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1 Modifying mixing and instability growth through the adjustment of initial conditions in a high-energy-density counter-propagating shear experiment on OMEGA E. C. Merritt, 1, a) F. W. Doss, 1 E. N. Loomis, 1 K. A. Flippo, 1 and J. L. Kline 1 Los Alamos National Laboratory, Los Alamos, NM, 87545, USA (Dated: 30 May 2015) Counter-propagating shear experiments conducted at the OMEGA Laser Facility have been evaluating the effect of target initial conditions, specifically the characteristics of a tracer foil located at the shear boundary, on Kelvin-Helmholtz instability evolution and experiment transition toward nonlinearity and turbulence in the high-energy-density (HED) regime. Experiments are focused on both identifying and uncoupling the dependence of the model initial turbulent length scale in variable-density turbulence models of k-ϵ type on competing physical instability seed lengths as well as developing a path toward fully developed turbulent HED experiments. We present results from a series of experiments controllably and independently varying two initial types of scale lengths in the experiment: the thickness and surface roughness (surface perturbation scale spectrum) of a tracer layer at the shear interface. We show that decreasing the layer thickness and increasing the surface roughness both have the ability to increase the relative mixing in the system, and thus theoretically decrease the time required to begin transitioning to turbulence in the system. We also show that we can connect a change in observed mix width growth due to increased foil surface roughness to an analytically predicted change in model initial turbulent scale lengths. I. INTRODUCTION Mixing due to hydrodynamic instabilities and turbulence 1,2 has been well studied in traditional fluid regimes. It has been these low-energy-density experiments, such as fluid/gas shock tubes, that were employed to develop and benchmark many computational turbulence models. The counter-propagating (CP) shear campaign 3 5 is focused on examining Kelvin-Helmholtz instability growth and its apparent transition to turbulence in the high-energy-density (HED) regime. Specifically, the CP shear campaign operates in an experimental regime relevant to inertial-confinement fusion (ICF) 6 and astrophysical 7 experiments, which are systems in which the approximations used to describe low-energydensity hydrodynamic instabilities begin to break down. The HED nature of the CP shear experiment fielded at the OMEGA Laser Facility 8 puts it at the extremes of the traditional fluid experiment regime without any additional engineering. The CP shear platform features experimental shear flow velocity differences of M c > 2; the bulk of traditional fluid mixing layer experiments can only reach velocity differences of M c 2. 9 At large Mach numbers, thermodynamic and compressibility effects (which scale roughly as M 2 ) can begin having significant contributions to the mixing dynamics in the systems. The use of a kj-laser drive allows the experiment to reach Mbar level flow pressures using initially solid targets. Solid targets allow for the engineering of large density ratios (and Atwood numbers) at the shear interface, as well the ability to set the initial interface condia) Electronic mail: emerritt@lanl.gov tions from which the instabilities and mixing grow, which is often not possible in low-energy-density experiments. These experiments were conducted at the OMEGA facility, despite the greater drive capabilities and experiment duration times available at NIF, 5 to take advantage of the greater available number of experiment shots to test this wide range of initial target parameters. Comparisons between previous NIF and OMEGA experiments have shown that results from OMEGA experiments are yielding NIF relevant information at early times. The comparison of experimental results between targets with different drivers and sizes builds confidence that the physics results are not dependent on the experimental setup. Moreover, if one had a high degree of confidence in the early-time Euler scaling demonstrated in Doss et. al., 5 and implemented here in Sec. IV, one could imagine OMEGA campaigns replacing rarer NIF shots for some future parameter studies, reserving the NIF shots for late time excursions, for these or other experiments. Building a body of knowledge to permit this efficient use of facilities in the future is among the motivations for exploring the limits and behavior of the OMEGA experiments. The CP shear experiment is designed to test the universality of the shear-production aspects of k-ϵ turbulent mix models, 10,11 specifically the Besnard- Harlow-Rauenzahn (BHR) 12,13 model implemented in the RAGE 14 hydrocode, in the HED regime. The platform design using pressure-balanced counter-propagating flows (Fig. 1), as opposed to other work with HED blast waves, about a shear interface allows relative isolation of the shear instability physics by making any pressure imbalance small during the experiment KH growth phase. This reduction in the model complexity allows us to conduct a series of focused experiments to exam-

2 2 ine both the relationship between experiment and model initial conditions, specifically potential initial instability seed scales, and their role in determining instability and apparent turbulence onset times in the system. Previous work has shown that early experiments can only be matched in simulation with use of a mix model, where the mix model initial conditions were determined empirically to match the data. A goal of the CP shear campaign is to check model predictions that the experimental mixing rate should become independent of initial conditions after the onset of turbulence; thus checking what model behavior is trustworthy even in simulations without physical analogues to empirically set the model initial conditions. Another goal of the CP shear campaign is to study the relationship between the model initial turbulent length scale s 0, which is not well defined in terms of physical quantities, and actual initial scales in the experiment. This is part of ongoing efforts to develop even rudimentary predictive ability for determining s 0 in shear flow systems. To these ends we