There is significant simulation and experimental evidence suggesting that hydrodynamic instability induced flows may be dependent on how the initial conditions are set up. The initial surface perturbations, density disparity, and the strength of the shockwaves could all be factors that lead to a completely different flow field in later stages.

The nonlinear stage starts when the amplitude of the unstable flow feature becomes significant. This chapter first studies the nonlinear growth of the interface amplitude and its associated terminal velocity with potential flow models, both for RM and RT. Next, one describes several models intended to predict the evolution of the bubble and spike heights, and the corresponding velocities, for the nonlinear stage. The success and limitations of each model are assessed with comparison to experiments and numerical simulations. The sensitivities to viscosity, density ratio and Mach number are discussed.

I will describe how certain external factors, such as rotation and time-dependent acceleration/deceleration, could suppress the evolution of the hydrodynamic instabilities.

Considers the swimming of bacterial cells, sedimentation and swimming near surfaces.

The classical theory of the interaction of light with the electron clouds of atoms and molecules will be discussed in this chapter. The discussion will begin with the interaction of a steady electric field with a collection of point charges, leading to the development of terms describing the electric dipole and quadrupole moments. The classical Lorentz model is then introduced to describe interaction of an oscillating electric field with the electron cloud of an atom, and the concepts of absorption and emission are introduced. The propagation of a light wave through a medium with electric dipoles is then discussed. Finally, the classical theory of radiation from an oscillating dipole is discussed.

By necessity, experimental studies have been the key to advancement in fluid dynamics for centuries. However, with the rapid increase of computational capabilities, numerical approaches have become an acceptable surrogate for experiments. Calculations must resolve the Navier–Stokes equations or approximate methods constructed from them. I will discuss the pros and cons of various types of approaches used, including direct numerical simulations, subgrid models, and implicit grid-discretization-based large-eddy simulation.

This chapter contains a discussion of the coupling of a magnetic field, through the framework of magnetohydrodynamics (MHD), to the hydrodynamic body forces. This leads to an additional body force, namely the Lorentz force on electrical currents in the fluid. Due to their conductivity, this effect is especially important for ionized plasmas. The intuitive result is that the magnetic field lines follow the flow, and they have an effective tension that can stabilize the RTI. As with the RTI, the RMI can be suppressed by a magnetic field.

Laser absorption spectroscopy is widely used for sensitive and quantitative detection of trace species. In this chapter, the density-matrix approach is used to introduce laser absorption spectroscopy. Spectroscopic quantities that characterize the absorption process are defined, and the relationships among these quantities are discussed. Broadening processes for spectral line shapes are also discussed, and the Doppler, Voigt, and Galatry profiles are introduced. The chapter concludes with a detailed example calculation featuring NO absorption.

The challenge confronting researchers is significant in many ways. One can start by noting that multiple instabilities might exist simultaneously and interact with each other. As an example, oblique shocks generate all three instabilities: RT, RM, and KH. In this chapter, several combined instabilities are discussed: RTI and RMI, RTI and/or RMI with KHI.

Introduces mesoscopic forces including DLVO, steric potentials, depletion and bridging forces, hydrophobic interactions and adhesion.

The interaction of electromagnetic radiation with single-photon resonances in diatomic molecules is discussed in this chapter. The properties of the electric dipole moment of the molecule are determined primarily by the electron cloud that binds the two nuclei together, and these properties can be understood by considering a reference frame fixed to the molecule. However, the response of the molecule must be averaged over all possible orientations of the molecule in the laboratory frame. Using irreducible spherical tensors greatly simplifies the orientation averaging of the molecular response. The Born–Oppenheimer approximation is invoked to initially account for the effect of the electronic, vibrational, and rotational modes of the molecule. Corrections are applied to account for the coupling and interactions of the different modes, including Herman–Wallis effects. Tables of rotational line strengths are presented for singlet, doublet, and triplet electronic transitions. These tables incorporate the use of Hund’s case (a) basis state wavefunctions for increased insight into radiative interactions for levels intermediate between Hund’s cases (a) and (b).

In this chapter, we will focus on the statistical spectral dynamics which are paramount to understanding the development of the integrated mixing quantities described in Chapter 5. Reynolds flow averaging and the turbulent kinetic energy are introduced. In addition, I will discuss how the energy of the flows is transferred from large scale to small scale modes, as well as the impact of the shockwave and gravity on the isotropy of the flows. The flow spectra allow several important length scales to be defined. Numeric simulations and experimental data will be offered to provide insights on the mixing processes.