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| Education | |||
| PhD M.S. B.E. |
Mechanical and Aerospace Engineering, UC San Diego Mechanical and Aerospace Engineering, UC San Diego Engineering Mechanics, Zhejiang University |
2005 2002 2001 |
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| Research Interests | |||
| Theoretical and numerical studies of differential equations and dynamical systems in the context of environmental, geophysical and industrial fluid dynamics. | |||
| Appointments | |||
| Assistant Professor Postdoctoral Associate Postdoctoral Researcher |
Arizona State University Massachusetts Institute of Technology UC San Diego |
2008-present 2006-2008 2005-2006 |
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| Awards and Honors | |||
| 2009-2010 ProjectNExT Fellow CoPI: "SCREMS: Visualization of Complex Spatio-Temporal Multiscale Fluid Dynamic Phenomena", 2009-2010 CoPI: "CMG: Multiscale Modeling of Urban Atmospheres in a Changing Climate", 2009-2013 |
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| CV | |||
| 2009-2010 Colloquia/DLS | |||
| Chaotic Mixing |
| The understanding of a flow system is beyond quantification of ensemble averages. It is in fact very important in applications to identify the patterns with which fluid (and maybe other) particles mix. To understand these patterns, we use Dynamical Systems Methods to extract attractors and repellers in a chaotic flow, and so find the precise organizing structures of the materials of interest. Some applications include identifying turbulence structures in atmospheric flows and understanding the organizing patterns of bacteria subject to nutrient release in a turbulent ocean environment (also vastly many other applications by different research groups). I'm interested in further developing mathematical tools such as individual based models for particles and microorganisms in turbulent flows which will be useful in understanding, e.g., ecology in a chaotic environment. Overall the question that needs to be answered is: Given some resolved flow (from model or observations) what can we tell about the dynamics of different materials of interest and what interesting dynamics will that bring to our understandings of physical/biological processes in the environment? |
| Internal Gravity Waves |
| Internal gravity waves (IGW) is the stratified analog to surface waves. Basically it's the distortion of isopycnals due to some global flow over rugged topography. Energy is converted from the global flow to supply wave motion. It's significance in the ocean is such that after the generation at the site IGW can propagate away and break. This could create elevated mixing away from topography in the ocean interior. Experiments, simulations and analytical models have been developed to address the generation of IGW in the lab or in the ocean. Of particular interest are the total rate of energy conversion, modal composition of wave energy and nonlinear waves generated from topography. Analytical models have been developed in 2D and 3D for subcritical topography. Such a theory is only available for supercritical topography in very special cases in 2D. One feature of IGW is that wave reflection over the topography conserve its angle of attack with respect to the vertical axis. For two supercritical topography close by, there could be a configuration such that wave will reflect and form a closed orbit. This leads to the break down of linear inviscid theory. I'm interested in further developing analytical visco-linear models to address such a problem, and also look for extension to 3D configurations. |
| Stratified Mixing |
| We live in a stratified environment where turbulence is ubiquitous. Stratification creates spatial anisotropy which may inhibit (stable stratification) or enhance (unstable stratification) turbulent motion. On the other hand, as opposed to stirring in an unstratified flow, stratification allows fluid particles of different density to mix and irreversibly change the global density profile. Such a process requires extraction of energy from the global flow. One way to quantify stratified mixing is through the flux Richardson number, which is a ratio between buoyancy flux and total energy consumption (B.F.+Dissipation). Measurements and observations suggest that this number is between 0.1-0.5 for strongly turbulent flows, depending on the different driving forces. This could in turn be used in a parameterization for flow models. Using a mathematical tool we can rigorously estabilish that under typical shear forcing and evaluated over long time 0.1-0.5 is the range of accessible flux Richardson numbers, if turbulence manifests itself to maximize buoyancy flux. I'm interested in generalizing these results to stratified turbulent flows subject to different forcings and seek the possibility of implementing this quantification in real parameterizations. |
MAT462(FA09) |
Applied Partial Differential Equations (LN74670) | Syllabus | Office Hours: TTh12:30-2pm,F10:30-11:30am | |||||||||
Second-order partial differential equations, emphasizing Laplace, wave, and diffusion equations. Solutions by the methods of characteristics, separation of variables, and integral transforms. |
