The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially non-oscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical and phenomenological linear and nonlinear, impulsive, perturbation and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Pade model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically. In Part II [Phys. Fluids (2006)], a comprehensive investigation of mixing induced by the reshocked single-mode Richtmyer-Meshkov instability is performed using the present simulation data to assess and quantify the effects of reshock and other waves on the mixing dynamics, including the post-reshock growth, circulation deposition, mixing profiles and fractions, baroclinic circulation deposition, energy spectra and statistics.

The University of Manchester hosted the 28th International Symposium on Shock Waves between 17 and 22 July 2011. The International Symposium on Shock Waves first took place in 1957 in Boston and has since become an internationally acclaimed series of meetings for the wider Shock Wave Community. The ISSW28 focused on the following areas: Blast Waves, Chemically Reacting Flows, Dense Gases and Rarefied Flows, Detonation and Combustion, Diagnostics, Facilities, Flow Visualisation, Hypersonic Flow, Ignition, Impact and Compaction, Multiphase Flow, Nozzle Flow, Numerical Methods, Propulsion, Richtmyer-Meshkov, Shockwave Boundary Layer Interaction, Shock Propagation and Reflection, Shock Vortex Interaction, Shockwave Phenomena and Applications, as well as Medical and Biological Applications. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 28 and individuals interested in these fields.

This volume collects the edited and reviewed contributions presented in the 5th iTi Conference in Bertinoro covering fundamental aspects in turbulent flows. In the spirit of the iTi initiative, the volume is produced after the conference so that the authors had the possibility to incorporate comments and discussions raised during the meeting. Turbulence presents a large number of aspects and problems, which are still unsolved and which challenge research communities in engineering and physical sciences both in basic and applied research. The book presents recent advances in theory related to new statistical approaches, effect of non-linearities and presence of symmetries. This edition presents new contributions related to the physics and control of laminar-turbulent transition in wall-bounded flows, which may have a significant impact on drag reduction applications. Turbulent boundary layers, at increasing Reynolds number, are the main subject of both computational and experimental long research programs aimed at improving our knowledge on scaling, energy distribution at different scales, structure eduction, roughness effects to name only a few. Like previous editions several numerical and experimental analysis of complex flows, mostly related to applications, are presented. The structure of the present book is as such that contributions have been bundled according to covering topics i.e. I Theory, II Stability, III Wall bounded flows, IV, Complex flows, V Acoustic, VI Numerical methods. The volume is dedicated to the memory of Prof. Rudolf Friedrich who prematurely died in Münster/Germany on the 16th of August 2012. In his honor the conference has started with a special session dedicated to his work.