performed a series of experiments to independently vary two initial types of scale lengths in the experiment, the thickness of a tracer layer at the shear interface and the spectrum of tracer layer surface perturbation scales (surface roughness). In addition, we also performed experiments using tracer layers of different materials to address engineering concerns associated with reducing the thickness of the tracer foils. From the current OMEGA initial condition parameter scan, we find that thinner tracer foils and larger surface roughness increasing the relative layer expansion after the onset of Kelvin-Helmholtz (KH) instability growth. In addition, we find that thinner, higher-density tracer foil experiments are an avenue to decreasing the delay before apparent turbulence onset while preserving early-time hydrodynamics to test the turbulent mixing s 0 independence assumptions. We also find that we can connect a change in foil surface roughness to a change in s 0, which suggests that experiments elucidating the connection between s 0 and various physical scales are potentially achievable. We will present our results as well as discussions on both how this may apply to KH vs. higher order instability growth, turbulence studies and future plans to apply this to CP shear experiments on NIF. II. INITIAL CONDITION INFLUENCE ON ENERGY COUPLING DISCUSSION One aspect of the CP shear campaign is to study the relationships between instabilities, mixing dynamics of the shear layer, and the initial boundary conditions in the experiments. This platform s placement of a thin metal tracer layer (Fig. 1) at the shear boundary has both the engineering advantage of enabling the use of counter-propagating pressure-balanced flows and the motivating advantage of resembling shear flow geometries around small mixing layers of variable densities, e.g. at FIG. 1. Diagram of the target geometry: Target includes a cylindrical beryllium shock tube around a physics package consisting of two hemi-cylindrical CH foams separated by a metallic tracer layer. Ablator caps are located at both ends of the shock tube and are directly irradiated by lasers to launch shock waves into the system. Hemi-cylindrical gold plugs are located on opposing ends of the shock tube to serve as shock stops, leading to counter-propagating shocks in the experiment. FIG. 2. Cartoon displaying possible vorticity seed scales, in the CP shear target geometry, from both the tracer foil thickness as well as the foil surface roughness. the interfaces of the bubbles and spikes observed in ICF implosions. The existence of this finite-width separation layer means that the initial boundary conditions include both the surface characteristics of the layer and the layer thickness, which we can modify separately to adjust the experiment initial conditions. The ability to manipulate the surface roughness (i.e. spatial amplitude spacing of surface density perturbations) and layer thickness allows us to study the balance of energy coupling into the shear layer. The KH instability couples energy into coherent spanwise (across the foil, perpendicular to the flow) structures with dimensions on the order of the layer thickness and width (represented roughly by the large vortices in Fig. 2). Additionally, the interaction of the flow with the surface perturbations could couple energy into higher order instabilities with smaller, relative to the layer dimensions, typical scale lengths (represented roughly by the surface detail view in Fig. 2). The balance of the energy coupling has the potential to set the dominant

3 3 scales of mixing observed in the system. Kelvin-Helmholtz instability growth couples energy into the entire shear layer, where the linear instability growth rate scales as V /l0, where V is the velocity difference between the counter-propagating flows and l0 is the initial thickness of the shear layer. For an idealized model of this experiment with a smooth foil, this growth rate scaling is the only combination of variables with a net time dimension locally available to the center of the tube. This scaling suggests that the tracer layer thickness is the scale that should have a significant influence on mixing due to KH growth. The KH instability classically leads to 2D coherent structures along the entire plane of the tracer, since the entire tracer layer is acting as single shear boundary between two flows.19 Thus, if energy couples preferentially into the KH instability we expect the mixing in the system to occur in these largescale vortices. Competing with the above, energy coupling into the surface roughness of the tracer layer happens as the shock passes over the surface and the flow at the boundary is perturbed by the surface variations. This is the same energy deposition/vorticity generation mechanism described by Hurricane22 in the limit of a very thick foil, applied here for a range of surface perturbation scales. Since the surface roughness intrinsically contains a spectrum of small-scale (relative to the layer thickness) random surface variations, coupling energy into the surface roughness provides a mechanism for initiating turbulent mixing at earlier times in the experiment. At high Reynolds number, small scale structures can perturb the KH 2D coherent structures and let energy and material mix between the discrete rollers, potentially leading to the destabilization of the large structures.23,24 This can effectively shorten the unsteady system s time to transition to nonlinear and turbulent behavior25 over the purely-shear driven case by directly populating the shorter energy scales without having them develop solely by driving from the outermost scale. III. EXPERIMENTAL PLATFORM The CP shock platform is a directly laser-driven platform. The targets consist of a beryllium shock tube containing an internal physics package, as well as two orthogonal backlighter targets for x-ray radiography. The shock tube physics package consists of two hemi-cylindrical low density (60 mg/cm3 ) CH foams separated by a solid density metal tracer foil, as shown diagrammatically in Fig. 1 and in as-built preshot radiography in Fig. 3. Located at opposing quadrants of the shock tube are two hemicylindrical 200-µm thick gold plugs. At each end of the shock tube is a 75-µm