A. Prabhu

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Response of a turbulent boundary layer to a step change in surface heat flux

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0 is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

Equilibrium and relaxation in turbulent wakes

In order to study the memory of the larger eddies in turbulent shear flow, experiments have been conducted on plane turbulent wakes undergoing transition from an initial (carefully prepared) equilibrium state to a different final one, as a result of a nearly impulsive pressure gradient. It is shown that under the conditions of the experiments the equations of motion possess self-preserving solutions in the sense of Townsend (1956), but the observed behaviour of the wake is appreciably different when the pressure gradient is not very small, as the flow goes through a slow relaxation process before reaching final equilibrium. Measurements of the Reynolds stresse show that the approach to a new equilibrium state is exponential, with a relaxation length of the order of 103 momentum thicknesses. It is suggested that a flow satisfying the conditions required by a self-preservation analysis will exhibit equilibrium only if the relaxation length is small compared with a characteristic streamwise length scale of the flow.

Turbulent heat flux variation over the Monsoon-Trough region during MONTBLEX-90

Tower data collected during the Monsoon-Trough Boundary Layer Experiment (MONTBLEX-90) have been analysed to understand the observed structure of the surface layer over an arid region (Jodhpur) and a moist region (Kharagpur) during active and weak phases of the 1990 southwest monsoon. Turbulent heat and momentum fluxes are estimated by the eddy correlation method using sonic data. The turbulent momentum flux at both Jodhpur and Kharagpur was larger when the winds were stronger, reaching a maximum of the order of 0.5 N m −2 on 5 and 6 August when a low pressure system was located over the region. The heat flux at Jodhpur is high during weak monsoon days, the maximum being 450 W m −2 , whereas during active days the flux never exceeds 200 W m −2 . At Kharagpur, the flux does not vary significantly between active and weak monsoon days, the maximum in either phase being 160 W m −2 . At Jodhpur, there is significant contrast in the near-surface air temperature, being higher during weak monsoon days as compared to active days. Cloud cover did not vary significantly in both the regions. The turbulent heat flux variation at both the sites appears to be correlated mainly with soil mixture, and less sensitive to cloud cover.

Estimation of drag coefficient at low wind speeds over the monsoon trough land region during MONTBLEX‐90

Using observational data acquired during the Monsoon Trough Boundary Layer Experiment (MONTBLEX-90), the drag coefficient CD is estimated over two land stations, Jodhpur (arid region) and Kharagpur (moist region), by eddy correlation of velocity data from sonic anemometers. At low winds CD varies with wind speed according to a power law, which at Jodhpur takes the form CD=0.04 Ū10−1.06 (Ū10 being the mean wind speed at 10 m). The large values of the drag coefficient at low winds are associated with both near-neutral and strongly unstable situations. On the other hand, the CD values at Kharagpur are less than at Jodhpur by nearly 50% for wind speeds > 3ms−1, and cannot be explained by the different roughness lengths at the two sites.

Boundary-layer heights over the monsoon trough region during active and break phases

The thermodynamic structure and the heights of the boundary layer over the monsoon trough region of the Indian southwest monsoon are presented for the active and break phases of the monsoon. Results indicate significant and consistent variation in boundary-layer heights between the active and break phases.

Relaminarization in highly favourable pressure gradients on a convex surface

The active stiffening and active compensation analyses are carried out to present the influence of active stiffness on the dynamic behaviour of piezo-hygro-thermo-elastic laminates. A coupled piezoelectric finite element formulation involving a hygrothermal strain field is derived using the virtual work principle and is employed in a nine-noded field consistent Lagrangian element. The closed-loop system is modelled with elastic stiffness, active stiffness introduced by isotropic actuator lamina and geometric stiffness due to stresses developed by hygrothermal strain. Through a parametric study, the influence of active stiffening and active compensation effects or the dynamics of cross-ply and angle-ply laminated plates and shells are highlighted. The active stiffening on thin shells is significantly influenced by boundary effects and the actuator efficiency further decreases with increase in curvature. The reduction in natural frequencies of cross-ply laminates due to hygrothermal strain is actively compensated by active stiffening; however, it is observed that the actuator performance reduces significantly with increase in curvature particularly in angle-ply laminates, which demands the use of directional actuators. The active stiffening and active compensation effects are low in moderately thick piezo-hygro-thermo-elastic plates and shells, which are less influenced by boundary conditions

MONTBLEX tower observations: Instrumentation, data acquisition and data quality

Tower platforms, with instrumentation at six levels above the surface to a height of 30 m, were used to record various atmospheric parameters in the surface layer. Sensors for measuring both mean and fluctuating quantities were used, with the majority of them indigenously built. Soil temperature sensors up to a depth of 30 cm from the surface were among the variables connected to the mean data logger. A PC-based data acquisition system built at the Centre for Atmospheric Sciences, IISc, was used to acquire the data from fast response sensors. This paper reports the various components of a typical MONTBLEX tower observatory and describes the actual experiments carried out in the surface layer at four sites over the monsoon trough region as a part of the MONTBLEX programme. It also describes and discusses several checks made on randomly selected tower data sets acquired during the experiment. Checks made include visual inspection of time traces from various sensors, comparative plots of sensors measuring the same variable, wind and temperature profile plots, calculation of roughness lengths, statistical and stability parameters, diurnal variation of stability parameters, and plots of probability density and energy spectrum for the different sensors. Results from these checks are found to be very encouraging and reveal the potential for further detailed analysis to understand more about surface layer characteristics.

Injection slot location for boundary-layer control in shock-induced separation

An experimental investigation of the effect of tangential air injection in controlling shock-induced turbulent boundary-layer separation is presented, in particular when the injection slot is located inside of what would otherwise have been the recirculating zone in a separated flow. The experiments were carried out at a freestream Mach number of 2.5 in the separated flow induced by a compression corner with a 20 ° angle. The observations made were wall static pressures, pitot profiles, and schlieren visualizations of the flow. The results show that the present location for injection is more effective in suppressing boundary-layer separation than the more conventional one, where the slot is located upstream of where separation would occur in the absence of injection.

Turbulent non-equlibrium wakes

We consider here the detailed application of a model Reynolds stress equation (Narasimha 1969) to plane turbulent wakes subjected to pressure gradients. The model, which is a transport equation for the stress exhibiting relaxation and diffusion, is found to be consistent with the observed response of a wake to a nearly impulsive pressure gradient (Narasimha & Prabhu 1971). It implies in particular that a wake can be in equilibrium only if the longitudinal strain rate is appreciably less than the wake shear. We then describe a further series of experiments, undertaken to investigate the range of validity of the model. It is found that, with an appropriate convergence correction when necessary, the model provides excellent predictions of wake development under favourable, adverse and mixed pressure gradients. Furthermore, the behaviour of constant-pressure distorted wakes, as reported by Keffer (1965, 1967), is also explained very well by the model when account is taken of the effective flow convergence produced by the distortion. In all these calculations, only a simple version of the model is used, involving two non-dimensional constants both of which have been estimated from a single relaxation experiment.