Stationary Crossflow Instability Research Articles

DeHNSSo: The Delft Harmonic Navier-Stokes Solver for nonlinear stability problems with complex geometric features

A nonlinear Harmonic Navier-Stokes (HNS) framework is introduced for simulating instabilities in laminar spanwise-invariant shear layers, featuring sharp and smooth wall surface protuberances. While such cases play a critical role in the process of laminar-to-turbulent transition, classical stability theory analyses such as parabolized or local stability methods fail to provide (accurate) results, due to their underlying assumptions. The generalized incompressible Navier-Stokes (NS) equations are expanded in perturbed form, using a spanwise and temporal Fourier ansatz for flow perturbations. The resulting equations are discretized using spectral collocation in the wall-normal direction and finite-difference methods in the streamwise direction. The equations are then solved using a direct sparse-matrix solver. The nonlinear mode interaction terms are converged iteratively. The solution implementation makes use of a generalized domain transformation to account for geometrical smooth surface features, such as humps. No-slip conditions can be embedded in the interior domain to account for the presence of sharp surface features such as forward- or backward-facing steps. Common difficulties with Navier-Stokes solvers, such as the treatment of the outflow boundary and convergence of nonlinear terms, are considered in detail. The performance of the developed solver is evaluated against several cases of representative boundary layer instability growth, including linear and nonlinear growth of Tollmien-Schlichting waves in a Blasius boundary layer and stationary crossflow instabilities in a swept flat-plate boundary layer. The latter problem is also treated in the presence of a geometrical smooth hump and a sharp forward-facing step at the wall. HNS simulation results, such as perturbation amplitudes, growth rates, and shape functions, are compared to benchmark flow stability analysis methods such as Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS), or Direct Numerical Simulations (DNS). Good agreement is observed in all cases. The HNS solver is subjected to a grid convergence study and a simple performance benchmark, namely memory usage and computational cost. The computational cost is found to be considerably lower than high-fidelity DNS at comparable grid resolutions. Program summaryProgram Title: DeHNSSoCPC Library link to program files:https://doi.org/10.17632/9bnms99kk2.1Developer's repository link:https://github.com/SvenWesterbeek/DeHNSSoLicensing provisions: GPLv3Programming language: MatlabSupplementary material: The supplementary material contains the code as well as a user manual.Nature of problem: Fluid flows are subject to laminar-to-turbulent transition following the growth of instabilities. To avoid computationally demanding Direct Numerical Simulations (DNS), perturbation theory is often applied to their analysis. However, classical stability methods based on the Orr-Sommerfeld equation or the Parabolized Stability Equations neglect the influence of streamwise gradients in varying degrees. The validity of these assumptions is difficult to estimate a priori.Solution method: The Delft Harmonic Navier-Stokes Solver (DeHNSSo) solves the harmonic Navier-Stokes equations nonlinearly on domains featuring sharp and smooth spanwise invariant surface features using a generalized grid approach in combination with an embedded boundary method. This allows the user to include the effects of streamwise gradients on flow at a fraction of the cost of DNS.Additional comments including restrictions and unusual features: In DeHNSSo, the equations are solved using direct matrix solvers. As such, memory is treated as a scarce resource. The problem is formulated in a mode-independent manner such that left-hand side matrices need only be computed and stored once despite incorporating nonlinear terms. Additionally, DeHNSSo offers the user the possibility to prescribe inhomogeneous boundary conditions to introduce and solve the receptivity problem or manipulate instabilities. Due to the double Fourier expansion, the solver is restricted to spanwise and temporally periodic problems.

Miniaturization and Model-Integration of the Optical Measurement System for Temperature-Sensitive Paint Investigations.