thick Rexolite ablator disc. Lasers directly irradiate the ablators to launch 110 µm/ns shocks into the system. The gold plugs block the shocks from propagating along their corresponding foams, setting up pressure balanced counter-propagating shock- FIG. 3. Pre-shot radiographs of targets with four types of tracer foils, with both edge-on (profile) and through the foil (plan) views. Gold spatial fiducial grids can be seen in the plan view radiographs. generating flows. This experimental setup has been discussed in more detail in Doss et. al.,3 with the exception that the experiments reported here used a solid density metal tracer layer cut from a piece of rolled foil. Data used in Doss et al. 3 is not included in this study since those experiments used a metallic coating on one of the foams that had initial conditions very different, due to the coating process, than solid density tracer layers. The tracer layer coating potentially had asymmetric surface roughness between the free surface and the bonding surface to the foam as well as inhomogeneous ρr due to the sputtering deposition method. RAGE simulations of the experiment with 20-µm Al foils predict 2 Mbar post-shock pressures and 70 µm/ns post shock flow speeds in the foams, as well as foam postshock temperatures of approximately 40 ev and densities of 0.2 g/cm3 ( 3.5X increase). Simulations using a soliddensity 20-µm Al tracer layer predicted post-shock layer temperatures of approximately 15 ev. The experiment has bulk Reynolds number defined in terms of shear velocity δ V /ν , where V is the velocity difference between the flows from one side of the shock tube to the other, δ is the outer scale of the mixing layer,25 and

4 4 Material Al Ti Thickness 20 µm 40 µm 12 µm 20 µm Surface Finish smooth rough smooth smooth rough smooth (Ra) µm µm µm µm µm µm TABLE I. Characteristics of all tracer foil variations used in this series of experiments. FIG. 4. Representative probability density functions (pdf) for the height distributions of the surface roughness for smooth and rough (a) Al and (b) Ti foils. Each pdf is normalized such that the area under the curve equals one. the ion viscosity ν for the lower limit was calculated using the method described in the NRL formulary 26 and the upper limit was calculated using the method described in Hurricane. 22 The two orthogonal backlighter views are oriented to image the target both edge-on to the tracer foil (profile view), to examine the mix width of the shear layer, as well as through the tracer foil (plan view), to examine the evolution of surface structures in the plane of the shear layer. Pre-shot radiographs of equivalent views for both orientations for a variety of targets are shown in Fig. 3. This paper concentrates on a study of the profile mix width evolution of the tracer foils. Variations in the experiments come from changing the initial characteristics of the tracer layer. The tracer foils in these experiments do not include sinusoidal single-mode imposed perturbations, as used in early HED KH experiments to ensure the development of non-linear structure in the available experimental time windows. 15,16,22 Instead, any perturbations on the tracer foil are due to initial or enhanced amplitude surface finish, analogous to some of the more recent blast-wave driven HED KH experiments. 18,27,28 We used tracer layers of two different materials, aluminum and titanium, as well as multiple layer thicknesses and surface finishes for each material (summarized in Table I). Foils with increased surface roughness were supplied by General Atomics and were manufactured using a coining process with sandblasted dies to create a random noise pattern with a nominally reproducible surface roughness. The roughened foils were designed to have a surface roughness between 4 10 times that of the smooth foils, which were fabricated with a rolling process, of the same material, where the roughness metric is the average surface roughness Ra, the arithmetic average of the absolute surface heights, taken separately for each side of each foil. In addition, the sandblasting increased the amplitude of the surface roughness while maintaining a similar, but broader, noise spectrum to the previous foils to minimize the seeding of any new single-mode instabilities. Figure 4 shows the measured probability density functions (pdf) of the surface height deviation for representative smooth and rough foils in both Al and Ti. Increasing the surface roughness broadens the pdf from FWHM < 1.5 µm in both Al and Ti to 3.5 µm in Ti (approximately 3X increases) and 9.0 µm in Al (approximately 6X increases). So, while Ti shows the larger increase in Ra with roughening, Al shows a larger increase in pdf broadness which means a larger increase in the spectrum of instability scales the foils can possibly seed. Due to the greater hardness of Ti compared to Al, it was difficult to achieve larger surface roughness than those shown with this sandblasted die coining method. IV. EXPERIMENTAL RESULTS A variety of target types were chosen to observe the effects of independently varying two initial types of scale lengths in the experiment, the thickness and the surface roughness of the tracer layer. In support of this, we also performed experiments using mass-matched tracer layers of two different materials to address engineering concerns associated with reducing the thickness of the tracer foils. The first set of experiments were designed to study the ability to change tracer foil material while preserving the early-time hydrodynamic response of the system. If

