In this paper the skewness of streamwise velocity fluctuations in a canonical zero pressure gradient turbulent boundary layer is spectrally decomposed via the bispectrum. In particular, it is shown that the real part of the bispectrum allows the individual triad interactions contributing to the skewness to be characterized. These measurements are presented for a range of wall-normal locations associated with positive, zero and negative skewness. The individual contributions are also summed to obtain partial and cumulative sums of the skewness as a function of frequency. Complementary conditional sampling measurements demonstrate that the main contribution to boundary layer skewness is intimately associated with ejection-sweep and sweep-ejection events and the degree of asymmetry of their characteristic velocity signatures.

This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in terms of spatial evolution equations. The technique is used to examine the effect of localized periodic actuation at a given temporal frequency, based on an experimental set-up in which an active large-scale is introduced into the outer layer of a turbulent boundary layer. First, the large-scale structures associated with the phase-locked modal velocity field obtained from spatial input-output analysis are shown to closely match those computed based on hot-wire measurements. The approach is then used to further investigate the response of the boundary layer to the synthetically generated large-scale. A quadrant trajectory analysis indicates that the spatial input-output response produces shear stress distributions consistent with those in canonical wall-bounded turbulent flows in terms of both the order and types of events observed. The expected correspondence between the dominance of different quadrant behavior and actuation frequency is also observed. These results highlight the promise of a spatial input-output framework for analyzing the formation and streamwise evolution of structures in actuated wall-bounded turbulent flows.

In this paper, surface-mounted arrays of pulsed-DC dielectric barrier discharge plasma actuators are used to achieve skin friction drag reduction in turbulent boundary layers. The arrays are designed to produce a near-wall plasma-induced spanwise flow for the purpose of preventing the lift-up of low-speed streaks. Two array designs are demonstrated. One produces a unidirectional spanwise flow and the other a series of opposed wall jets. Both configurations are shown to produce unprecedented levels of drag reduction in excess of 70%. The amount of drag reduction achieved is shown to scale on the number of viscous wall units between adjacent surface electrodes which effectively sets the number of low-speed streaks under simultaneous control. In particular, the level of drag reduction increases logarithmically as the number of streaks under simultaneous control decreases. Furthermore, due to the low-power input required by the pulsed-DC actuator, this level of drag reduction is achieved with net power savings.

The dynamic response of a zero pressure gradient turbulent boundary layer (TBL) to a novel active flow control actuator was experimentally studied. The TBL has a relatively low Renumber, and does not have any discernable large-scale structure in the outer region. The periodically pulsed plasma actuator, placed inside the wake region of TBL, introduces a synthetic large-scale structure. Using a phase-locked analysis of the velocity across the boundary layer, it was found that the largescale structure has a modulating effect on the turbulent structure in the near wall region, similar to the modulation that is observed in canonical TBLs at high Reynolds numbers. INTRODUCTION In recent years, the large-scale structures (LSS) in turbulent boundary layers (TBL) and their effect on technologically relevant flow properties (friction drag, noise, aero-optical distortions, flow separation etc.) have been extensively investigated [1,2,3] and it was unequivocally demonstrated that the dynamics of LSS and near-wall small-scale turbulence is correlated [3,4]. Furthermore, the influence of the LSS in TBL dynamics was shown to increase with Reynolds number [3]. In canonical boundary layers, thin shear layers, separating low-speed and high-speed regions (so-called uniform momentum regions), have been observed and studied in the last few years [5,6]. These thin shear layer structures, combined with the low momentum flow underneath them, are believed to be parts of a coherent structure, also known as the Attached Eddy. A more recent investigation