Hypersonic boundary layers exhibit diverse transition pathways, influenced by various flow conditions and environments. Non-modal mechanisms, such as the lift-up effect, are recognized as pivotal contributors to transition, particularly over complex geometries like rough walls or blunted forebodies. In this study, we investigate the impact of steady streaks on the transition to turbulence in hypersonic boundary layers. Streaky baseflows are generated using optimal disturbances at the inlet, forming the basis for our analysis. We conduct linearized direct numerical simulations on these baseflows at Mach number $M_\infty=6.0$, using white noise forcing to trigger instabilities. An efficient extension of the SPOD method is applied to identify and track the instabilities originating from the broadband forcing on the 3D non-homogeneous baseflows. The results highlight the dominant influence of low-frequency first-mode instabilities and streak-associated instabilities in the linear regime. These findings emphasize the critical role of streaks in hypersonic boundary layer transition and provide valuable insights into this complex phenomenon.
We employ global input-output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock/boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat flux striations at the wall near flow re…
The self-excited spanwise homogeneous perturbations arising in shock-wave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of molecular nitrogen over a double wedge are investigated using the kinetic Direct Simulation Monte Carlo (DSMC) method. The flow has transitional Knudsen and unit Reynolds numbers of 3.4 x 10$^{-3}$ and 5.2 x 10$^4$ m$^{-1}$, respectively. Strong thermal nonequilibrium exists downstream of the Mach 7 detached (bow) shock generated due to the upper wedge surface. A linear instability mechanism is expected to make the pre-computed 2-D base flow potenti…
Although the roll/streak structure is ubiquitous in pre-transitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the roll/streak structure has been invoked to explain its appearance as resulting from chance occurrence in the free-stream turbulence (FST) of perturbations configured to optimally excite it. However, there is an alternative interpretation which is that FST interacts with the roll/streak structure to destabilize it. Statistical state dynamics (SSD) provides analysis met…
It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an `amplified' streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to $Re_τ\simeq 2000$ where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang \& Cossu,…
We utilize resolvent and weakly nonlinear analyses in combination with direct numerical simulations (DNS) to identify mechanisms for oblique transition in a Mach 5 hypersonic flow over an adiabatic slender double-wedge. Even though the laminar separated flow is globally stable, resolvent analysis demonstrates significant amplification of unsteady external disturbances to the linearized flow equations. These disturbances are introduced upstream of the separation zone and they lead to the appearance of oblique waves further downstream. We demonstrate that large amplification of oblique waves ari…
High-amplitude free stream turbulence and surface roughness elements can excite a laminar boundary layer flow sufficiently to cause streamwise oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Downstream, the vortices `wobble' through an inviscid secondary instability mechanism and, ultimately, transition to turbulence. We formulate an optimal control algorithm to suppress the growth rate of the streamwise vortex system. Considering a high Reynolds number asymptotic framework, we reduce the full compressible…
Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 quiet wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second instability acoustic mode is the key modulator of the transition process. The second mode experiences a rapid growth and a very fast annihilation due to the effect of bulk viscosity. The second mode interacts strongly with the first vorticity mode to directly promote a fast growth of the latter and leads to immediate transition to turbulence.