The Richtmyer-Meshkov instability is a fundamental fluid instability that occurs when perturbations on an interface separating gases with different properties grow following the passage of a shock. This instability is typically studied in shock tube experiments, and constitutes a fundamental example of a complex hydrodynamic flow. Numerical simulations and models for the instability growth and evolution have also been used to further understand the physics of the Richtmyer-Meshkov instability. In the present work, the formally high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method using a third-order total-variation diminishing (TVD) Runge-Kutta time-evolution scheme (as implemented in the HOPE code [57]) is applied to simulate the single-mode Richtmyer-Meshkov instability with reshock in two spatial dimensions. The initial conditions and computational domain for the simulations are modeled after the Collins and Jacobs [23] single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment. The following boundary conditions are used: (1) periodic in the spanwise direction corresponding to the cross-section of the test section; (2) outflow at the entrance of the test section in the streamwise direction, and; (3) reflecting at the end wall of the test section in the streamwise direction. The present investigation has three principal motivations: (1) to provide additional validation of the HOPE code against available experimental data; (2) to provide numerical simulation data for detailed analysis of mixing induced by the Richtmyer-Meshkov instability with reshock, and; (3) to systematically investigate the dependence of mixing properties on both the order of WENO reconstruction and spatial resolution. The present study constitutes the first comprehensive application of the high-resolution WENO method to the Richtmyer-Meshkov instability with reshock, as well as analysis of the resulting mixing. First, analytical, semi-analytical, and phenomenological models for the growth of a single- and multi-mode perturbation are reviewed (impulsive, vortex, perturbation, potential flow, and asymptotic power-law growth models), including models for diffuse and reshocked interfaces. A model for baroclinic circulation deposition is also reviewed. Numerical simulations are performed using the third-, fifth-, and ninth-order WENO method with spatial resolutions corresponding to a uniform grid with 128, 256, and 512 points per initial perturbation wavelength. The density from the fifth- and ninth-order simulation is compared to the corrected experimental PLIF images of Collins and Jacobs at selected times. The amplitude obtained from the fifth-order simulation at a resolution of 256 points per initial perturbation wavelength is compared to the experimental data of Collins and Jacobs and to the predictions of linear and nonlinear amplitude growth models before and after reshock. The prediction of the Zhang-Sohn nonlinear amplitude growth model is in best agreement with the simulation data prior to reshock. The simulation data is also in excellent agreement with the experimentally-measured amplitude prior to reshock. The absence of the initial rarefaction wave (resulting from the rupture of the membrane that generates the first shock in the experiment) in the numerical simulations results in a time lag between the numerical and experimental interface evolution following reshock. The results of this component of the present investigation also serve as an additional validation of the HOPE code as applied to a shock-induced hydrodynamic instability. Second, local and global properties of the mixing during the linear, nonlinear, pre- and post-reshock, and late-time phases are investigated and discussed, including a quantitative investigation of the time-dependence and structure of various related mixing parameters defined in terms of the mole fraction and one-dimensional energy spectra. Spatial averaging of quantities along the spanwise (periodic) flow direction yields streamwise profiles, and is used to define instantaneous Reynolds and Favre averages and fluctuations. The fluctuations are Fourier-transformed along the spanwise direction to define time-dependent energy (abstract truncated).

This book illustrates the latest progress on the hydrodynamic instabilities induced by a shock wave, particularly RM (Richtmyer–Meshkov) instability. The hydrodynamic instabilities play crucial roles in various industrial and scientific fields, such as inertial confinement fusion, supersonic combustion, supernova explosion, etc. This book experimentally and theoretically explores the shock-driven instabilities of complex gas-gas and gas-liquid interfaces. The main difficulty in performing an experimental study on RM instability, especially in a shock-tube circumstance, lies in creating an idealized initial interface because the RM instability is extremely sensitive to the initial condition. This book introduces new experimental methods to generate shape-controllable two-dimensional gaseous interfaces, thickness-controllable gas layers, and water droplets embedded with a vapour bubble in the shock-tube experiments. It covers the latest experiments and theories on the shock-driven hydrodynamic instabilities of multi-mode, multi-layer, and multi-phase interfaces. It explores the effects of the mode-competition, interface-coupling, and phase-transition on interface evolution, respectively. This book establishes a universal nonlinear theory to predict the RM instability of a shocked multi-mode interface based on spectrum analysis. This book quantifies the effects of interface-coupling and reverberating waves on the hydrodynamic instabilities of a shocked multi-layer interface. This book provides the experimental studies of the interaction of a shock wave and a multi-phase droplet and proposes a modified Rayleigh-Plesset equation to predict the vapour bubble collapse inside a droplet.

The ninth-order weighted essentially non-oscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike perturbation amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock [Latini, Schilling and Don, Phys. Fluids (2007), in press]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe reshock. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney and Zabusky [J. Fluid Mech. 269, 45 (1994)] model and linear instability theory. The time-evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the circulations are equal before, as well as after reshock, until the interaction of the reflected rarefaction with the layer leads to flow symmetry breaking and different evolutions of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in very good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and molecular mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating entropy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops non-trivial spectral content from its inception. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing, followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction approaches unity across the layer at the latest time, signifying nearly complete mixing. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra are consistent with most of these scalings over short wave number ranges. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is shown that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.

The first comprehensive reference guide to turbulent mixing driven by Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instabilities.