Mechanical Engineering - Research Publications
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ItemStructure Inclination Angles in the Convective Atmospheric Surface Layer(SPRINGER, 2013-04)
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ItemMultiscale Geometry and Scaling of the Turbulent-Nonturbulent Interface in High Reynolds Number Boundary Layers(AMER PHYSICAL SOC, 2013-07-24)The scaling and surface area properties of the wrinkled surface separating turbulent from nonturbulent regions in open shear flows are important to our understanding of entrainment mechanisms at the boundaries of turbulent flows. Particle image velocimetry data from high Reynolds number turbulent boundary layers covering three decades in scale are used to resolve the turbulent-nonturbulent interface experimentally and, for the first time, determine unambiguously whether such surfaces exhibit fractal scaling. Box counting of the interface intersection with the measurement plane exhibits power-law scaling, with an exponent between -1.3 and -1.4. A complementary analysis based on spatial filtering of the velocity fields also shows power-law behavior of the coarse-grained interface length as a function of filter width, with an exponent between -0.3 and -0.4. These results establish that the interface is fractal-like with a multiscale geometry and fractal dimension of Df≈2.3-2.4.
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ItemScaling of the turbulent/non-turbulent interface in boundary layers(CAMBRIDGE UNIV PRESS, 2014-07)Abstract Scaling of the interface that demarcates a turbulent boundary layer from the non-turbulent free stream is sought using theoretical reasoning and experimental evidence in a zero-pressure-gradient boundary layer. The data-analysis, utilising particle image velocimetry (PIV) measurements at four different Reynolds numbers ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\delta u_{\tau }/\nu =1200\mbox{--}14\, 500$), indicates the presence of a viscosity dominated interface at all Reynolds numbers. It is found that the mean normal velocity across the interface and the tangential velocity jump scale with the skin-friction velocity$u_{\tau }$and are approximately$u_{\tau }/10$and$u_{\tau }$, respectively. The width of the superlayer is characterised by the local vorticity thickness$\delta _{\omega }$and scales with the viscous length scale$\nu /u_{\tau }$. An order of magnitude analysis of the tangential momentum balance within the superlayer suggests that the turbulent motions also scale with inner velocity and length scales$u_{\tau }$and$\nu /u_{\tau }$, respectively. The influence of the wall on the dynamics in the superlayer is considered via Townsend’s similarity hypothesis, which can be extended to account for the viscous influence at the turbulent/non-turbulent interface. Similar to a turbulent far-wake the turbulent motions in the superlayer are of the same order as the mean velocity deficit, which lends to a physical explanation for the emergence of the wake profile in the outer part of the boundary layer.
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ItemThe turbulent/non-turbulent interface and entrainment in a boundary layer(CAMBRIDGE UNIV PRESS, 2014-03)Abstract The turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number ($\mathit{Re}_\tau =14\, 500$) is examined using particle image velocimetry. An experimental set-up is utilized that employs multiple high-resolution cameras to capture a large field of view that extends $2\delta \times 1.1\delta $ in the streamwise/wall-normal plane with an unprecedented dynamic range. The interface is detected using a criteria of local turbulent kinetic energy and proves to be an effective method for boundary layers. The presence of a turbulent/non-turbulent superlayer is corroborated by the presence of a jump for the conditionally averaged streamwise velocity across the interface. The steep change in velocity is accompanied by a discontinuity in vorticity and a sharp rise in the Reynolds shear stress. The conditional statistics at the interface are in quantitative agreement with the superlayer equations outlined by Reynolds (J. Fluid Mech., vol. 54, 1972, pp. 481–488). Further analysis introduces the mass flux as a physically relevant parameter that provides a direct quantitative insight into the entrainment. Consistency of this approach is first established via the equality of mean entrainment calculations obtained using three different methods, namely, conditional, instantaneous and mean equations of motion. By means of ‘mass-flux spectra’ it is shown that the boundary-layer entrainment is characterized by two distinctive length scales which appear to be associated with a two-stage entrainment process and have a substantial scale separation.
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ItemSelf-similarity in the inertial region of wall turbulence(AMER PHYSICAL SOC, 2014-12-24)The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013)] connects the asymptotic value of κ with an emerging condition of dynamic self-similarity on an interior inertial domain that contains a geometrically self-similar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ. It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same self-similarity that is analytically shown to exist between any given layer and its position, then κ≡Φ(-2)=0.381966..., where Φ=(1+√5)/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ=Φ(-2). Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wall-parallel plane, and the other pertains to the changing size of these motions in the wall-normal direction. In accord with self-similar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the self-similar geometric structure indicated by the analysis, and in particular the special form of self-similarity shown to correspond to κ=Φ(-2).