of adverse pressure gradient TBLs demonstrated that the local flow physics is largely dominated by an embedded shear layer associated with the inflectional instability of the outer mean velocity profile inflection point [7]. Using scaling laws developed for free shear-layers but applied to the adverse pressure gradient (APG) TBL, profiles of mean velocity and turbulence quantities exhibited a remarkable collapse. The generic applicability of the embedded shear layer scaling was demonstrated by collapsing multiple APG turbulent boundary layer data sets from the AFOSR-IFP-Stanford Conference compiled by Coles and Hirst [8]. Further support for the influence of the shear layer structure on the near-wall TBL dynamics was recently provided by a study demonstrating that the presence of a free shear layer just outside a TBL has a significant effect on the near-wall burst/sweep events [9]. Collectively, the results described above strongly suggest that embedded shear layers are a generic feature of all TBLs irrespective of whether or not the mean velocity profile is inflectional. Although more apparent in APG boundary layers with inherent inflectional mean velocity profiles, transient and non-localized inflectional instabilities could well account for the enhancement of outer large-scale boundary layer structure that has been documented in previous studies of high Reynolds number zero pressure gradient TBLs. These shear-layer-like structures likely play an important role in determining LSS dynamics and ultimately in the global properties of the TBL. An intriguing aspect of the presence of shear layers in the TBL is that they are very amenable to control. The ability to independently control outer layer LSS in the TBL offers new possibilities for uncovering their underlying dynamic. This aspect has been largely unexplored and most studies and models regarding the relationship between the smalland the large-scale structures deal with natural un-manipulated TBLs, and apply various conditional-averaging techniques to study their interactions [4]. Only a small number of studies have investigated modifying the LSS directly. In [10,11] an oscillating vertical plate was used to introduce a controlled traveling wave into the log-region of the boundary layer, and triadic interactions between the induced periodic structure and various scales in the boundary layer were studied. In [9] the turbulent boundary layer was externally forced by a shear layer and the turbulence inside the boundary layer was found to be both amplified and modulated by the external forcing. Motivated, in part, by the results in [9], in this paper, active flow control is used to introduce periodic disturbances into the outer wake region of the turbulent boundary layer. The turbulent boundary layer Reynolds number is low enough that there is no naturally occurring outer large-scale structure present. By introducing periodic distortions, a synthetic large-scale structure was introduced into the boundary layer, and the boundary layer response to this structure was studied. EXPERIMENTAL SET-UP All of the experimental results presented in this paper were obtained using the 2’ x 2’ subsonic in-draft wind tunnel facility in the Hessert Laboratory at the University of Notre Dame. The overall dimensions of the tunnel test section are 2’ x 2’ x 7’. For this experiment, a 2 meter long boundary layer development 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11) Southampton, UK, July 30 to August 2, 2019 2 plate with a roughness element attached to the leading edge was installed into the test section. CTA anemometer with a single boundary layer hot-wire probe (Dantec Type 55P15) 5 μm diameter and l = 1.5 mm (l+ =26) long was used to collect time series of the streamwise velocity component. The hot-wire was placed on a computer-controlled traverse system to position the hot-wire probe at different wall-normal locations. The traverse stage was inserted through the top wall of the tunnel along the middle of the tunnel span to allow a hot wire anemometer probe to be positioned at different streamwise locations. A plasma actuator, as described below, was attached to the boundary layer development plate at a fixed streamwise location of 140 cm from the leading edge of the boundary layer development plate. The experimental set-up with a plasma actuator, a hot wire probe and the coordinate system can be seen in Figure 1. A pitot probe was also inserted upstream of the plasma actuator through the side wall of the tunnel in order to measure the free stream velocity of the tunnel in order to