edge and very near the wall. In the zero-pressure-gradient boundary-layer flow, very near the wall the high frequency pulses were found to occur mostly when the longitudinal velocity fluctuation u was positive (i.e. above the mean), whereas in the outer part of the boundary layer the pulses more often occurred when u was negative. During acceleration this correlation between the fine-scale motion and the sign of u was less marked.

Experiments on the fine structure of turbulence

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but $\overline{u^{\prime}v^{\prime}} $ tends to become zero at a reasonably well-defined point. During reverse transition $\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$ also decreases as the flow moves downstream and Lissajous figures taken with u’ and v’ signals confirm this trend. There is approximate similarly between $\overline{u^{\prime 2}} $ profiles if the value of $\overline{u^{\prime 2}_{\max}} $ and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of $\overline{u^{\prime 2}} $ is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

M. A. Badri Narayanan

Papers

The ‘bursting’ phenomenon in a turbulent boundary layer

On the criteria for reverse transition in a two-dimensional boundary layer flow

Similarities in Pressure Distribution in Separated Flow Behind Backward-Facing Steps

Experiments on the fine structure of turbulence

An experimental study of reverse transition in two-dimensional channel flow