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Zhi (George) Lin

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  • Passive Scalar Intermittency Show/Hide Background Info

    The mixing and transport phenomena in various fluids are often characterized by the behavior of fluctuation fields of submerged physical observables, many of which can be modeled as passive scalars, such as temperature, moisture, and chemical concentrations. "Passive" means that they do not affect the underlying flow. These quantities not only are the subject matters in environmental control, combustion, and biochemical reactions but also serve as proxies for the study of turbulence.

    Scalar intermittency refers to the non-Gaussian scalar statistics widely observed in laboratory and field experiments. These "intermittent" probability distributions usually possess heavy tails indicating "anomalously" high probabilities for large and rare fluctuations than a normal distribution would suggest. In other words, they are inconsistent with the general Gaussian assumptions used, on account of their mathematical simplicity, in operational meteorology and climatology and they may drastically change the estimates concerning the current and future states of the environment.

    R. Camassa, ZL and R. M. McLaughlin, Evolution of the probability measure for the Majda model: new invariant measures and breathing PDFs, Journal of Statistical Physics, 130(2): 343--371 (2008).

    J. Bronski, R. Camassa, ZL, R. M. McLaughlin and A. Scotti, An explicit family of probability measures for passive scalar diffusion in a random flow, Journal of Statistical Physics, 128(4): 927--968 (2007).

    (Resources: '07 Talk at U. Michigan, '07 Talk Video at MSRI)

  • Mixing Measures Show/Hide Background Info

    When it comes to describing how well-mixed a body of fluid is with some dye in it, there's really no concensus on what measure to use. Scalar statistics is one such measure; traditionally the mean-squared displacement of scalar particles is also one. Spatial variances are yet another common class which measures the homogeneity: after all, they are what we preceive looking at these pictures. Depending on the physics involved, the most natural measure to use and consequently, the mathematical challenges, approaches can vary.

    Using different measures for the same problem sometimes can lead to conflicting and confusing results, while at other times, they can be complementary to each other and put together a comprehensive picture of the science. With a particular choice of the mixing measure, it's also possible to derive flow-control strategies are to optimize the flow-enhanced scalar mixing and transport in industrial applications like microfluidics.

    ZL, J.-L. Thiffeault and C. R. Doering, Optimal stirring strategies for passive scalar mixing, Journal of Fluid Mechanics, 675: 465--476 (2011)..

    ZL, K. Bodova and C. R. Doering, Models and measures of mixing and effective diffusion, Discrete and Continuous Dynamical Systems - A, 28(1): 259--274 (2010).

    R. Camassa, ZL and R. M. McLaughlin, The Exact Evolution of the Scalar Variance in Pipe and Channel Flow, Communications in Mathematical Sciences, 8(2): 601--626 (2010).

    (Resources: SIAM DS09 Talk; '10 UMN Talk)

  • Biogenic Mixing Show/Hide Background Info

    Vertical mixing and transport in the ocean have always been central research topics for oceanographers and even more so for marine biologists. These mechanisms, by controlling the upwelling and sinking of nutrients/toxics and living species, play a vital role in almost all biological and chemical processes and eventually in the genesis and evolution of life on earth, especially in periods of climate change.

    While the winds and tides have been naturally considered to be among the obvious driving forces, but: Do fish stir the ocean? And other marine species like whales and shrimps and planktons? Apparently their terrestrial and amphibious relatives such as earthworms and crabs are known to shape the geometry and composition of their surroundings. For decades scientists have been arguing about the significance of biogenic mixing in the oceans only based on some rough, top-down/energy budget/scaling calculations.

    ZL, J.-L. Thiffeault and S. Childress, Stirring by squirmers, Journal of Fluid Mechanics, 669: 167--177 (2011).

    (Resources: '10 IMA Poster; Coverage 1, 2 and 3 feat. JLT and SC)

  • Underwater Turbulent Plumes and Jets Show/Hide Background Info

    The recent Deepwater Horizon blowout in the Gulf of Mexico caused catastrophic damages to the local ecology and human society. This is one prominent example of how a better knowledge of underwater turbulent plumes and jets would have saved billions (of lives). One huge problem after the crisis was that the oil plumes got trapped and spreaded below the water surface which made the skimming impossible. Knowing when and how this happened will provide valuable insights in environmental loss estimation and prevention.

    R. Camassa, ZL and R. M. McLaughlin, Internal trapping of plumes in stratified environments, in preparation.

    (Resources: UNC Experiment on Youtube; Coverage 1 and 2 feat. RMM and RC)

  • Homogenization and Asymptotic Methods

  • Parallel Computing with GPUs

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