The temperature-sensitive paint (TSP) method, an optical measurement technique, is used for qualitative skin friction visualizations in a wide variety of aerodynamic applications. One such application is the visualization of the laminar-turbulent boundary-layer transition. Optical access to the surface of interest is mandatory for the measurement system, which consists of scientific cameras and LEDs. But the optical access to the area of interest is often impeded by the available windows of the wind tunnel and the wind tunnel model itself, reducing the field of view and the spatial resolution. In some cases, it is of interest to increase the flexibility of the installation of the optical measurement system by reducing its physical dimensions and placing the installation inside the plenum. The DLR Swept flat PlatE Cross-flow TRAnsition (SPECTRA-A) configuration was selected to investigate the influence of two-dimensional steps on the cross-flow-induced boundary layer transition by means of TSP, as part of the EU project Clean Sky 2. The SPECTRA-A configuration consists of two main elements: a flat plate and a displacement body mounted within a very close distance of each other, creating a narrow gap between the two elements. The surface of interest is the area on the flat plate facing the displacement body. The narrow gap limits the utilization of an external camera setup due to poor optical access. A new optical setup consisting of four miniature CMOS machine-vision cameras and five miniature high-power LEDs was integrated into the displacement body. The characteristics of the camera system were analyzed in laboratory tests, establishing that the miniature CMOS machine-vision cameras are suitable for qualitative TSP skin friction visualizations. This was confirmed by successfully measuring the laminar-turbulent boundary-layer transition on the SPECTRA-A configuration. The integrated TSP system is capable of resolving even small variations of the transition location caused by changing the amplitude of the stationary cross-flow instability. The quality of the TSP visualization with the integrated optical system allows for the measurement of the transition location and the wavelength of the stationary cross-flow instability. Overall, a cost-effective TSP visualization system with small space requirements was developed and tested for future applications in wind tunnel models, model support, or side walls of wind tunnels.

Effect of slip on the linear stability of the rotating disk boundary layer

The linear stability of the rotating disk boundary layer with surface roughness is investigated. Surface roughness is modeled using slip boundary conditions [M. Miklavčič and C. Y. Wang, Z. Angew. Math. Phys. 55, 235–246 (2004)], which establish concentric grooves, radial grooves, and isotropic roughness. The effect on the stationary crossflow and Coriolis instabilities is analyzed by applying slip conditions to the undisturbed flow and linear disturbances. This analysis builds on the work of Cooper et al. [Phys. Fluids 27, 014107 (2015)], who modeled slip effects on the base flow but applied the no-slip condition to the linear perturbations. Neutral stability curves and critical parameter settings for linearly unstable behavior are computed for several radial and azimuthal slip length settings. The application of slip on the linear disturbances has a significant impact on the flow stability. In particular, the Coriolis instability undergoes considerable destabilization in the instance of concentric grooves (i.e., radial slip) and radial grooves with sufficiently large azimuthal slip lengths. In addition, concentric grooves destabilize the crossflow instability when the radial slip length is small. Moreover, in the instance of isotropic roughness, the stabilizing effect is markedly less than the observations of Cooper et al. [Phys. Fluids 27, 014107 (2015)]. Finally, an energy analysis is undertaken to ascertain the physical mechanisms brought about by surface roughness.

Improved Amplification Factor Transport Transition Model for Transonic Boundary Layers

Linear-stability-theory-based method plays an important role in boundary-layer transition prediction of aeronautical flows. Based on the simplification of linear stability theory (Drela and Giles, AIAA J, 1987), the amplification factor transport (AFT) equation for Tollmien–Schlichting waves using local variables was first proposed in 2013 (Coder and Maughmer, AIAA J, 2014). However, in transonic high-Reynolds-number flows, the AFT model seriously overestimates the value of . To fix this problem, we have conducted many linear stability analyses to rebuild the formulations of AFT model. Compressibility effect, which has a significant impact on the prediction of value, has been considered in the improved version. Coupled with the model for crossflow instabilities (Xu et al., CJA, 2020), the improved AFT model is established for transonic boundary layers. Several classic test cases are successfully employed to validate present AFT model, including a flat plate, an airfoil, an infinite swept wing, a sickled-shape wing, a 6:1 inclined prolate spheroid, the NASA Common Research Model, and ARA Transonic Swept Wing. Our prediction results show that both Tollmien–Schlichting instabilities and stationary crossflow instabilities can be captured and predicted well by the improved model in subsonic and transonic boundary layers.