5 5 changes in the early-time hydrodynamic response of the experiment are negligible, then this opens an avenue to expand future experiments to thinner tracer layers than are possible using Al by using foils of higher density material. The early-time hydrodynamic response experiments here were conducted using two different tracer layer materials, Al and Ti, but keeping the overall mass of the tracer layer constant, 20-µm Al vs. 12-µm Ti. The second set of experiments varied only the tracer layer thickness while holding the material constant, for both Ti and Al. Finally, the third set of experiments kept both the material and thickness constant but increased the random roughness of the foil surface finish. The increase in amplitude of the surface perturbations on the increased roughness foils raises questions about potential contributions to the mixing layer growth from shock driven Richtmyer-Meshkov (RM) instabilities. Due to the counter-propagating flow geometry, the greatest acceleration of the tracer layer is experienced near the ends of the shock tubes where there is the greatest time delay before the second (counter-) shock reaches that position. We take the maximum layer surface velocity at these positions, estimated to be Vs 20 µm/ns from simulation, as an upper limit. Using derivations from Drake7 of the RM growth rate (which depends on Vs ) and the variable density KH growth along a single surface (which depends on V /2) of the mixing layer, we find that the KH growth is a factor of two larger than any predicted RM growth independent of mode number. This is even assuming decreased velocity difference, due to shock strength decay over the experiment duration, at a single surface of V /2 30 µm/ns. The KH growth rate increases to a factor of four larger at late-times in the experiment, when the KH growth depends on the difference in velocities between both CP flows. Since this method uses the layer translational velocity at the experiment edges, it should significantly overestimate the RM growth in the pressure-balanced region in the center of the tube, where the layer translational motion is negligible. Thus, we assume that the layer growth is KH dominated, even for the increased surface roughness foils. The mix half-width is determined from an averaged lineout, orthogonal to the tracer layer, extracted from an edge-on radiograph, as shown in Fig. 5. Radiographs of the Al foils were taken using the 4.3 kev Heα scandium line and pinhole-apertured, point-projection backlighting29 radiography with a nominal magnification of 24x onto an x-ray framing camera. Radiographs of the Ti foils were taken using either the 5.2 kev He-α vanadium line or the 5.7 kev He-α chromium line. The radiographs were taken primarily on a CCD with the exception of the Dec experiments where the radiographs were taken on Delta 3200 film. The lineout is taken approximately centered between the shocks, with some location variation to avoid noise from transient structures in the experiment. The lineout is averaged in the streamwise direction over an approximately 10-µm window. After a quadratic background subtraction, we fit a gaussian to FIG. 5. Radiograph (top) of a CP shear target with a 20µm Ti tracer layer at 12 ns (Shot 71415) after the drive turned on. The post-background-subtraction lineout plot (bottom), corresponds to the white line in the radiograph. The gaussian fit to the truncated data section is indicated by the red dashed line. lineout values of 80% of the peak lineout value. The data peak exclusion is to avoid errors introduced by peak saturation due to an effectively zero xray transmission through the center of the Ti foils. The mix half-width reported here is taken to be l1/2 = 2.5σ, where σ is the standard deviation of the fitted gaussian. The blurring effect of the pinhole size is then removed from the mix half-width by subtracting the effect of a normally distributed point-spread function from the one-dimensional lineout. The error is based on the statistical deviance of the model using the sum of squares of the residuals of the gaussian fit, where the fitted gaussian was varied through a range of fixed σ with a fixed center while allowing the height to vary. The error bars are given by the sigma values corresponding to the 95% area values of the sum of squares of the residuals curve. A useful tool for comparing the mix width growth between experiments is hydrodynamic scaling of the characteristic time scales. The hydrodynamic responses of the systems are governed by two primary mechanisms: early in time the hydrodynamics are dominated by the response of the tracer layer to the passing shocks and

6 6 Euler Scaling KH Scaling Foil Type τ Eu /τ Eu,0 Interval τ KH /τ KH,0 Interval 20 µm Al smooth ns ns 40 µm Al smooth ns ns 12 µm Ti smooth ns ns 20 µm Ti smooth ns ns TABLE II. Temporal scaling information for both Euler and KH scaling of all smooth foil data sets, where all data sets are scaled to the nominal smooth 20-µm Al foil data. late in time the system is dominated by the initial phases of KH instability growth. Euler scaling can be used to help quantify the similarity of the experiments during the shock dominated compression phase. 5,30,31 The relationship between the characteristic times, τ Eu, for two experiments 1 and 2 is given by ( ) ( ) L2 ρ2 τ Eu,2 = τ Eu,1, (1) L 1 where L is the initial foil thickness, ρ is the initial foil density, and assuming hydrodynamic equivalence holds between the experiments and the system pressures are the same. Similarly, a time scaling given for the KH instability growth when the shear flow velocities are the same can be expressed as τ kh,2 = ( L2 L 1 ρ 1 ) τ kh,1, (2) which resembles the Euler scaling but is only dependent on the layer thickness and does not have a mass dependence. Thus, we expect early-time mix width growth in the experiments should be determined by both the foil material and thickness and late-time growth to be solely determined by the foil thickness. For comparative purposes we have calculated the relative time scaling factors for the appropriate time intervals for all the presented experiments relative to the original 20-µm Al experiments and listed them in Table II. A. Matched foil ρr The mass matching experiments were conducted with 20-µm Al foils and 12-µm Ti foils. The total mass of each foil was matched to within 34% of the nominal mass of 38 µg, as calculated from the limits of the foil machining tolerances, and ρr matched in the direction between the foams to within 30%. Figure 6(a) shows a comparison of the mix half-widths for both mass matched foils types for experiment times between 6 ns and 16 ns after the laser drive. At early times t 7 ns, the difference between the mix half-widths for each foil type is < 10 µm and agrees within the measurement error at 7 ns. The early-time compression rates for the 20-µm Al foils and 12-µm Ti foils, as listed in Table III, are different by approximately 60%. However, we can also compare