Despite the nonlinear nature of wall turbulence, there is evidence that the mechanism underlying the energy transfer from the mean flow to the turbulent fluctuations can be ascribed to linear processes. One of the most acclaimed linear instabilities for this energy transfer is the modal growth of perturbations with respect to the streamwise-averaged flow (or streaks). Here, we devise a numerical experiment in which the Navier--Stokes equations are sensibly modified to suppress these modal instabilities. Our results demonstrate that wall turbulence is sustained with realistic mean and fluctuati…
The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with h…
Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the formation of the roll/streak structures that arise from free-stream turbulence (FST) and are associated with bypass transition in boundary layers. Roll structures in the cross-stream/spanwise plane and associated streamwise streaks are shown to arise as a linear instability of interaction between the FST and the mean flow. In this interaction incoherent Reyn…
Linear global instability of the three-dimensional (3-D), spanwise-homogeneous laminar separation bubble (LSB) induced by shock-wave/boundary-layer interaction (SBLI) in a Mach 7 flow of nitrogen over a $30^{\circ}-55^{\circ}$ double wedge is studied. At these conditions corresponding to a freestream unit Reynolds number, $Re_1=5.2\times 10^{4}$ m$^{-1}$, the flow exhibits rarefaction effects and comparable shock-thicknesses to the size of the boundary-layer at separation. This, in turn, requires the use of the high-fidelity Direct Simulation Monte Carlo (DSMC) method to accurately resolve uns…
Global stability analysis and direct numerical simulation (DNS) are performed to study boundary layer flows with an isolated roughness element. Wall-attached cuboids with aspect ratios $η=1$ and $η=0.5$ are investigated for fixed ratio of roughness height to displacement boundary layer thickness $h/δ^*=2.86$. Global stability analysis is able to capture the frequency of the primary vortical structures. For $η=1$, only varicose instability is seen. For the thinner roughness element ($η=0.5$), the varicose instability dominates the sinuous instability, and the sinuous instability becomes more pr…
Wall cooling has substantial effects on the development of instabilities and transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional DNSs is used to analyze Mach~6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability radiates energy. Fluid-thermodynamic analysis shows that this radiation comprises both acoustic as well as vortical waves. 2D simulations show that the conventional "trapped" nature of second-mode instability is ru…
We study physical mechanisms that trigger transient growth in a high-speed spatially-developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power-iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstr…
Global and local absolute instabilities of 2D wakes are known to be stabilized by spanwise periodic modulations of the wake profile. The present study shows that this stabilizing effect is of general nature and can be mimicked by enforcing spanwise periodic modulations of the wave advection velocity in the generalized complex Ginzburg-Landau equation. The first order sensitivity of the absolute and global growth rate to the enforced modulation is zero, exactly as in the Navier-Stokes case. We show that a second order sensitivity analysis is effective to quantify and interpret the observed stab…
The instability of a streak and its nonlinear evolution are investigated by direct numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It is suggested that there exists a traveling-wave solution (TWS). The TWS is localized around one of the two walls and notably resemble to the coherent structures observed in experiments and DNS so far. The phase space structure around this TWS is similar to a saddle point. Since the stable manifold of this TWS is extended close to the quasi two dimensional (Q2D) energy axis, the approaching process toward the TWS along the stable manifold is appr…
In this work, we apply, for the first time to spatially inhomogeneous flows, a recently developed data-driven learning algorithm of Mori-Zwanzig (MZ) operators, which is based on a generalized Koopman's description of dynamical systems. The MZ formalism provides a mathematically exact procedure for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. The algorithm developed in this work applies Mori's linear projection operator an…
We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interp…
We investigate flow instability created by an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock causes the boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations and the flow bifurcates from its original laminar state. We utilize Direct Numerical Simulation (DNS) and Global Stability Analysis (GSA) to show that this first occurs at a cri…
In this paper, we present experimental results and reveal that strong perturbations are not necessary for elastic instability to occur in straight-channel, inertialess, visco-elastic flows at high elasticity. We show that a non-normal mode bifurcation is followed by chaotic fluctuations, self-organized as stream-wise streaks, and elastic waves due to weak disturbances generated by a small cavity at the center of the top channel wall. The chaotic flow persists in the transition, elastic turbulence, and drag reduction regimes, in agreement with previous observations for the case of strong pertur…
