Jimmy Philip

Bio: Jimmy Philip is an academic researcher from University of Melbourne. The author has contributed to research in topics: Turbulence & Reynolds number. The author has an hindex of 19, co-authored 88 publications receiving 1270 citations. Previous affiliations of Jimmy Philip include École Polytechnique & Technion – Israel Institute of Technology.

The turbulent/non-turbulent interface and entrainment in a boundary layer

Abstract: The turbulent/non-turbulent interface in a zero-pressure-gradient turbulent boundary layer at high Reynolds number (Re = 14500) 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 2δ× 1:1δ in the streamwise/wallnormal 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. © 2014 Cambridge University Press. ;

The Turbulent/Non-turbulent Interface and Entrainment in a Boundary Layer

Abstract: 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.

Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers.

Abstract: 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 $\ensuremath{-}1.3$ and $\ensuremath{-}1.4$. 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 $\ensuremath{-}0.3$ and $\ensuremath{-}0.4$. These results establish that the interface is fractal-like with a multiscale geometry and fractal dimension of ${D}_{f}\ensuremath{\approx}2.3--2.4$.

Large-scale eddies and their role in entrainment in turbulent jets and wakes

Abstract: A large-scale or energy-containing eddy model of turbulent axisymmetric jets and wakes is developed, wherein eddies are randomly distributed in the azimuthal and convecting in the axial directions. The mean velocities and second order statistics obtained from the models agree well with the various available experimental data. There is an average inflow into the turbulent jet at the boundary, which is virtually non-existent for wakes. These eddy contributions are used to reconsider the entrainment process, which has to date been largely conceived as either an “engulfment” or “nibbling” process. Here we suggest that entrainment in turbulent jets be viewed as a three-part-process wherein non-turbulent fluid is “induced” and “engulfed” into the turbulent core due to large-scale eddies, which is converted into turbulent motion by the action of small-scale eddies via “nibbling.” However, in wakes there is no induced flow and the primary cause of entrainment is envisaged to be large-scale “engulfment” combined w...

Distance-from-the-wall scaling of turbulent motions in wall-bounded flows

Abstract: An assessment of self-similarity in the inertial sublayer is presented by considering the wall-normal velocity, in addition to the streamwise velocity component. The novelty of the current work lies in the inclusion of the second velocity component, made possible by carefully conducted subminiature ×-probe experiments to minimise the errors in measuring the wall-normal velocity. We show that not all turbulent stress quantities approach the self-similar asymptotic state at an equal rate as the Reynolds number is increased, with the Reynolds shear stress approaching faster than the streamwise normal stress. These trends are explained by the contributions from attached eddies. Furthermore, the Reynolds shear stress cospectra, through its scaling with the distance from the wall, are used to assess the wall-normal limits where self-similarity applies within the wall-bounded flow. The results are found to be consistent with the recent prediction from the work of Wei et al. [“Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows,” J. Fluid Mech. 522, 303–327 (2005)], Klewicki [“Reynolds number dependence, scaling, and dynamics of turbulent boundary layers,” J. Fluids Eng. 132, 094001 (2010)], and others that the self-similar region starts and ends at z+∼O(δ+) and O(δ+), respectively. Below the self-similar region, empirical evidence suggests that eddies responsible for turbulent stresses begin to exhibit distance-from-the-wall scaling at a fixed z+ location; however, they are distorted by viscous forces, which remain a leading order contribution in the mean momentum balance in the region z+≲O(δ+), and thus result in a departure from self-similarity.

Boundary Layer Theory

Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

The Structure of Turbulent Shear Flow

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

Extremes and Recurrence in Dynamical Systems

Abstract: This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its relevance for mathematics, natural sciences, engineering, and social sciences. After exploring the basics of the classical theory of extreme events, the book presents a careful examination of how a dynamical system can serve as a generator of stochastic processes, and explores in detail the relationship between the hitting and return time statistics of a dynamical system and the possibility of constructing extreme value laws for given observables. Explicit derivation of extreme value laws are then provided for selected dynamical systems. The book then discusses how extreme events can be used as probes for inferring fundamental dynamical and geometrical properties of a dynamical system and for providing a novel point of view in problems of physical and geophysical relevance. A final summary of the main results is then presented along with a discussion of open research questions. Finally, an appendix with software in Matlab programming language allows the readers to develop further understanding of the presented concepts.

Physical Fluid Dynamics

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A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime

Abstract: Direct numerical simulations (DNS) are conducted for turbulent flow through pipes with three-dimensional sinusoidal roughnesses explicitly represented by body-conforming grids. The same viscous-scaled roughness geometry is first simulated at a range of different Reynolds numbers to investigate the effects of low Reynolds numbers and low , where is the pipe radius and is the roughness height. Results for the present class of surfaces show that the Hama roughness function is only marginally affected by low Reynolds numbers (or low ), and observations of outer-layer similarity (or lack thereof) show no signs of sensitivity to Reynolds number. Then, building on this, a systematic approach is taken to isolate the effects of roughness height and wavelength in a turbulent wall-bounded flow in both transitionally rough and fully rough regimes. Current findings show that while the effective slope (which for the present sinusoidal surfaces is proportional to ) is an important roughness parameter, the roughness function must also depend on some measure of the viscous roughness height. A simplistic linear–log fit clearly illustrates the strong correlation between and both the roughness average height (which is related to ) and for the surfaces simulated here, consistent with published literature. Various definitions of the virtual origin for rough-wall turbulent pipe flow are investigated and, for the surfaces simulated here, the hydraulic radius of the pipe appears to be the most suitable parameter, and indeed is the only virtual origin that can ever lead to collapse in the total stress. First- and second-order statistics are also analysed and collapses in the outer layer are observed for all cases, including those where the largest roughness height is a substantial proportion of the reference radius (low ). These results provide evidence that turbulent pipe flow over the present sinusoidal surfaces adheres to Townsend’s notion of outer-layer similarity, which pertains to statistics of relative motion.