Considers diffusion and statistical models for bacterial motility from the perspective of anomalous transport.

Turbulent flow is a notoriously difficult topic in its own right because it is a truly multi-scale problem with strong nonlinearities. However, in this chapter, I will provide a framework for the key concepts, statistical measurements, and implications for the mixing process, so that the reader can better understand this issue. Both the classic engineering treatment of turbulence as well as the modern statistical closure theories will be introduced and brought together to show the reader how they can be synthesized to describe turbulence mixing induced by hydrodynamic instability driven flows. Some of the key concepts that I will elaborate on include energy transfer and interacting scales. The energy spectrum, and its applicability to RMI and RTI flow, is discussed.

Due to the time-consuming nature of fully 3D simulations of turbulence mixing induced by hydrodynamic instabilities, it is desirable to run computations in 2D when possible. But does 2D turbulence resemble 3D turbulence? The relevance of idealized 2D turbulence to certain aspects of atmospheric motion has been emphasized in many works. Yet molecular mixing occurs at the interfaces of the fluids, and the ratios of area-to-volume in three dimensions are very different than the length-to-area ratios in two dimensions. This has prompted some well-known scientists to claim that "two-dimensional turbulence, ... is a consequence of the construction of large computers." I will investigate this issue in detail and point out that the large-scale structures evolve over a similar time scale in 2D and 3D, indicating that 2D simulations are useful for providing some indication of the amount of instability growth at an interface.

Intense lasers are now being used to probe the physics of fluid dynamics in the high energy density physics (HEDP) regime, a term roughly referring to thermodynamic pressures greater than 1 Mbar. This approach allows us to design dedicated experiments to examine the issue of fluid instabilities in isolation. These laser platforms are also employed to recreate aspects of astrophysical phenomena in the laboratory, a specialized research area frequently referred to as laboratory astrophysics. Studying astrophysical phenomena in the laboratory with intense lasers offers many advantages: Repeatability, advanced diagnostics, controlled initial conditions, etc.

Inertial Confinement Fusion (ICF) recently became the first technology to achieve ignition of hydrogen nuclear fusion fuel in the laboratory. Unlike magnetically confined fusion plasmas such as tokamaks, ICF requires high fuel compression. This implies a high convergence and high velocity implosion, usually driven with laser beams. This allows hydrodynamic instabilities to develop, primarily RTI and RMI. During the initial shock and acceleration phase when the shell is brought up to the peak implosion velocity, RMI instabilities at the various interfaces are followed by ablation front RT growth as the low-density plasma accelerates the dense shell of solid ablator and fuel. The implosion deceleration at the center is also unstable. The resulting spikes and bubbles prevent efficient fuel compression, and can also inject contaminants. I will discuss the measurement and mitigation of this problem. Z-pinch machines, which instead use an electrical current to compress the plasma, will illustrate the role of MHD in the ICF application.

Material strength is important for planetary science and planetary formation dynamics. Inspecting RTI growth in solid-state samples in a high-energy-density setting can be key to determining the strength of a number of materials, such as iron, lead, or tantalum. One of the important applications is the enhanced mixing in the scramjet; I will address this issue as well as detonation in the combustion chamber. Moreover, I will discuss the reactive RMI in detail to address several issues related to turbulence-flame interactions, such as an incident shock wave passing the interface and shock initiation of flow instabilities. Ejecta occurs when small pieces of the material are forced out as a result of stellar explosions or other sharp impacts in the engineering process. RMI is key to understanding the physics processes for the production and distribution of ejecta. Extensive data from numeric simulations and experimental evidence will be offered to provide a comprehensive picture about this topic.