the early-time hydrodynamic response between the experiments using our hydrodynamic scaling methods: the Euler scaling between the time scales for these two experiments is τ Eu,Al = 1.3 τ Eu,Ti. The hydrodynamically scaled Ti compression rate agrees with the Al compression rate within 35%. Thus, the hydrodynamic response of both foils matches to approximately the error of the target machining tolerances. At later times in the experiment we expect a difference in measured mix half-widths between the 20-µm Al foils and 12-µm Ti foils because of the different foil thicknesses; we will discuss this in more detail in the next section. Overall the mass matched foils have similar hydrodynamic response to the shocks and shock generated flows; the foils experience similar compression and show no signs of shocks breaking through the foil and into the other flow. The hydrodynamic response between the experiments is in good agreement in light of some discrepancies between the experiments, such as different foil responses to direct-drive preheat and other equation-ofstate effects. Thus it is feasible to design experiments for initial thickness studies that are early-time hydroequivalent to our current experiments but able to use thinner, high-density foils. B. Late-time mix half-width vs. foil thickness Foil thickness effect experiments were designed to compare the mix width growth between both foils of the same material but different thicknesses (20-µm vs. 40-µm Al, 12-µm vs. 20-µm Ti) as well as foils of different materials but the same thickness (20-µm Al vs. 20-µm Ti), which have the same early-time hydro-dynamic response to the shocks, in order to test the predictions that mix width growth due to the onset of the KH instability should be dependent on the shear layer s thickness but not its mass. Figure 6 shows a comparison of the thickness matched data (b) and the material matched data for Al (c) and Ti (d). For both single material cases, at times t < 13 ns the mix half-widths of the thicker foils are smaller than the mix half-widths of the thinner foils. In the Al case the absolute difference is small, approximately within measurement error, but this implies that the relative fraction of the layer that is mixing is larger for the thinner foil. Similarly, not only is relative mixing fraction larger for the thinner Ti case, but the absolute difference in the Ti mix-widths is notable as well. For times between ns, the Ti foils show mix half-width differences of µm and an average corresponding effective time offset of t 2 ns, with the thinner 12-µm foil having the larger mix half-widths. For t > 13 ns the thicker foils show greater mix halfwidths than the thinner foils. The effect is more pronounced at 14 ns for both the Al foils and Ti foils, with 18 µm and 15 µm increases in the mix widths respectively. In both comparisons, the mix width growth rate

7 7 FIG. 6. Material comparison experiments: Mix half-width measurements for (a) mass matched tracer foils of 20-µm Al (squares) and 12-µm Ti (diamonds), (b) thickness matched tracer foils of 20-µm Al and 20-µm Ti. Thickness comparison experiments: Mix half-width comparison plots for different foil thickness for (c) 20-µm vs. 40-µm Al and (d) 12-µm vs. 20-µm Ti. For both materials, for t < 13 ns the larger thickness foils display greater mix half-widths than the smaller foils. Similarly, for t > 13 ns the thicker foils display smaller mix half-widths than the thinner foils. Data for t > 15 ns (represented in gray) may not be as indicative of overall trends in the data due to temporal proximity to the recrossing of reflected shock at shock tube center that effectively ends the experiment. The shot number for each data point is included in the plots. Linear fits for each data set, corresponding to the growth rates listed in Table III, are indicated by dashed, solid, and dotted lines. Compression Rate [µm/ns] Growth Rate [µm/ns] Foil Type Interval (t) dl 1/2 /dt Interval (t*) dl1/2/dt Interval (t) dl 1/2 /dt Interval (t*) dl1/2/dt 20 µm Al smooth 6 7 ns ns ns ns ns µm Al smooth 8 10 ns ns ns ns µm Ti smooth 6 8 ns ns ns ns µm Ti smooth 6 7 ns ns ns ns ns µm Al roughened 8 10 ns (Dec.) ns (Dec.) ns (May) µm Ti roughened ns 9.7 TABLE III. Compression/growth rates for all data sets. All rates were found using a linear fit to the original (Fig. 6 & Fig. 8) or hydrodynamically scaled (Fig. 7) half-width data over the indicated time intervals.

8 8 FIG. 7. Plot of scaled mixing half-width (l /2) vs. scaled time (t ) for all smooth foil data sets, where the time scaling for each data set is dictated by the Euler and KH scaling ratios and time intervals given in Table II. Linear fits for each data set, corresponding to the growth rates listed in Table III, are indicated by dotted and solid lines. The vertical gray dashed line denotes the value of t corresponding to the time required to develop turbulence in the experiment s inertial range predicted by the Zhou scaling criteria. 25 between 8 14 ns (10 14 ns for 40-µm Al) is larger for the thicker foils due to the late-time jump in mix-half-width (Table III). Comparing foils with different materials but the same thickness shows similar mix half-widths during early expansion of the mix layer, until about 14 ns when the Ti foil growth displays a jump in mix width. The mix width growth rates between 8 14 ns are also similar, to within 6%. Interestingly, while the Ti foil has a larger mix width at the end of the experiment, the mix half-width growth rate for both the 20-µm Al and Ti foils is 6 µm/ns for ns. The decrease in growth rate may indicate the ending of the experiment due to return of decaying reflected shock to the center of the shock tube. For early times (t 8 ns) in these experiments we do observe a larger difference in both the mix widths and compression rates between the thickness matched Al and Ti foils compared to the mass matched foils, which is expected since the mass matching was employed to make the system behaviors hydrodynamically similar. C. Hydrodynamic scaling of the smooth foil results Applying hydrodynamic scaling to the data sets for the four smooth foil types allows us to compare the mix half-width growth more directly. The times for each data set were scaled by dividing the original time step between