Compressibility corrections to extend a smooth local correlation-based transition model to transonic flows

AbstractThis paper presents progress towards a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are developed and investigated to extend commonly used empirical correlations to transonic flight conditions while retaining their accuracy at low speeds. A compressibility correction for Tollmien-Schlichting instabilities is developed and applied to a smooth local correlation-based transition model and a stationary crossflow instability compressibility correction is included by adding a new crossflow source term function. Two- and three-dimensional transonic transition test cases demonstrate that the Tollmien-Schlichting compressibility correction produces substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications where the effects of flow compressibility are expected to be more significant, such as the NASA CRM-NLF wing-body configuration, while the crossflow compressibility correction prevents an inaccurate, upstream transition front. The compressibility corrections and modifications do not significantly affect the numerical behaviour of the model, which provides an efficient alternative to non-local and higher-fidelity approaches, and can be applied to other transport-equation-based transition models with low-speed empirical correlations without affecting their predictive capability in the incompressible regime.

Cancellation of crossflow instabilities through multiple discrete roughness elements forcing

The presented work introduces a novel cancelation technique, based on the linear superposition of stationary crossflow instabilities (CFI) through the application of a streamwise series of optimally positioned discrete roughness elements (DRE) arrays on a swept wing surface. The DRE arrays are designed and arranged with suitable amplitude and phase shift to induce velocity disturbance systems that destructively interact, ultimately damping the developing CFI. This results in the suppression of monochromatic CFI, reducing their amplitude and growth and delaying the boundary layer transition to turbulence.

Unsteady disturbances in a swept wing boundary layer due to plasma forcing

This work investigates the response of a transitional boundary layer to spanwise-invariant dielectric barrier discharge plasma actuator (PA) forcing on a 45° swept wing at a chord Reynolds number of 2.17×106. Two important parameters of the PA operation are scrutinized, namely, the forcing frequency and the streamwise location of forcing. An array of passive discrete roughness elements is installed near the leading edge to promote and condition a set of critical stationary crossflow (CF) instability modes. Numerical solutions of the boundary layer equations and linear stability theory are used in combination with the experimental pressure distribution to provide predictions of critical stationary and traveling CF instabilities. The laminar–turbulent transition front is visualized and quantified by means of infrared thermography. Measurements of velocity fields are performed using hotwire anemometry scans at specific chordwise locations. The results demonstrate the inherent introduction of unsteady velocity disturbances by the plasma forcing. It is shown that, depending on actuator frequency and location, these disturbances can evolve into typical CF instabilities. Positive traveling low-frequency type III modes are generally amplified by PA in all tested cases, while the occurrence of negative traveling high-frequency type I secondary modes is favored when PA is operating at high frequency and at relatively downstream locations, with respect to the leading edge.

Optimizing control of stationary cross-flow vortices excited by surface roughness

Stationary cross-flow vortices are excited within the swept Hiemenz boundary layer via surface roughness and actively controlled using an optimally configured control device. Control is modeled using localized wall motion, but in practice the optimization strategy could be applied to other laminar flow control technologies. A sensor-control iterative procedure, based on solutions of the forward and adjoint linearized Navier–Stokes equations, is applied to both feedforward and feedback loop systems. The former strategy only allows the control settings to be configured once, while the latter approach permits the repeated reoptimization of the control device. Surface roughness establishes a stationary cross-flow disturbance with a predefined set of flow conditions, but an unknown amplitude and phase. A sensor measures the local amplitude of the perturbation and relays the information to the control mechanism. Solutions of the adjoint linearized Navier–Stokes equations are coupled with the sensor measurements to configure and optimize the control mechanism, and establish an anti-phase wave that brings about destructive wave interference. The amplitude of the stationary cross-flow instability is reduced by an order 103 for the feedforward system, while amplitude reductions of the order 103 per iteration and 108 overall are realizable for the feedback modeling approach. Similar levels of flow control are realizable for a multiple controller configuration. However, stationary cross-flow disturbances could not be eliminated indefinitely. Inevitably, the cross-flow instability started to grow again, albeit at a considerably lower magnitude. The analysis is extended to include the effects of systematic error in the sensors measuring capability.