This article presents a modelling of the formation of spanwise vorticity in the turbulent streaks of the oblique bands and spots of transitional plane Couette flow. A functional model is designed to mimic the coherent flow in the streaks. The control parameters of the model are extracted from Direct Numerical Simulations (DNS) statistical data. A Reynolds stress is proposed to study the effect on the instability of this additional force maintaining the baseflow. Local (quasi-parallel) temporal stability analysis is performed on that model to investigate the linear development of the spanwise v…
In this study, the kinetic inviscid flux (KIF) is improved and an implicit strategy is coupled. The recently proposed KIF is a kind of inviscid flux, whose microscopic mechanism makes it good at solving shock waves, with advantages against the shock instability phenomenon. When developing the implicit KIF, a phenomenon is noticed that the kinetic flux vector splitting (KFVS) part in boundary layers not only reduces the accuracy, but seriously reduces the Courant-Friedrichs-Lewy (CFL) number as well. As a result, in this paper, a new weight is proposed about how to combine the KFVS method well …
In the present treatise, a stability analysis of the bottom boundary layer under solitary waves based on energy bounds and nonmodal theory is performed. The instability mechanism of this flow consists of a competition between streamwise streaks and two- dimensional perturbations. For lower Reynolds numbers and early times, streamwise streaks display larger amplification due to their quadratic dependence on the Reynolds number, whereas two-dimensional perturbations become dominant for larger Reynolds numbers and later times in the deceleration region of this flow, as the maximum amplification o…
Direct numerical simulation has been carried out on one attached and two separated boundary layer flows (involving small and large separation) under the influence of an adverse pressure gradient. A unified picture of the pre-transitional boundary layer for the three cases has been provided that reveals a "mixed-mode" instability, involving contribution from instability waves and streamwise streaks. A time-frequency analysis of the transitional velocity signals has been performed which shows that as the Reynolds number decreases, the character of the time traces evolves continuously from a "spo…
The vectoral wind structure of daytime atmospheric boundary layer (ABL) turbulence is strongly dependent on the balance between shear-driven turbulence production of horizontal fluctuations (driven by winds at the mesoscale), and buoyancy-driven turbulence production of vertical velocity fluctuations (driven by solar heating), characterized by the global instability state parameter $-z_i/L > 0$. In the fully shear-driven neutral limit $-z_i/L \rightarrow 0$, the surface layer is dominated by coherent streamwise-elongated concentrations of negative streamwise fluctuating velocity (low-speed str…
The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation (DNS) and global stability analysis, and compared to isolated roughness elements at the same Reh. Small spanwise spacing ($λ_z = 2.5h$) inhibits the formation of counter-rotating vortices (CVP) and as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $λ_z = 5h$, the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal peri…
Machine Learning (ML) is becoming increasingly popular in fluid dynamics. Powerful ML algorithms such as neural networks or ensemble methods are notoriously difficult to interpret. Here, we introduce the novel Shapley Additive Explanations (SHAP) algorithm (Lundberg & Lee, 2017), a game-theoretic approach that explains the output of a given ML model, in the fluid dynamics context. We give a proof of concept concerning SHAP as an explainable AI method providing useful and human-interpretable insight for fluid dynamics. To show that the feature importance ranking provided by SHAP can be interpre…
A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a solution that corresponds to the rolls and streaks instability and exhibits its streamwise localized nature. The effect of random phases as a device to control the transfer of energy to the small scales is studied both for the shell and the boundary layer models. In spite of the simplified nature of the models, they also provide some insight on the prospects for a…
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. In this work, we show that there is constant $0 < c_0 \ll 1$, independent of $\textbf{Re}$, such that sufficiently regular disturbances of size $ε\lesssim \textbf{Re}^{-2/3-δ}$ for any $δ> 0$ exist at least until $t = c_0ε^{-1}$ and in general evolve to be $O(c_0)$ due to the lift-up effect. Further, after times $t \gtrsim \textbf{Re}^{1/3}$, the streamwise dependence of the solution is rapidly diminishe…
Superhydrophobic surfaces dramatically reduce skin friction of overlying liquid flows. These surfaces are complex and numerical simulations usually rely on models for reducing this complexity. One of the simplest consists in finding an equivalent boundary condition through an homogenisation procedure, which in the case of channel flow over oriented riblets, leads to the presence of a small spanwise component in the homogenized base flow velocity. This work aims at investigating the influence of such a three-dimensionality of the base flow on stability and transition in a channel with walls cov…
Following the findings in \cite{wangsawijaya2020}, we re-examine the turbulent boundary layers developing over surfaces with spanwise heterogeneous roughness of various roughness wavelengths $0.32 \leq S/\overlineδ \leq 3.63$, where $S$ is the width of the roughness strips and $\overlineδ$ is the spanwise-averaged boundary-layer thickness. The heterogeneous cases induce counter-rotating secondary flows, and these are compared to the large-scale turbulent structures that occur naturally over the smooth wall. Both appear as meandering elongated high- and low-momentum streaks in the instantaneous…