data points by the appropriate scaling ratio for each time interval shown in Table II, such that t i+1 = t i + (τ 0 /τ )(t i+1 t i ). (3) We scaled based on time step to allow for cases where τ Eu τ KH in a single experiment. The scaled times are adjusted so that the initial shock crossing time, t = 6 ns, remains unaltered. The mix half-widths for each data set were scaled using the ratio of the initial foil thickness to l 0,nom = 20 µm for the nominal Al experiments, where the scaled mix width is given by l = (l 0,nom /l 0 )l. (4) Figure 7 shows the mix half-width vs. scaled time data for all the smooth foil experiments. The error bars correspond to both the measured mix half-width error and error introduced by the scaling, where the scaling error is based on the initial foil thickness tolerance. We assume l 0 = l 0 ± δl, where δl = 2 µm is the machining tolerance for all data sets; actual foil thickness variations across a single data should be smaller, 1 µm, assuming all foils were cut from the same initial stock. The mix width scaling error is given by l ± l = 1/(l 0 ± δl) 1/l 0 l 0,nom l. (5) The mix half-width scaling error was then added in quadrature to the measured mix half-width error scaled by l 0,nom /l 0 to get the total error in l. Assuming an initial foil thickness error also introduces a temporal error bar due to the dependence of τ Eu and τ KH on l 0. The temporal error is cumulative since the time scaling is based on time step. Figure 7 shows that the early-time compression behavior varies based on mass, while late-time mix half-width growth is very similar across all experiments. In addition, the 20-µm Al and Ti foil curves show agreement within error of the scaled mix widths. For t > 8 ns the scaled mix half-width growth rate for 12-µm Ti agrees to within < 5% with the 20-µm Al data (Table III). A small difference in mix half-width amplitude between the 12-µm and 20-µm data persists even with scaling and accounting for error; this offset is possibly an indication of a greater effect of preheat on the thin Ti foil. Unfortunately, preheat was not well characterized experimentally for these experiments and is a subject of ongoing study. Overall, there is good agreement in the instability growth dynamics for the three experiments with significant extension into the instability regime. Hydrodynamic scaling also highlights the relative instability growth time for each foil thickness. The 40- µm foil experiences only a small amount of instability growth over the entire experiment duration, with an effective growth interval of t 3 ns as compared to the t 6 8 ns interval for the 20-µm Al and Ti. In contrast, the 12-µm foil experiment extends to much later scaled times, as seen in the extent of the corresponding curve in Fig. 7, for a effective growth interval of t 13 ns. Thus, the use of thinner foils effectively increases the accessible duration of the experiment.

9 9 Scaling criteria 25 yield a required time interval estimate of t 10 ns of sustained shear flow to develop turbulence in the inertial range of the experiment. Thus, since the shear flow regime of the experiment begins after shock crossing at t = 6 ns, experiments with time intervals of t > 16 ns are useful for studying the system transition towards turbulence and perhaps welldeveloped HED turbulence itself if the experiments can be extended to long-enough time intervals. The 12-µm Ti experiments are already able to extend the experiment duration to t > 16 ns and future experiments are planned with even thinner foils with high-density materials such as copper or tungsten. In addition to extending the effective experiment lifetime, this experiment progression may also allow us to increase the shear layer Atwood number to ICF-relevant-values close to unity. D. Late-time mix half-width vs. foil surface roughness Experiments with 20-µm Al foils with enhanced roughness show increased late-time mix half-width growth compared with the smooth Al foils and consistent mix half-widths between foil types early in the experiment. For t 10 ns the mix half-widths between the roughened and smooth Al foils agree on the order of the experimental error, suggesting that surface roughness effects don t become prominent until the onset of instability growth. For times between ns, the roughened foils show mix width enhancements of 6 12 µm for the Dec data set and µm for the May 2014 data set. Preshot foil surface roughness measurements are comparable for both the Dec. and May 2014 experiments, making the decrease in measured mix width enhancement most probably a diagnostic effect. All mix width radiographs, except those for Dec. 2014, were taken on a CCD detector. The Dec radiographs were taken on film, leading to a decreased signal to noise ratio at the edges of the mixing layer, as shown in Fig. 9. The decreased ability to distinguish the tails of the signal peak, which are associated with low-density mixing along the tracer layer surface, may have led to underestimating the overall mix-width of the tracer layer. This effect would only be exacerbated by the fact that the foil roughness is hypothesized to specifically increase mixing at the tracer boundary, making the introduced error non-constant and larger at later times. However, the half-width growth rate for both roughened foil experiments is comparable between experiments (Table III) and displays an approximately 20% increase over the growth rate for the smooth Al. In addition, if we extrapolate the ns data for smooth Al and the May roughened foils, we find an approximate time offset between the curves of t = 1.75 ns. Thus roughening the foils was able to effectively increase the experiment duration by that time offset, similar to what we saw with decreasing the foil thickness. But, unlike for the smooth foil thickness analysis, hydrodynamic scaling is not ob- FIG. 8. Mix half-width comparison plots for different foil surface roughnesses for (a) Al and (b) Ti. The shot number for each data point is included in the plots. Linear fits for each data set, corresponding to the growth rates listed in Table III, are indicated by dashed, solid, and dotted lines. FIG. 9. Comparison of the relative signal to noise response of the mix width lineouts for a CCD vs. film detector for two analogous shots.