Improved crossflow transition predictions for the one-equation [formula omitted] transition model

A variant of the local correlation-based transition model (LCTM) γ is presented to account for the prediction of transition due to stationary crossflow instabilities. The presented Tc1 crossflow criterion is a local approximation of the well-known C1 criterion by Arnal (1984), evaluated locally through auxiliary functions expressed by the solution of the Falkner–Skan–Cooke (FSC) equations. The criterion, originally proposed by Menter and Smirnov (2014), uses the wall-normal directional change of the normalized vorticity as indicator of the crossflow strength. Hereafter, an original calibration FSC-based of Menter & Smirnov criterion is proposed. A local approximation of the sweep angle is included in order to achieve better results on non-wing-like geometries. The capability of this model variant to predict stationary crossflow transition is therefore discussed. A validation study is presented using experimental data on the 6:1 prolate spheroid and the sickle wing.

Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

Receptivity of crossflow instability to discrete roughness amplitude and location

The effect of discrete roughness elements on the development and breakdown of stationary crossflow instability on a swept wing is explored. Receptivity to various element heights and chordwise locations is explored using a combination of experimental and theoretical tools. Forcing configurations, determined based on linear stability predictions, are manufactured and applied on the wing in a low turbulence facility. Measurements are performed using infrared thermography, quantifying the transition front location, and planar particle image velocimetry, providing a reconstruction of stationary crossflow instabilities and their associated growth. Measurements are corroborated with simulations based on nonlinear parabolised stability equations. Results confirm the efficacy of discrete roughness elements in introducing and conditioning stationary crossflow instabilities. Primary instability amplitudes and resulting laminar-turbulent transition location are found to strongly depend on both roughness amplitude and chordwise location. The Reynolds number based on element height is found to satisfactorily approximate the initial forcing amplitude, revealing the importance of local velocity effects in non-zero-pressure gradient flows. Direct estimation of initial perturbation amplitudes from nonlinear simulations suggests the existence of pertinent flow mechanisms in the element vicinity, active in conditioning the onset of modal instabilities. Dedicated velocimetry planes, elucidate the development of a momentum deficit wake which rapidly decays downstream of the element followed by mild growth, representing the first experimental evidence of transient behaviour in swept wing boundary layers. The outcome of this work identifies a strong scalability of the transition dynamics to roughness amplitude and location, warranting the upscaling of roughness elements to more accessible, measurable and spatially resolved configurations in future experiments.

Experimental study of hypersonic traveling crossflow instability over a yawed cone

Boundary layer transition is an important factor in the design process of hypersonic vehicles, and crossflow instability is a critical mode. In this paper, the traveling crossflow instability in a laminar boundary layer at Mach 6 is experimentally investigated. Experiments were performed over a 7∘ half-angle cone at 6∘ angle of attack, with the unit Reynolds number of Re∞=5.75×106 m−1. Flush-mounted fast-response pressure transducers and time-averaging temperature-sensitive paint were used to capture the traveling crossflow instability and the stationary crossflow instability, respectively. The traveling crossflow waves with characteristic frequencies between 10 and 25 kHz are detected in the planes with the azimuthal angle between 23∘ and 143∘ away from the leeward ray. The three-dimensional amplitude growth was obtained. In general, the amplitude growth of the traveling crossflow instability is roughly leeside-forward and windside-aft. Although the traveling crossflow instability grows earlier on the leeward side, it has a larger amplitude on the windward side. Compared with the stationary mode, the traveling mode grows faster and reaches the highest amplitude earlier. In addition, a high-frequency instability with characteristic frequencies between 100 and 200 kHz is observed. It may be the secondary instability of the traveling crossflow waves, but whether it is true or not needs further experimental and numerical studies.

