The secondary instability was investigated in high-speed boundary layers over flat plates by numerical methodology. The numerical simulation suggests that the main streaky structures in 2D hypersonic boundary transition process are resulted from the secondary instability theory caused by the primary 2D Mack mode. The secondary instability analysis found that a new family called fundamental family of solutions was found which is the least stable secondary instability when the amplitude of the primary mode instability reaches a threshold value. It is helpful for us to understand the fundamental breakdown in hypersonic boundary layers.

This paper presents the understanding of the fundamentals when designing a numerical schemes for hyperbolic problems with discontinuities as parts of their solutions. The fundamentals include the consistency with hyperbolic balance laws in integral form rather than PDE form, spatial-temporal coupling, thermodynamic consistency for computing compressible fluid flows, convergence arguments and multidimensionality etc. Some numerical results are shown to display the performance.

Richtmyer-Meshkov Instability (RMI) in a spherical geometry is studied via direct numerical simulation using a high-order three-dimensional in-house solver. Specifically, a six-order compact difference scheme coupled with localized artificial diffusivity method is adopted in order to capture discontinuities with high accuracy. A pure converging shock propagation in a sphere is simulated and the result agrees well with Guderley's theory. For RMI in a spherical geometry, the development of mixing width and its growth rate at different stages are examined and the underlying mechanism is also briefly analyzed. Particularly addressed is the effect of Mach number on the growth rate of perturbations and turbulent mixing process.

The paper presents a study of the influence of the domain size and LBM collision models on fully developed turbulent channel flows. The results using spectral method show that a smaller domain size will increase the velocity fluctuations in the streamwise direction. And MRT-LBM with different collision models gives reliable results at least for low order flow statistics compared with those from spectral method and finite-difference method.

In this paper, a thick disk with aspect ratio greater than $1/10$ is directly simulated by adaptive mesh refinement-immersed boundary-lattice Boltzmann flux solver (AMR-IB-LBFS). The AMR-IB-LBFS model is a combination of the adaptive mesh refinement (AMR) technique and immersed boundary-lattice Boltzmann flux solver (IB-LBFS). Four different aspect ratio disks are numerically simulated, and the numerical results are in good agreements with theoretical results. In addition, these disks with different aspect ratios are compared with trajectories and gestures.

As the analogue of helicity, the concept of stream helicity proposed in 2007 provides a quantitative measurement for entanglement of streamlines for an incompressible flow field or magnetic field lines for a magnetic field. It is found that the helical-wave decomposition can serve as a convenient mathematical physics tool for the calculation of helicity and stream helicity. However, for a multiply connected domain such as a torus under the background of TOKAMAK, the analysis presents some peculiarities due to the nature of multiple-value of some involving potentials. Here we give a full derivation of stream helicity for such a case, together with some detailed analysis. Particularly, it is found that a maximum of absolute helicity under prescribed energy could be attained by a pure potential field.

The linear stability of supersoinc mixing layer with the mean velocity profile approximated by the hyperbolic tangent is studied. The convective Mach number of mixing layer is 2 and the temperature ratio is 1. A new classification of disturbance mode of mixing layer is presented to unify the existing results in literature and the new results in this paper. The mixing layer has supersonic and subsonic modes according to the disturbance phase speed. Then the supersonic mode can be classified into mixing mode and acoustic mode. The mixing mode can be further classified into subsonic-supersonic mode and supersonic-subsonic mode according to the relative speed between disturbance phase speed and the free flow speed of mixing layer, which correspond to fast mode and slow mode, respectively. The phase speed of acoustic mode is supersonic with respect to the free flow in both sides of mixing layer and some unstable acoustic modes are found. The acoustic mode has radiation characteristics in both sides of mixing layer and results in a series of expansion and compression fans.

In this paper, Lagrangian tracking of a specific material surface and Lagrangian-averaged vorticity deviation (LAVD) are applied to experimental data sets of two kinds of wall-bounded flows to detect coherent structures. One is used for laminar boundary layer with wall-mounted hemisphere, the other is used for turbulent boundary layer. Lagrangian coherent structures detected in a hemisphere protruded laminar boundary layer show some similarity with Eulerian-detected hairpin vortices. However, the LAVD-based vortices and the evolution of material surface demonstrated in turbulent boundary layer are different from the patterns in the wake of the hairpin shedding hemisphere. The wavelike deformed material surfaces appear to support the importance of three-dimensional wave structures in the near-wall turbulence production process. The Lagrangian methods provide another perspective in understanding coherent structures in wall-bounded flows.

In this paper, direct numerical simulation (DNS) of spatially evolving flat-plate hypersonic turbulent boundary layer with free-stream Mach number 8 is used to study the effects of wall temperature on compressibility and Reynolds stress contribution. The DNS contains two cases with different wall temperatures, $T_w$/$T_\infty$=$10.03$ and $1.9$. The results show that lower wall temperature enhances both the compressibility and injection-and-sweeping motions near the wall.