10 10 viously applicable to the roughened foil data: the hydrodynamic scaling for our experiments relies solely on the nominal initial densities and thicknesses of the foils, which remain unchanged in the roughness experiments. The scaling analysis does not have an obvious way to describe the surface roughness. However, we can use the roughened foil data to infer information about some initial conditions in the BHR-2 turbulence model. We use the results of an analysis 32 which, for this flow configuration, connects the initial turbulence length scale s 0 in the model to the time at which the layer achieves its asymptotic growth rate. Assuming the drive conditions are constant across all experiments (a shear velocity difference across the tracer layer of V = 86 µm/ns and a pressure inside the shock tube of P = 2 Mbar), 32 the s 0 dependence can be reduced to s 0 s 0 (ρ 0, l 0, t). So we can compute how s 0 would need to change to account for the time offset between data sets for smooth and roughened foils of the same initial material and thickness. This analysis is not easily applicable to the smooth foil analysis because of the changes in material and l 0 between data sets. Assuming t = 0 for the nominal case of the smooth Al foil, then the initial turbulent scale is s 0 = 3.1 µm. For the t = 1.75 ns between the smooth and rough foil curves, the adjusted turbulence scale is s 0 = 9.0 µm for an increase of s 0 6 µm over the smooth foil case. This suggests that the surface roughness of the foil is a possible avenue for setting different turbulence scales in the experiment. While we can calculate a change in the initial turbulence scale, examining the exact relationship between the model turbulence scale and the many physical scales in the experiment problem is a point of ongoing research. For example, s 0 6 µm is both of the same magnitude as the total roughness amplitude added to the Al foils, 2 (2 3) µm, and s 0 /s 0 3 is of the same order as the 5 7 times increase in surface roughness between the campaigns. However, s 0 = 3.1 µm does not have an obvious connection to either the surface roughness or the layer thickness for the smooth Al foils. Uniquely identifying the connection between changes in the experiment and the behavior of the model could increase understanding of capabilities and limitations of these types of models. That the analysis could connect a change in the model to a change in an experiment initial condition suggests that this goal is potentially achievable and that future campaigns with controlled roughness variations are a good avenue for pursuing this research. The experiments with roughened Ti foils did not show measurable mix width enhancement, but rather yielded smaller mix widths overall for the roughened vs. smooth foils. There are several potential explanations for the smaller mix widths. First, the ability to resolve low density signals at the tails of the signal peak suffered from the same degradation from the switch to film that the Al data experienced. The May 2014 Ti data shows an 19 µm offset between the film and CCD data, which is very close to the 18 µm offset seen between the Al film and CCD data. While a signal-to-noise decrease may account for why the roughened foils do not show mix width enhancement over the smooth foils, the decrease in the overall mix widths may be a thickness effect. The thickness tolerance available for the Ti foils was 12 ± 2 µm, resulting in a measured pre-roughening thickness of 14 µm for the roughened foils. With a surface roughness of 1 µm this may have brought the effective thickness of the foil up to 16 µm. RAGE simulations for the titanium experiments suggest that initial width variations of 6 µm would by themselves account for 9% variations in evolved layer thickness. The May 2014 mix width measurement at 12 ns is between the corresponding mix widths for the 12-µm and 20-µm Ti foils, making the May measurement at least consistent with that of a foil thickness between µm. V. CONCLUSIONS The OMEGA CP shear experiment has recently completed a series of experiments testing the effects of shear layer thickness, material, and surface roughness on the growth rate of a shear layer due to KH instability. We found that we can manipulate the amount and rate of KH mixing in the system through the variation of the tracer layer initial conditions. Decreasing the shear layer thickness or increasing the layer surface roughness (in the Al experiments) both have the ability to increase the mixing rate of the experiment, where we were able to increase the mixing rate by a comparable amount using either mechanism alone. Since a primary motivation for the CP shear experiments is to study KH instability growth transition to turbulence in the HED regime, then the sooner the system begins to transition the greater the available time interval for examining turbulence dynamics before target disassembly. While the mechanisms to increase the mixing rate and turbulence onset are not expected to increase the instability growth rate in the OMEGA experiments enough to observe fully developed turbulence they are an avenue, using the demonstrated Euler scaling techniques, for informing the NIF CP shear turbulence experiments. The increase in KH mixing due to increased surface roughness was also suggestive of an increase in the initial turbulence scale size s 0 employed in the BHR-2 turbulent mix model. This ability to connect a change in the model to a change in an experiment initial conditions suggests that future experiments with controlled roughness variations are an avenue for identifying the unique connection between s 0 and the physical scale sizes present in our shear system, which could increase our understanding of the overall capabilities and limitations of the model.