Plasma-Based Forcing Strategies for Control of Crossflow Instabilities

The present work experimentally investigates two forcing strategies toward controlling stationary crossflow instability (CFI) induced transition manifesting on a swept wing at subsonic conditions. The effectiveness of upstream flow deformation (UFD) and the base-flow modification strategies, realized through the application of spanwise-modulated and spanwise-uniform dielectric barrier discharge plasma actuation, respectively, is compared experimentally. Specialized, patterned actuators that generate spanwise-modulated plasma jets have been fabricated using a spray-on technique and positioned near the leading edge. An array of discrete roughness elements (DREs) is installed upstream of the plasma forcing to lock the origin and evolution of the critical stationary CFI vortices in the boundary layer. The impact of the phase relation between the spanwise-modulated plasma jets and the incoming CFI vortices is inspected. Infrared thermography is employed to detect and quantify the transition location. A delay in transition is observed with all tested forcing configurations. However, as the incoming CFI vortices are highly amplified due to the application of DREs, the acquired results suggest that with spanwise-modulated forcing the control mechanism responsible for the observed transition delay is not purely UFD; rather the beneficial effects observed leverage on a combination of direct attenuation of the CFI vortices and localized base-flow modification, depending on the aforementioned phase relation. For all forcing strategies and configurations, a simplified drag reduction efficiency estimation is performed using the experimentally measured transition location and the electrical power use of the actuators. A net gain is found for selected configurations.

Linear amplification factor transport equation for stationary crossflow instabilities in supersonic boundary layers

Based on the database from linear stability theory (LST) analysis, a local amplification factor transport equation for stationary crossflow (CF) waves in low-speed boundary layers was developed in 2019. In this paper, the authors try to extend this transport equation to compressible boundary layers based on local flow variables. The similarity equations for compressible boundary layers are introduced to build the function relations between non-local variables and local flow parameters. Then, compressibility corrections are taken into account to modify the source term of the transport equation. Through verifications of different sweep angles, Reynolds numbers, angles of attack, Mach numbers, and different cross-section geometric shapes, the rationality and correctness of the new transport equation established in this paper are illustrated.

Improved local amplification factor transport equation for stationary crossflow instability in subsonic and transonic flows

Transition prediction is a hot research topic of fluid mechanics. For subsonic and transonic aerodynamic flows, eN method based on Linear Stability Theory (LST) is usually adopted reliably to predict transition. In 2013, Coder and Maughmer established a transport equation for Tollmien-Schlichting (T-S) instability so that the eN method can be applied to general Reynolds-Average-Navier-Stokes (RANS) solvers conveniently. However, this equation focuses on T-S instability, and is invalid for crossflow instability induced transition which plays a crucial role in flow instability of three-dimensional boundary layers. Subsequently, a transport equation for crossflow instability was developed in 2016, which is restricted to wing-like geometries. Then, in 2019, this model was extended to arbitrarily shaped geometries based on local variables. However, there are too many tedious functions and parameters in this version, and it can only be used for incompressible flows. Hence, in this paper, after a large amount of LST analyses and parameter optimization, an improved version for subsonic and transonic boundary layers is built. The present improved model is more robust and more concise, and it can be applied widely in aeronautical flows, which has great engineering application value and significance. An extensive validation study for this improved transition model will be performed.

Mechanisms of stationary cross-flow instability growth and breakdown induced by forward-facing steps

Mechanisms of stationary cross-flow instability growth and breakdown induced by forward-facing steps

Investigation of stationary-crossflow-instability induced transition with the temperature-sensitive paint method

The Temperature-Sensitive Paint (TSP) method is used for surface-based flow visualizations on a swept-wing wind-tunnel model with a generic natural laminar-flow airfoil. Within the investigated parameter range the stationary crossflow instability is the dominating instability mechanism. Based on the TSP results the location of the laminar-turbulent transition and the most amplified wavenumber of the stationary crossflow instability are determined. The test is performed with three different conditions of the leading-edge surface: highly polished, unpolished, and highly polished with discrete roughness elements applied. The Temperature-Sensitive Paint method has proven to have sufficient spatial resolution and temperature sensitivity to resolve skin friction variations to detect the footprint of stationary crossflow vortices even inside of turbulent wedges. With the discrete roughness elements, i.e. cylindrical elements with micron-sized height, the transition could be delayed successfully for certain conditions. Local low-frequency movement of the beginning of turbulent wedges was detected for some data points with an unpolished leading edge.