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MAT452(FA09) |
Intro Chaos/Nonlinear Dynamics (LN74668) | Syllabus | Office Hours: TTh12:30-2pm,F10:30-11:30am | |||||||||
Properties of nonlinear dynamical systems; dependence on initial conditions; strange attractors; period doubling; bifurcations; symbolic dynamics; Smale-Birkhoff theorem; and applications. |
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APM560(SP09) |
Applied Dynamical Systems Methods | Syllabus | ||||||||||
Applies modern dynamical systems methods to fluid mechanics: bifurcations, normal forms, nonlinear dynamics, pattern formation, mixing, and Lagrangian chaos. |
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MAT267(SP09) |
Calculus For Engineers III | Syllabus | ||||||||||
Vector-valued functions of several variables, partial derivatives, multiple integration. |
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| 1. Finite-size Pollutant Particle Transport in Urban Street Canyon (right click to play flash movie) | |
Attracting Lagrangian Coherent Structures (LCS) inside an urban street canyon for finite-size inertial particles. The LCS are computed from the slow manifoid velocity derived from simulation data. The forward-time motion shows that an inertial particles is attracted to the local maxima of the Direct Lyapunov Exponent field. The backward-time motion shows the results for inversion of the finite-size particle using different schemes. Reference: Locating an atmospheric contamination source using slow manifolds (2009), Tang, W., Haller, G., Baik, J.-J. & Ryu, Y.-H., Phys. Fluids, 21, 043302. |
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| 2. Lagrangian signatures of a jet stream and balloon measurements | |
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Comparison between the repelling LCS generated from model data and atmospheric characteristics estimated by weather balloon measurements. Color contour is the Forward-time DLE. Black line originating from the big island is the balloon trajectory, green curve is refractive index structure constant Cn2 and blue curve is the dissipation rate. Reference: Lagrangian Coherent Structures Near a Subtropical Jet Stream (2009), Tang, W., Mathur, M., Haller, G., Hahn, D.C. & Ruggiero, F.H., J. Atmos. Sci., submitted. |
| 3. Turbulent structures near Hong Kong International Airport | |
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Phillip Walker is a graduate student in the Mechanical Engineering department. His research interests are Micro Electronic Mechanical Sysytems, Thermofluids, Computational Fluid Dynamics, Control System Design, and Partial Differential Equations. |
| Refereed Journal Publications |
| 1. | Reynolds number dependence of an upper bound for the long-time-averaged buoyancy flux in a plane stratified Couette flow (2004) Caulfield, C.P., Tang, W. & Plasting, S.C., J. Fluid Mech. 498, 315 - 332. [pdf] DOI: 10.1017/S0022112003006797 |
| 2. | Bounds on dissipation in stress-driven flow (2004) Tang, W., Caulfield, C.P. & Young, W.R., J. Fluid Mech. 510, 333 - 352. [pdf] DOI: 10.1017/S0022112004009589 |
| 3. | Bounds on dissipation in stress-driven flow in a rotating frame (2005) Tang, W., Caulfield, C.P. & Young, W.R., J. Fluid Mech. 540, 373 - 391. [pdf] DOI:10.1017/S0022112005005926 |
| 4. | Locating an atmospheric contamination source using slow manifolds (2009), Tang, W., Haller, G., Baik, J.-J. & Ryu, Y.-H., Phys. Fluids, 21, 043302. [pdf] URL: http://link.aip.org/link/?PHF/21/043302 DOI: 10.1063/1.3115065 |
| 5. | A prediction for the optimal stratification for turbulent mixing (2009), Tang, W., Caulfield, C.P. & Kerswell, R.R., J. Fluid Mech., 634, 487-497. [pdf] DOI:10.1017/S0022112009990711 |
| Conference Proceedings |
| 1. | Lagrangian Coherent Structures and Turbulence Detection near the Hong Kong International Airport based on LIDAR Measurements (2009), Tang, W., Haller, G. & Chan, P.W., AMS 17th Conference on Atmospheric and Oceanic Fluid Dynamics. [pdf] |
| Recent submissions |
| 1. | Lagrangian Coherent Structures Near a Subtropical Jet Stream Tang, W., Mathur, M., Haller, G., Hahn, D.C. & Ruggiero, F.H., J. Atmos. Sci., (2009). |
| 2. | Lagrangian Coherent Structures and Internal Wave Attractors, Tang, W., & Peacock, T., Chaos, (2009). |
| To be submitted |
| 1. | Lagrangian Characterization of Terrain Induced Turbulence Based on LIDAR Observations. Part I: Turbulence StructureDetection, Tang, W., Chan, P.W. & Haller, G. (for J. Atmos. Sci.) |
| 2. | Lagrangian Characterization of Terrain Induced Turbulence Based on LIDAR Observations. Part II: Flow Characteristics and Airplane Approaches at Hong Kong International Airport, Tang, W., Chan, P.W. & Haller, G. (for J. Atmos. Sci.) |
| 3. | Stochastic Lagrangian Coherent Structures of Inertial Gravity Waves, Tang, W., Mahalov, A. (for J. Fluid Mech.) |
| I enjoy a variety of outdoor sports ---- skiing, sailing, scuba diving, etc. Now that I'm in the Grand Canyon State, there's no rival against the pair of hiking and landscape photography. Welcome to my photo gallery (click to obtain larger image)! | |
| Landscape Photos | Consuelo |
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