calibrate the hot wire probe. The plasma actuator, consisted of a thin rectangular plate and positioned parallel to the wall along the spanwise direction, was supported in the tunnel by two vertical NACA0010 airfoil supports 50 mm long and variable heights, H. The plasma actuator plate is W = 10 cm wide in the spanwise direction and L = 52 mm in the streamwise direction. The actuator plate was made from a 2 mm thick sheet of Ultem dielectric polymer. The leading edge of the actuator plate was rounded and the trailing edge was tapered to minimize the separation region behind the trailing edge of the plate. The alternating current (AC) plasma formed on the actuator was produced using a function generator, power amplifiers and a transformer [12]. Electrodes on the top and bottom of the actuator were connected to the high voltage AC source that provided a 40kV peak-to-peak sinusoidal waveform excitation to the electrodes at a frequency of 4 kHz. At this high actuation frequency, the plasma operates in a quasisteady mode, essentially creating a steady jet. To introduce periodic forcing, a fifty percent duty cycle was imposed on the waveform, with a repetition frequency, fp, which can be varied between 50 and 300 Hz. Figure 1. Schematic of the experimental set-up with a picture of the plasma actuator. Hot wire voltages, pitot probe transducer voltages and the output of the function generator were recorded simultaneously. The velocity at each point was sampled at fs = 30 kHz (corresponding to 2 (1/ ) / 0.2 s t f uτ ν + ∆ = = ) for 120 seconds, or about 25,000 δ/U∞. The hot wire probe was conditioned by a low pass filter with a cutoff frequency of 14 kHz to eliminate aliasing effects. DATA REDUCTION The measured voltages from the hot wire probe were converted into velocities, using a 3rd-order polynomial calibration. After the hot wire voltages were converted to velocities, the time mean, U, and root mean square (RMS) of the velocity, urms, were calculated at every point using standard methods. Since the actuator introduced periodic forcing into the flow, it is convenient to phase-lock the results to the actuation frequency. To do so, a triple phase-locked Reynolds decomposition of the velocity was considered, as shown in Eq.(1), uu(yy, tt) = UU(yy) + uu�(yy,φφ) + uu′(yy,φφ,nn) (1) where uu is the instantaneous velocity, U is the time mean component of velocity, uu� is a phase dependent or modal velocity component, uu′ is a residual fluctuating turbulent component, φ is the phase, defined by the relationship in Eq. (2), and n is the number of realizations as described below ttnn = � φφ 2ππ + nn�TTpp (2) Here ttnn is a time in the nntth realization, and is related to the phase angle, φ, by the period of the forcing repetition cycle, TTpp = 1/ffpp. The output of the function generator was used to ensure the data was phase locked with the repetition cycle of the plasma. These n realizations were then ensemble averaged to determine how the modal component of velocity varies as a function of the phase angle. The remaining fluctuating component of the velocity, uu′, was used to quantify as ensemble-averaged RMS of the residual fluctuating turbulence, [ ] ( )1/2 2 ' ( ) '( , ; ) rms n u y u y n φ = (3) Here the < > brackets denote ensemble averaging over all realizations. Later we will refer to this quantity as a residual turbulence level. RESULTS The baseline turbulent boundary layer characteristics at the measurement location were measured to ensure canonical behavior. These are summarized in Table 1. Skin friction velocity, uτ, was determined using Clauser method. Table 1. Boundary layer parameters δδ UU∞ uuττ CCff HH RReeθθ RReeτ 33.2 mm 6.95 m/s 0.304 m/s 0.0039 1.368 1,770 683 The mean velocity of the boundary layer in the inner units, is presented in

Longitudinal velocity-derivative skewness S-0 is directly proportional to the rate of enstrophy generation and hence is a key parameter for characterizing small-scale turbulence. Obtaining S-0 requires accurate measurements of the finest scales in the dissipation subrange. In this paper we define a derivative skewness of the inertial range scales that is readily accessible experimentally, and we derive its value analytically. The results depend on the filtering procedure of small scales. Analytically derived inertial range skewness is compared with those computed by high-resolution numerical simulations and obtained in laboratory and field experiments. An alternative definition of the derivative skewness in the full and the inertial range scales is examined to identify the effects of intermittency.

