Kapil Chauhan

Variations of von Kármán coefficient in canonical flows

The overlap parameters for the logarithmic law are obtained for available turbulent pipe and channel flow data using composite profiles fitted to the mean velocity. The composite profile incorporates κ, B, and Π as the varying parameters and their resulting behavior with Reynolds number is examined for these flows and compared to results from boundary layers. The von Karman coefficient in channel flow is smaller than the well-established value for zero pressure gradient turbulent boundary layers of 0.384, while in pipe flows it is consistently higher. In contrast, the estimates of the wake parameter Π are the smallest for channel flows and largest for boundary layers. Further, the Superpipe data are reanalyzed to reveal that κ=0.41 is a better value for the von Karman constant in pipe flow. The collective behavior of κ in boundary layers, pipes, and channels reveals that the von Karman coefficient is not universal and exhibits dependence not only on the pressure gradient but also on the flow geometry.

Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations accurately describe the local Cf behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, H, shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of Δ and δ asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter, Π, is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.

Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers

The asymptotic behavior of mean velocity and integral parameters in flat plate turbulent boundary layers under zero pressure gradient are studied for Reynolds numbers approaching infinity. Using the classical two-layer approach of Millikan, Rotta, and Clauser with a logarithmic velocity profile in the overlap region between “inner” and “outer” layers, a fully self-consistent leading-order description of the mean velocity profile and all integral parameters is developed. It is shown that this description fits most high Reynolds number data, and in particular their Reynolds number dependence, exceedingly well; i.e., within experimental errors.

Towards Reconciling the Large-Scale Structure of Turbulent Boundary Layers in the Atmosphere and Laboratory

A collaborative experimental effort employing the minimally perturbed atmospheric surface-layer flow over the salt playa of western Utah has enabled us to map coherence in turbulent boundary layers at very high Reynolds numbers,

Structure Inclination Angles in the Convective Atmospheric Surface Layer

{Re_{\tau}\sim\mathcal{O}(10^6)}

On the Development of Wall-Bounded Turbulent Flows

. It is found that the large-scale coherence noted in the logarithmic region of laboratory-scale boundary layers are also present in the very high Reynolds number atmospheric surface layer (ASL). In the ASL these features tend to scale on outer variables (approaching the kilometre scale in the streamwise direction for the present study). The mean statistics and two-point correlation map show that the surface layer under neutrally buoyant conditions behaves similarly to the canonical boundary layer. Linear stochastic estimation of the three-dimensional correlation map indicates that the low momentum fluid in the streamwise direction is accompanied by counter-rotating roll modes across the span of the flow. Instantaneous flow fields confirm the inferences made from the linear stochastic estimations. It is further shown that vortical structures aligned in the streamwise direction are present in the surface layer, and bear attributes that resemble the hairpin vortex features found in laboratory flows. Ramp-like high shear zones that contribute significantly to the Reynolds shear-stress are also present in the ASL in a form nearly identical to that found in laboratory flows. Overall, the present findings serve to draw useful connections between the vast number of observations made in the laboratory and in the atmosphere.

Study of the Streamwise Evolution of Turbulent Boundary Layers to High Reynolds Numbers

Recent improvements in three techniques for measuring skin friction in two- and three- dimensional turbulent wall-bounded shear flows are presented. The techniques are: oil-film interferometry, hot wires mounted near the wall, and surface hot-film sensors based on MEMS technology. First, we demonstrate that the oil-film interferometry technique can be used to measure the skin friction magnitude and its direction in two- and three-dimensional wall-bounded shear flows. The results also demonstrate that accurate measurements of the mean skin friction with MEMS sensors are possible. Second, fluctuating skin friction is measured in two- and three-dimensional turbulent boundary layers using a MEMS sensor and a wall-wire as reference. Statistics like skewness, flatness and spectra of the turbulent skin friction are presented to demonstrate the potential and limitations of the MEMS sensor. Finally, the skin friction is measured using the oil film technique with an accuracy of about 1.5%, over the range of Reynolds numbers 10,000 < Reθ < 70,000, in a zero pressure-gradient boundary layer. The results are very well represented by the log-law with κ = 0.38, C = 4.1.

Organised motions in turbulent boundary layers over a wide range of Reynolds number

Two-point correlations of the fluctuating streamwise velocity are examined in the atmospheric surface layer over the salt flats of Utah’s western desert, and corresponding structure inclination angles are obtained for neutral, stable and unstable conditions. The neutral surface-layer results supplement evidence for the invariance of the inclination angle given in Marusic and Heuer (Phys Rev Lett 99:114504, 2007). In an extension of those results it is found that the inclination angle changes drastically under different stability conditions in the surface layer, varying systematically with the Monin–Obukhov stability parameter in the unstable regime. The variation is parametrized and subsequently can be used to improve existing near-wall models in the large-eddy simulation of the atmospheric surface layer.