Fully Local Amplification Factor Transport Equation for Stationary Crossflow Instabilities

The traditional linear stability analysis for transition prediction includes the following steps: solving velocity profiles using boundary-layer equations or a computational fluid dynamics solver, guessing and searching operations for the eigenvalues, computing the linear perturbation equations, and integrating the amplification factor . It is difficult to implement into modern computational fluid dynamics solvers with parallel computations because it requires many nonlocal variables and coordinate system transformations. In this Paper, an amplification factor transport equation, which can be coupled with a modern computational fluid dynamics parallel solver, is established based on the analysis results through linear stability theory for stationary crossflow instabilities. According to the analysis results of Falkner–Skan–Cooke similarity velocity profiles using linear stability theory analysis, the source term of the present transport equation is formulated locally to describe the growth of stationary crossflow waves in the laminar boundary layer. This new equation is added to the equation proposed by Coder and Maughmer for Tollmien–Schlichting instabilities. Finally, coupling of these two amplification factor transport equations and Menter’s shear stress transport turbulence model completes an effective transition turbulence model. Comparisons between the present predictions, wind tunnel experiments and the standard linear stability theory analysis on an NLF(2)-0415 infinite swept wing, Petzold’s sickle-shaped wing and 6:1 inclined prolate spheroid validate the reasonable establishment of the present amplification factor transport equation for stationary crossflow instabilities.

Development of a computational fluid dynamics compatible mathematical model for boundary layer transitional flows in low-disturbance environment

Because of the great influence of transition phenomena in aerodynamic property calculations, boundary layer transition has always been a hot research topic in the past few decades. Meanwhile, the prediction methods for boundary layer transition need to be established, researched and enhanced. In order to build a computational fluid dynamics (CFD) compatible transition model, the authors propose a two-equation transport transition model in this paper considering analysis results through linear stability theory (LST). This new transition model consists of one transport equation for laminar fluctuation kinetic energy and another for intermittency factor. Without boundary layer integration and other nonlocal operations, all the variables in this new transition model can be calculated locally so that present model is compatible with CFD parallel computation. Laminar separation bubble induced transition, Tollmien–Schlichting (T–S) instabilities and stationary crossflow instabilities (CF) dominated transition are modeled in the transport equation. The validation tests have been conducted on the classical Schubauer & Klebanoff flat plate, natural laminar airfoil NLF(1)-0416, NLF(2)-0415 infinite swept wing, classical sickle swept wing and 6:1 inclined prolate spheroid using this fully-local transition model. Since all the test cases are in accord with experimental data, the present transition model could be widely applied to aeronautical flows in low-disturbance environment.

Interaction of a Backward-Facing Step and Crossflow Instabilities in Boundary-Layer Transition

A swept flat plate model with an imposed pressure gradient was experimentally investigated in a low-speed flow to determine the effect of a backward-facing step on transition in a stationary crossflow–dominated flow. Detailed hotwire measurements of boundary-layer flow were performed to investigate the upstream shift in transition due to a step height of 49% of the local unperturbed boundary-layer thickness. Increasing the initial stationary crossflow amplitude caused an upstream movement of the transition front for the backward-facing step case. The step caused a local increase in the growth of the stationary crossflow instabilities, but the stationary crossflow amplitude at transition was sufficiently low () so that stationary crossflow was not solely responsible for transition. The unsteady velocity spectra downstream of the step were rich with unsteady disturbances in the 80- to 1500-Hz range. Three distinct families of disturbances were identified based on phase speed and wave angle, namely, a highly oblique disturbance (possibly traveling-crossflow-like), a Tollmien–Schlichting-wave-like disturbance, and a shear-layer instability. The stationary crossflow disturbances caused a modulation of the unsteady disturbances, resulting in spatially concentrated peaks in unsteady disturbance amplitude. This modulation of the unsteady disturbances is believed to be the reason for the upstream movement of the transition front with increasing stationary crossflow amplitude.