The effects of combustion on turbulent statistics in a supersonic turbulent jet are investigated by using direct numerical simulation (DNS). To study the combustion effects, two DNS cases (reacting case and non-reacting case) are conducted and the comparison of turbulent statistics are used to study the combustion effects. The medium of jet is $85\%$ hydrogen with temperature $305K$ and the co-flow is hot air with temperature $1150K$. The Reynolds numbers based on the jet diameters are $22000$ and the jet Mach numbers are $1.2$. The DNS results show that combustion case has both larger decay rate constant of centerline streamwise mean velocity and larger spreading rate of half-velocity jet width than the non-reacting case. It also shows that the combustion case achieves the self-similarity slower. For reacting jet, the vortex structures are more smooth in the near field and vortex filament structures are larger in the far field. Combustion causes the turbulent zone to be delayed downstream and increases the probability of strong velocity pulsation.

Double-step interrogation schemes with decreasing window size are investigated. Particle image pairs are created by Monte Carlo methods based on a simulated hypersonic transitional boundary layer flow. Two types of initial-step interpolation, with and without non-slip conditions at the wall (so-called CSIN and CSI), are respectively investigated. It can be concluded that the non-slip condition is very important to the multi-grid interrogation scheme. CSIN has a good agreement with the preset results but CSI does not.  The error level of CSI near the wall is nearly 5 times that of CSIN.

Secondary instability of a streaky boundary layer under spanwise-localized free-stream vortical disturbances (FSVD) is investigated using BiGlobal instability analysis. The instability analysis is performed at different streamwise locations and at different instants in a whole time period and  the results in space-time $(x-t)$ plane are taken into consideration, such that unstable modes are found in four unstable zones. According to the comparison of mode growth accumulation, we find that the contribution of secondary instability to bypass transition is much more important than T-S waves and that the center strong streak plays the key role in secondary instability. The sinuous type outer mode at center low-speed streak is the dominant unstable mode and this agrees with experimental observation. The inner mode at center high-speed streak also has high growth rate, but its growth cannot keep accumulating, resulting in its unimportant role in secondary instability. All unstable modes found in this paper appear at Fjortoft inflection points of the basic flow in gradient direction, implying that the modes have the same physical nature, i.e., they are caused by inflectional instability of the shear flow.

Helicity plays an important role in the nonlinear dynamic process of compressible helical turbulence. We carry out direct numerical simulations (DNS) of compressible helical turbulence with different mean helicity at the grid resolution of $512^3$ and try to explore the physical mechanism of kinetic energy cascade under the effect of helicity. The filtering method of coarse-graining is employed for scale decomposition to get kinetic energy flux. We get some novel conclusions in contrast to pre-existing knowledge in incompressible helical turbulence. Firstly, helicity also hinders the process of compressible kinetic energy cascade and reduces viscous dissipation. Secondly, helicity weakens some exclusive features, such as coupling between compressible and solenoidal mode of fluctuating velocity, energy transformation between kinetic energy and internal energy, and shocklets which appear only in compressible turbulence and serves as the role of constraint.

Fully developed rotating turbulent channel flow (RTCF) has been numerically investigated using large-eddy simulation (LES). The subgrid-scale (SGS) eddy viscosity model is based on the SGS helicity dissipation balance and the spectral relative helicity. Posterior test has been implemented to RTCF with rotation in spanwise direction. The friction Reynolds number $Re_\tau=u_\tau\delta/\nu$ based on wall shear velocity $u_\tau$, half width of the channel $\delta$ and the kinematic viscosity $\nu$ is 180. Two rotation numbers $Ro_\tau=2\Omega\delta/u_\tau$ equal to 22 and 80 have been computed with respective grid resolution. The results from dynamic Smagorinsky model (DSM) and direct numerical simulation (DNS) are used as references. The results demonstrate that the eddy viscosity model can predict both the precise velocity profile and the turbulent intensity.

The energy spectrum and energy transfer in compressible homogeneous turbulent shear flow are numerically investigated via high-accuracy direct numerical simulation. The Helmholtz decomposition method is employed to decompose the velocity field into a solenoidal component and a compressive one. It is found that the spectra of different velocity modes are strongly anisotropic over all the resolved scales and the specific properties of small-scale anisotropy are significantly influenced by the flow compressibility. The anisotropy of energy transfer process comes from an additional kinetic energy production term which acts as a dominant source at relatively large scales in the streamwise direction. After the redistribution of turbulent kinetic energy caused by the pressure-dilatation correlation in different directions, the energy fluxes due to advection are also expected to be anisotropic. The streamwise energy flux is predominantly large and passes down the kinetic energy to smaller scales, whereas the cross-streamwise and spanwise energy fluxes are less significant and pronounce an inverse energy transfer at relatively large scales.