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Paul E. Dimotakis

Bio: Paul E. Dimotakis is an academic researcher from California Institute of Technology. The author has contributed to research in topics: Turbulence & Reynolds number. The author has an hindex of 41, co-authored 159 publications receiving 7910 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors proposed a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100-140 for turbulent mixing.
Abstract: Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.

546 citations

Journal ArticleDOI
TL;DR: In this article, a simple argument is proposed, based on the geometrical properties of the large-scale now structures of the subsonic, fully developed, two-dimensional mixing layer, which yields the entrainment ratio and growth of the turbulent mixing layer.
Abstract: It is observed experimentally that a spatially growing shear layer entrains an unequal amount of fluid from each of the freestreams, resulting in a mixed fluid composition that favors the high-speed fluid. A simple argument is proposed, based on the geometrical properties of the large-scale now structures of the subsonic, fully developed, two-dimensional mixing layer, which yields the entrainment ratio and growth of the turbulent mixing layer. The predictions depend on the velocity and density ratio across the layer and are in good agreement with measurements to date.

496 citations

Journal ArticleDOI
TL;DR: In this article, a turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 10^6, and it was argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.
Abstract: A turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 10^6. Flow visualization with dyes revealed (once more) large coherent structures and showed their role in the entrainment process; observation of the reaction of a base and an acid indicator injected on the two sides of the layer, respectively, gave some indication of where molecular mixing occurs. Autocorrelations of streamwise velocity fluctuations, using a laser-Doppler velocimeter (LDV) revealed a fundamental periodicity associated with the large structures. The surprisingly long correlation times suggest time scales much longer than had been supposed; it is argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.

396 citations

Journal ArticleDOI
TL;DR: In this article, a large increase or decrease in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation.
Abstract: Exploratory experiments have been performed on circular cylinders executing forced rotary oscillations in a steady uniform flow. Flow visualization and wake profile measurements at moderate Reynolds numbers have shown that a considerable amount of control can be exerted over the structure of the wake by such means. In particular, a large increase, or decrease, in the resulting displacement thickness, estimated cylinder drag, and associated mixing with the free stream can be achieved, depending on the frequency and amplitude of oscillation.

394 citations

Journal ArticleDOI
TL;DR: In this paper, an experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented, and the results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high speed stream entrapped in the cores.
Abstract: An experimental investigation of entrainment and mixing in reacting and non-reacting turbulent mixing layers at large Schmidt number is presented. In non-reacting cases, a passive scalar is used to measure the probability density function (p.d.f.) of the composition field. Chemically reacting experiments employ a diffusion-limited acid–base reaction to directly measure the extent of molecular mixing. The measurements make use of laser-induced fluorescence diagnostics and high-speed, real-time digital image-acquisition techniques. Our results show that the vortical structures in the mixing layer initially roll-up with a large excess of fluid from the high-speed stream entrapped in the cores. During the mixing transition, not only does the amount of mixed fluid increase, but its composition also changes. It is found that the range of compositions of the mixed fluid, above the mixing transition and also throughout the transition region, is essentially uniform across the entire transverse extent of the layer. Our measurements indicate that the probability of finding unmixed fluid in the centre of the layer, above the mixing transition, can be as high as 0.45. In addition, the mean concentration of mixed fluid across the layer is found to be approximately constant at a value corresponding to the entrainment ratio. Comparisons with gas-phase data show that the normalized amount of chemical product formed in the liquid layer, at high Reynolds number, is 50% less than the corresponding quantity measured in the gas-phase case. We therefore conclude that Schmidt number plays a role in turbulent mixing of high-Reynolds-number flows.

360 citations


Cited by
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Journal ArticleDOI
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Abstract: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

6,145 citations

Book ChapterDOI
01 Jan 1997
TL;DR: The boundary layer equations for plane, incompressible, and steady flow are described in this paper, where the boundary layer equation for plane incompressibility is defined in terms of boundary layers.
Abstract: The boundary layer equations for plane, incompressible, and steady flow are $$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

2,598 citations

Journal ArticleDOI
TL;DR: In this article, a review of recent developments in the hydro- dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts is presented.
Abstract: The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

1,988 citations

Book ChapterDOI
01 Jan 1989
TL;DR: In this paper, the authors use hot-wire (HW) or laser velocimetry (LV) to estimate the velocity, vorticity, and pressure fields of wake flows.
Abstract: One of the most challenging and time-consuming problems in experimental fluid mechanics is the measurement of the overall flow field properties, such as the velocity, vorticity, and pressure fields. Local measurements of the velocity field (i.e., at individual points) are now done routinely in many experiments using hot-wire (HW) or laser velocimetry (LV). However, many of the flow fields of current interest, such as coherent structures in shear flows or wake flows, are highly unsteady. HW or LV data of such flows are difficult to interpret, as both spatial and temporal information of the entire flow field are required and these methods are commonly limited to simultaneous measurements at only a few spatial locations.

1,798 citations

Journal ArticleDOI
Hassan Aref1
TL;DR: In this paper, it is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator, which is a very simple model which provides an idealization of a stirred tank.
Abstract: In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non-autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area-preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaotic advection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon.

1,730 citations