Previous Research

Stratified Turbulence(Edit)

The Ekman layer is the layer in a fluid where there is a force balance between pressure gradient force, Coriolis force and turbulent drag. In the atmosphere, the linear solution generally overstates the magnitude of the horizontal wind field because it does not account for the velocity shear in the surface layer. Small-scale processes in atmospheric boundary layer flows, which influence the vertical and horizontal exchange of quantities between the surface and the atmosphere as well as the mixing within the atmosphere, show great sensitivity to the turbulence model formulation. The representation of these processes using a turbulence model closure is non-trivial owing to the fact that there are many non-linear processes.

In the ocean, the Ekman layer, with its distinguishing feature the Ekman spiral, is rarely observed. The Ekman layer near the surface of the ocean extends only about 10 – 20 meters deep, and instrumentation sensitive enough to observe a velocity profile in such a shallow depth has only been available since around 1980. Also, wind waves modify the flow near the surface, and make observations close to the surface rather difficult. One of the greatest challenges in the simulation of ocean and, in turn, the global climate is the diapycnal mixing of the interior ocean. Unlike the atmosphere whose structure is determined predominantly by radiative transfer, the ocean is opaque to radiation below ~30m and therefore its interior structure is determined by the balance between the small scale mixing and large scale circulation. This way, small scale mixing is critical to the structure and intensity of the thermohaline circulation at global and millennial scales. To account for the observed oceanic thermohaline structure, the overall global diapycnal mixing coefficient is estimated to be of 10^-4m²/s, which is 1000 times larger than the molecular diffusivity. The major cause of this mixing is believed to be caused by turbulent mixing associated with internal wave breaking at the scales of meters/hours. Furthermore, in situ observations suggest vastly different mixing coefficient in the ocean, ranging from 10 times smaller in the oceanic thermocline to over 10 times larger in “hot spots” near abyssal ridges and oceanic boundaries. This suggests multiple and complex mechanisms for the mixing in different regions. The vast disparity of scales and the variety of mechanisms of the mixing poses a great challenge to multi-scale mathematical modeling.

Rotating Turbulence (Edit)

Rotating turbulence is of great importance in engineering and geophysics. The most significant application in the first case is the development and the design of turbo-machinery. Here one has to take into account the detailed properties of the turbulent fluids, which pass through the device and are rotated (e.g., by the motion of the turbine blades). A detailed understanding of rotational effects on flow characteristics is essential for an advanced layout of these machines. Second, the whole field of geophysics is crucially determined by planetary rotation, which influences both atmospheric and oceanic flows and affects global climate as well as short-term weather forecasting. Understanding the fundamental processes in these fluid layer forms the basis for a detailed analysis of complex phenomena such as the development of climate anomalies like El Nino, the formation of hurricanes and tidal waves, the spreading of pollutants, and the oceanic circulation of nutrients.

Many subgrid-scale (SGS) models have been used to simulate rotating turbulence. However, there still exists a need for a better understanding of SGS models, both because anisotropic characteristics may influence large-eddy simulation (LES) modeling, and because comparative studies of model performance in rotating turbulence are inadequate. At least two issues should be considered

• Algebraic eddy viscosity models predict global dissipation fairly accurately. Through these models, small scales drain kinetic energy from large scales. However, kinetic energy transfer from small to large scales is known to occur, especially in anisotropic turbulence. In rotating flows, although the rotation term (the Coriolis term) does not explicitly show up in the kinetic energy equation, rotation has an immediate effect on kinetic energy transfer and weakens the fundamental property of the energy cascade. Eddy viscosity models may have difficulty capturing this process.

• Most traditional SGS models are based on the assumption that the modeled small scale turbulence is nearly homogeneous and isotropic. In rotating turbulence, coherent structures (e.g., two-dimensionality, and cyclonic dominance) are affected by interactions between resonant velocity modes and between near-resonant modes. Our recent studies found that the different micro-length scales occur in different directions and that this property can influence LES modeling.

Isotropic Turbulence(Edit)

As an idealized turbulent flow, isotropic turbulence is of great importance for fundamental studies and turbulence model development. We tested various SGS models, including our recently developed nonlinear models, in freely decaying isotropic turbulent cases: a WISC case at a moderate Reynolds number and a JHU case at a high Reynolds number. Testing is performed for the first case through a comparison between direct numerical simulation results and LES results regarding resolved kinetic energy and energy spectrum. In the second case, we examine the resolved kinetic energy, the energy spectrum, as well as other key statistics including the probability density functions of velocities and velocity gradients, the skewness factors, and the flatness factors. Simulations using our nonlinear model are numerically stable, and results are satisfactorily compared with DNS results and consistent with statistical theories of turbulence.

Reacting Flow(Edit)

The next generation of turbulence modelling in computational fluid dynamics (CFD) will be LES. For the appropriate applications, such as reacting flows, LES can offer significant advantages over traditional Reynolds Averaged Navier Stokes (RANS) modelling approaches. The main advantage of LES over computationally cheaper RANS is the increased level of detail that LES can deliver. While RANS provides “averaged” results, LES can predict instantaneous flow characteristics and resolve turbulent flow structures. In engine research, this is particularly valuable in simulations involving chemical reactions. While the “averaged” concentration of chemical species may be too low to trigger a reaction, there can be localized areas of high concentration in which reactions will occur. LES is also significantly more accurate than RANS for flows involving flow separation or acoustic prediction. Thus, LES can be used to study cycle-to-cycle variability, provide more design sensitivity for investigating both geometrical and operational changes, and produce more detailed and accurate results. As inexpensive computing power increases, the ability to use LES in applications is increasing.

Design of Devices for Biomedical Engineering and Cell Biology (Edit)

Atherosclerotic plaques localize to regions of flow disturbance, i.e. bifurcations, branch points and regions of high curvature. Shear stress in these regions can be multi-directional due to complex flow patterns such as time-varying vortices. However, commonly used in vitro flow models are incapable of changing flow orientation to any direction other than the reverse. Using CFD tools is of important for reducing costs and saving time for applications. We have developed a novel in vitro flow system to enable changes in flow direction to any angle. When cells were pre-aligned in laminar shear, then rotated 90 degree, cells re-aligned over 24 hours. Re-alignment involved actin remodeling by gradual rotation of actin stress fibers. This device will enable analysis of how endothelial cells sense changes in flow direction as occur in vivo.