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Wenbo.Tang@asu.edu

Asst Professor
School of Math & Stat Sciences
Faculty
Mail Code: 1804

PSA 837 Arizona State University (Map)
(480)965-1476

Bio

Assistant Professor, School of Mathematical and Statistical Sciences, College of Liberal Arts and Sciences

Education

PhD Mechanical and Aerospace Engineering, 2005, UC San Diego
M.S. Mechanical and Aerospace Engineering, 2002, UC San Diego
B.E. Engineering Mechanics, 2001, Zhejiang University

Research

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, Wenbo Tang's group uses 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). Tang is 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. Tang is 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 Tang's group 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. Tang is interested in generalizing these results to stratified turbulent flows subject to different forcings and seek the possibility of implementing this quantification in real parameterizations.

Research Interests

Theoretical, Numerical studies of mixing and chaotic transport in environmental, geophysical and engineering flows

Courses

Spring 2014

Courses Taught This Semester
Course Number Course Title
APM 502 Differential Equations II
APM 792 Research
MAT 494 Special Topics

Fall 2013

Courses Taught This Semester
Course Number Course Title
APM 560 Applied Dynamical Systems
APM 792 Research
MAT 343 Applied Linear Algebra
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 494 Special Topics

Summer 2013

Courses Taught This Semester
Course Number Course Title
APM 792 Research

Spring 2013

Courses Taught This Semester
Course Number Course Title
APM 792 Research
MAT 343 Applied Linear Algebra
MAT 492 Honors Directed Study
MAT 493 Honors Thesis

Fall 2012

Courses Taught This Semester
Course Number Course Title
APM 792 Research
MAE 593 Applied Project
MAT 266 Calculus for Engineers II
MAT 492 Honors Directed Study
MAT 493 Honors Thesis

Spring 2012

Courses Taught This Semester
Course Number Course Title
APM 792 Research
MAT 266 Calculus for Engineers II
MAT 343 Applied Linear Algebra
MAT 493 Honors Thesis

Fall 2011

Courses Taught This Semester
Course Number Course Title
APM 591 Seminar
APM 792 Research
MAT 275 Modern Differential Equations
MAT 462 Applied Partial Diff Equations
MAT 492 Honors Directed Study
MAT 591 Seminar

Spring 2011

Courses Taught This Semester
Course Number Course Title
MAT 275 Modern Differential Equations
MAT 343 Applied Linear Algebra

Fall 2010

Courses Taught This Semester
Course Number Course Title
APM 560 Applied Dynamical Systems
MAT 343 Applied Linear Algebra

Spring 2010

Courses Taught This Semester
Course Number Course Title
MAT 462 Applied Partial Diff Equations
MAT 494 Special Topics
MAT 591 Seminar

Fall 2009

Courses Taught This Semester
Course Number Course Title
MAT 452 Intro Chaos/Nonlinear Dynamics
MAT 462 Applied Partial Diff Equations
MAT 494 Special Topics
MAT 591 Seminar

Publications and Other Intellectual ContributionsGoogle Scholar

  1. Wenbo Tang, Alex Mahalov. Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere.. Physics of Plasmas (2013).

  2. Wenbo Tang, Christopher Luna. Dependence of advection-diffusion-reaction on flow coherent structures. Physics of Fluids (2013).

  3. Wenbo Tang, Brent Knutson, Alex Mahalov, Reneta Dimitrova. The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models.. Physics of Fluids (2012).

  4. Wenbo Tang, Phillip Walker. Finite-time statistics of scalar diffusion in Lagrangian coherent structures.. Phys. Rev. E (2012).

  5. Wenbo Tang, Pak Wai Chan, George Haller. Lagrangian Characterization of Terrain Induced Turbulence Based on LIDAR Observations. Part I: Turbulence structure detection. J. Appl. Meteor. Clim. (2011).

  6. Wenbo Tang, Pak Wai Chan, George Haller. Lagrangian Characterization of Terrain Induced Turbulence Based on LIDAR Observations. Part II: Flow Characteristics and Airplane Approaches.. J. Appl. Meteor. Clim. (2011).

  7. Wenbo Tang, Jay Taylor, Alex Mahalov. Stochastic Lagrangian Coherent Structures of Inertia-Gravity Waves. Physics of Fluids (2010).

  8. Wenbo Tang, Manikandan Mathur, George Haller, Douglas C. Hahn and Frank H. Ruggiero. Lagrangian Coherent Structures near a subtropical jet stream. Journal of Atmospheric Sciences (2010).

  9. Wenbo Tang, Pak Wai Chan, George Haller. Accurate extraction of Lagrangian coherent structures over finite domains with application to flight data analysis over Hong Kong International Airport. Chaos (2010).

  10. Wenbo Tang, Thomas Peacock. Lagrangian Coherent Structures and internal wave attractors. Chaos (2010).

  11. Wenbo Tang, Colm Caulfield, Rich Kerswell. A prediction for the optimal stratification for turbulent mixing. Journal of Fluid Mechanics (2009).

  12. Wenbo Tang, George Haller, Jong-Jin Baik and Young-Hee Ryu. Locating an Atmospheric Contamination Source Using Slow Manifolds. Physics of Fluids (2009).

  13. Wenbo Tang, George Haller and Pak Wai Chan. Lagrangian Coherent Structures and Turbulence Detection near the Hong Kong International Airport based on LIDAR Measurements. American Meteorological Society 17th Conference on Atmospheric and Oceanic Fluid Dynamics

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Research Activity Research Awards

  1. Tang,Wenbo * . Collaborative Research: Theories and experiments on scalar mixing in chaotic flows. NSF-MPS-DMS (9/1/2012 - 8/31/2015).
  2. Kostelich,Eric John * , Armbruster,Hans Dieter , Czygrinow,Andrzej Michal , Fishel,Susanna , Gelb,Anne , Jacobs,Mark , Kawski,Matthias , Kuang,Yang , Mahalov,Alex , Moustaoui,Mohamed , Platte,Rodrigo B , Tang,Wenbo , . MCTP: Mathematics Mentoring Partnership Between Arizona State University and the Maricopa County Community College District. NSF-MPS-DMS (7/15/2012 - 6/30/2017).
  3. Mahalov,Alex * , Fernando,H J S , Huang,Huei-Ping , Moustaoui,Mohamed , Tang,Wenbo , . CMG Research: Multiscale Modeling of Urban Atmosphere in a Changing Climate. NSF-MPS-DMS (9/1/2009 - 8/31/2014).
  4. Mittelmann,Renate M * , Fernando,H J S , Herrmann,Marcus , Huang,Huei-Ping , Lopez,Juan Manuel , Mahalov,Alex , Tang,Wenbo , . Plant Fund: SCREMS: Visualization of Complex Spatio-Temporal Multiscale Fluid Dynamic Phenomena. NSF-MPS-DMS (8/1/2009 - 7/31/2010).

* principal investigator

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Service

  1. American Physical Society Division of Fluid Dynamics annual conference 2012., Chair of a session (2012)
  2. The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications., Special session 27 co-organizer and co-chair (2011 - 2012)
  3. Basis Scottsdale High School, Invited speaker (2011)
  4. 16th US National Congress of Theoretical and Applied Mechanics., Session Co-chair (2010)
  5. 8th AIMS conference on Dynamical Systems, Differential Equations and Applications, Session Co-chair (2009 - 2010)
  6. Math Colloquia and Distinguished Lectures, Co-chair (2009 - 2010)
  7. Basis Scottsdale High School, Invited speaker (2009)
  8. Math Colloquia and Distinguished Lectures, Co-chair (2008 - 2009)

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