Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 10⁶ m⁻¹ are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.

In this work, the stability of hypersonic flow over a curved compression ramp is studied using several stability analysis tools and direct numerical simulations (DNS). The free-stream Mach number and the unit Reynolds number are 7.7 and $4.2 \times 10^6$ m $^{-1}$ , respectively. Corner rounding is considered to alter the separation bubble flow so as to suppress the intrinsic instability of the compression-ramp flow. The variation of intrinsic instability is confirmed by global stability analysis. Subsequently, resolvent analysis is employed to examine the response of intrinsically stable flows to external disturbances. It is shown that the considered flows strongly amplify low-frequency streamwise streaks with a preferential spanwise wavelength. This result is verified using DNS by introducing a random forcing upstream of the separation point. Furthermore, both resolvent analysis and DNS demonstrate that the separation bubble contributes little to the selection of the spanwise wavelength of streamwise streaks. The combined effects of convective and intrinsic instabilities are also explored using DNS. A better agreement with experimental data is achieved after introducing upstream disturbances in an inherently unstable flow.

In this study, a modified Block A* algorithm is applied to the path planning of hybrid-driven underwater gliders, which combine the buoyancy-driven mode of underwater gliders and the propeller-driven mode of autonomous underwater vehicles, in the ocean environment characterized by strong currents. The objective is to predict a sequence of steering directions and the appropriate driving mode, such that vehicles can minimize their energy consumption to reach the goal region. In this work, we modify the path generation approach of the original Block A* algorithm to gain more realistic paths for hybrid-driven underwater gliders and apply an effective energy consumption model in the heap value calculation to find energy-cost optimal paths. Zermelo's function is also incorporated to select the driving mode. The performance of the presented method is then discussed by conducting simulations in three different ocean environments. The results indicate that compared to other methods, the modified Block A* method avoids local turbulent flow and gains feasible paths for hybrid-driven underwater gliders at a lower energy cost.

This paper investigates a Mach 6 oblique breakdown via direct numerical simulation in conjunction with stability and quadrant analyses. Particular emphasis is placed on, first, the heat transfer and mean flow distortion in the near-wall and outer transitional boundary layer, and, second, the flow events that are responsible for the production of the Reynolds stress. The energy budget reveals that enhancement of viscous dissipation due to mean flow distortion dominates the heat transfer overshoot, while the dissipation due to fluctuations is lesser but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (non-dimensionalized by the freestream temperature and local boundary layer thickness) varies little, owing to the occurrence of breakdown and the establishment of self-similarity. Renormalized by the boundary layer thickness, a new correlation of the Stanton number shows no overshoot or difference between the original overshoot region and the turbulent region, which indicates the possibility of similarity once breakdown has occurred. In the outer region, enhanced advective heat exchange strongly reshapes the mean temperature profile. Because of successive modal growth and nonlinear saturation, the contributions of the primary oblique mode, streak mode, and a superharmonic to the outer advective heat transfer are found to compete near the location of the peak heat flux. From the perspective of fluid motions, quadrant analysis highlights the evenly and broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress, while the PDF is concentrated around zero in the turbulent region. The flow event Q2 (ejection) overtakes Q4 (sweep) in the outer boundary layer of the transitional region, mainly owing to the primary mode, while the two events become attenuated and nearly achieve balance when transition is complete.

The present paper finds that the coexistence of multiple primary instability waves may cause a non-trivial nonlinear interaction and breakdown process, which has not been reported before. In the considered Mach 6 flat-plate boundary layer, a global resolvent analysis reports three optimal disturbances (local maxima): a high-frequency planar wave, a low-frequency oblique wave and a stationary streak. For the dominant planar and oblique waves, a parabolised stability equation analysis identifies the initial non-modal transient growth and downstream modal growth. Initiated by these two optimal disturbances jointly, the complete linear and nonlinear instability processes until breakdown to turbulence are shown with direct numerical simulation. Owing to the transient growth, the oblique wave may be more significant than the planar wave in the breakdown. The oblique wave and scales of nonlinear interactions are pronounced in the outer layer, whose significance may not be comprehensively characterised by the wall pressure measurement. Fourier modes characterising the oblique-wave oblique breakdown, the planar-wave fundamental resonance, the planar-wave subharmonic resonance and the combination resonance related to a detuned mode are observed successively. The detuned mode seems to dominate the near-wall dynamics in the late nonlinear stage, characterised by $\varLambda$ -like structures. Meanwhile, the existence of this detuned mode is independent of the initial amplitude ratio and the absolute amplitude of the oblique and planar waves. Weakly nonlinear stability analyses demonstrate that the detuned mode is mainly a consequence of the secondary instability under the combination of planar and oblique primary waves. Wave vector plots reveal the resonant state of multiple triads. Energy budget and amplitude-correction analyses provide a clear physical image of energy transfer.

The compressible-boundary-layer stability can be considerably influenced by base flow distortion. The distortion may originate from perturbations of flow parameters, such as the Mach number. In this paper, sensitivities of the boundary layer stability to certain flow parameters are derived analytically by utilizing the homotopy analysis (with codes shared), in conjunction with a direct-adjoint stability theory. The sensitivities can be categorized according to the routes the distortion evolves. Route I is that parameters distort the base flow (Sensitivity A), which, in turn, affect the eigenvalue of the linear stability equation (Sensitivity B). Route II gives rise to the effects of flow parameters onto eigenvalues caused by direct perturbation of the linear operators (Sensitivity C). Results indicate that Sensitivity A is characterized by the only peak found on the sensitivity profile that corresponds to the maximum gradient of base flow; for Sensitivity B, production terms, e.g., the mean-shear terms, are found to be significant, while for Sensitivity C, which is rarely discussed in existing literature, the pressure gradient terms in the momentum equations are dominant in affecting the stability via route II. Furthermore, route II can be more significant than route I. Having examined the variation of the mean shear gradient, $d(\overline{\rho }d\overline{u}/dy)/dy$ , near the critical layer y_c, it is proven that the sensitivity of the eigenvalue to the velocity or temperature distortion is negative at y_c under certain assumptions, particularly for the temperature-relevant sensitivity that has hardly been discussed before.