The interaction between the near-wall and logarithmic layer in a high Reynolds number zero pressure gradient turbulent boundary layer is examined in terms of polyspectal measurements. The near wall velocity fluctuation skewness is decomposed in frequency space via the real part of the autobispectrum. Similarly, the crossbicoherence is used to examine the nonlinear phase coupling between the near wall region and logarithmic layer. These measurements clearly show the importance of quadratically nonlinear mechanisms in characterizing the near wall-outer layer interaction. To this end, a Volterra nonlinear system model containing both linear and quadratically nonlinear system transfer functions is proposed to model the near-wall outer layer interaction, It is demonstrated that the transfer functions may be determined via measured polyspectal quantities and the system output due to linear, quadratic and linear-quadratic coupling mechanisms quantifield. INTRODUCTION It is now widely accepted that large-scale vortical structures are an important and universal feature of the outer region of wall bounded turbulent flows (e.g. Hutchins and Marusic (2007), Adrian (2007), Monty et al (2007), Marusic et al (2010), Smits, McKeon and Marusic (2011) and others). It has also been demonstrated that these outer layer structures impose their imprint on the near-wall region of the turbulent boundary layer in the form of the amplitude and phase modulation of near-wall velocity and wall shear stress fluctuations (e.g. Hutchins and Marusic (2007), Mathis et al (2009), Ganipathisubramani et al (2009)). In addition, Mathis et al (2011) demonstrate that the skewness of velocity fluctuations in the near-wall region is directly linked to amplitude modulation. The nature of the interation between outer and inner regions of wall bounded flows is of both fundamental and practical interest since the near-wall region is responsible for turbulence production. Schoppa and Hussain (2002) described a streak transient growth (STG) mechanism for the self-sustaining mechanism of near-wall turbulence generation. They suggested that STG was the dominant streamwise vortex generation mechanism from otherwise normal mode stable low-speed streaks. In related work, Schoppa and Hussain (1998) proposed a large-scale strategy for skin friction drag reduction which was demonstrated in channel flow DNS. By imposing a streamwise-independent, spanwise velocity component along the channel wall by means of either a pair of counter-rotating streamwise vortices, or opposed wall jets significant drag reduction was achieved. The flow control served to prevent the lift-up of lowspeed streaks, thereby limiting their flanking wall-normal vorticity component which in their formulation, is a critical parameter for onset of STG. More recently, their channel flow drag reduction work was revisited by Canton et al (2016), where comparable levels of sustained drag reduction were achieved by a volumetric forcing approach. Motivated by this work a novel, nonintrusive, flush surface-mounted pulsed-DC plasma actuator was recently designed at the University of Notre Dame to be the first to actively intervene in the STG mechanism by producing a near-wall spanwise flow component that prevents the lift-up of low-speed streaks. Experiments show the abiliy of the actuator to very significnatly decrease or increase drag depending on the magnitude of the imposed spanwise velocity (Thomas et al (2016)). Aside from the practical aspects pertaining to drag reduction, the pulsed-DC actuator also provides an experimental tool by which the nature of the outer region-inner layer interaction can be investigated under both reduced and enhanced drag conditions and compared to the natural flow. Furthermore, in order to characterize the dynamic interaction between the near-wall and outer regions of the TBL a second-order Volterra nonlinear system model is applied. This model involves the determination of both linear and nonlinear system transfer functions that characterize the interaction. A particular focus of this paper is to describe and motivate the application of the nonlinear sytem model to the turbulent boundary layer. EXPERIMENTAL FACILITY The turbulent boundary layer measurements were conducted in a large in-draft wind tunnel facility located at the University of Notre Dame with a test section cross sectional area of 1.5 m ×1.5 m, a working test section length of 15.25m, and a maximum speed of approximately 13.5m/s. The inlet is 3.05 m × 3.05 m and corresponds to a contraction ratio of 4:1. A screen box is placed behind the inlet consisting of 4 stainless steel turbulence reduction screens (mesh spacing = 1 mm and wire diameter = 0.1 mm) with