11 11 ACKNOWLEDGMENTS The authors would like to extend their gratitude for their experiment contributions to Tom Sedillo and the LANL P-24 operations team, the MST-7 target fabrication team, especially Deanna Capelli, Tana Cardenas, Derek Schmidt and Jim Williams (now at Sandia National Laboratory), and Emilio Giraldez and the rest of the General Atomics target fabrication team. We thank Ricardo Mejia-Alvarez (LANL P-23) for useful fluid dynamics discussions and Jonathan Hager for physics and experiment design discussions. This work was supported by the U.S. Department of Energy and performed by Los Alamos National Laboratory, operated by Los Alamos National Security under Contract DE-AC52-06NA H. Tennekes and J. Lumley, A First Course in Turbulence (MIT PRess, 1972). 2 R. Livi and A. Vulpiani, The Kolmogorov Legacy in Physics (Springer-Verlag, 2003). 3 F. W. Doss, E. N. Loomis, L. Welser-Sherrill, J. R. Fincke, K. A. Flippo, and P. A. Keiter, Phys. Plasmas 20, (2013). 4 K. A. Flippo, F. W. Doss, B. DeVolder, J. R. Fincke, E. N. Loomis, J. L. Kline, and L. Welser-Sherrill, J. Phys.: Conf. Ser. 8th IFSA 2013: to be published. 5 F. W. Doss, J. L. Kline, K. A. Flippo, T. S. Perry, B. G. De- Volder, I. Tregillis, E. N. Loomis, E. C. Merritt, T. J. Murphy, L. Welser-Sherrill, and J. R. Fincke, Accepted to Phys. Plasmas (2015). 6 S. Atzeni and J. Meyer-ter-vehn, The Physics of Inertial Fusion (Oxford University Press, 2004). 7 R. Drake, High-Energy-Density-Physics (Springer-Verlag, 2006). 8 T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, and C. P. Verdon, Optics Communications 133, 495 (1997). 9 S. K. Lele, Annu. Rev. Fluid Mech. 26, 211 (1994). 10 F. H. Harlow and P. I. Nakayama, Phys. Fluids 10, 2323 (1967). 11 B. E. Launder and D. B. Spalding, Comp. Meth. Applied Mech. and Engineering 3, 269 (1974). 12 D. Besnard, F. H. Harlow, R. M. Rauenzhan, and C. Zemach, Tech. Rep. LA MS (Los Alamos National Laboratory, 1992). 13 A. Banerjee, R. A. Gore, and M. J. Andrews, Phys. Rev. E 82, (2010). 14 M. Gittings, R. Weaver, M. Clover, T. Betlach, N. Byrne, R. Coker, E. Dendy, R. Hueckstaedt, K. New, W. R. Oakes, D. Ranta, and R. Stefan, Comput. Sci. Discov. 1, (2008). 15 E. C. Harding, J. F. Hansen, O. A. Hurricane, R. P. Drake, H. F. Robey, C. C. Kuranz, B. A. Remington, M. J. Bono, M. J. Grosskopf, and R. S. Gillespie, Phys. Rev. Lett. 103, (2009). 16 O. A. Hurricane, J. F. Hansen, H. F. Robey, B. A. Remington, M. J. Bono, et al., Phys. Plasmas 16, (2009). 17 O. A. Hurricane, J. F. Hansen, E. C. Harding, V. A. Smalyuk, B. A. Remington, G. Langstaff, H.-S. Park, H. F. Robey, C. C. Kuranz, M. J. Grosskapf, and R. S. Gillespie, Astrophys. Space Sci. 336, 139 (2011). 18 C. A. Di Stefano, G. Malamud, M. T. Henry de Frahan, C. C. Kuranz, A. Shimony, S. R. Klein, R. P. Drake, E. Johnsen, D. Shvarts, V. A. Smalyuk, and D. Martinez, Phys. Plasmas 21, (2014). 19 G. L. Brown and A. Roshko, J. Fluid Mech. 64, 775 (1974). 20 R. Breindenthal, J. Fluid Mech. 109, 1 (1981). 21 L. Bernal and A. Roshko, J. Fluid Mech. 170, 499 (1986). 22 O. A. Hurricane, High Energy Density Phys. 4, 97 (2008). 23 P. E. Dimotakis and G. L. Brown, J. Fluid Mech. 78, 535 (1976). 24 M. M. Koochesfahani and P. E. Dimotakis, J. Fluid Mech. 170, 83 (1986). 25 Y. Zhou, Phys. Plasmas 14, (2007). 26 J. D. Huba, NRL Plasma Formulary, O. A. Hurricane, V. A. Smalyuk, K. Raman, O. Schilling, J. F. Hansen, G. Langstaff, D. Martinez, H.-S. Park, B. A. Remington, H. F. Robey, J. A. Greenough, R. Wallace, C. A. Di Stefano, R. P. Drake, D. Marion, C. M. Krauland, and C. C. Kuranz, Phys. Rev. Lett. 109, (2012). 28 V. A. Smalyuk, O. A. Hurricane, J. F. Hansen, G. Langstaff, D. Martinez, H.-S. Park, K. Raman, B. A. Remington, H. F. Robey, O. Schilling, R. Wallace, Y. Elbaz, A. Shimony, D. Shvarts, C. Di Stefano, R. P. Drake, D. Marion, C. M. Krauland, and C. C. Kuranz, High Energy Density Phys. 9, 47 (2013). 29 D. K. Bradley, O. L. Landen, A. B. Bullock, S. G. Glendinning, and R. E. Turner, Opt. Lett. 27, 134 (2002). 30 D. Ryutov, R. P. Drake, J. Kane, E. Liang, B. A. Remington, and W. M. Wood-Vasey, Astrophysical Journal 581, 821 (1999). 31 D. Ryutov, B. A. Remington, H. F. Robey, and R. P. Drake, Phys. Plasmas 8, 5 (2001). 32 F. W. Doss, J. R. Fincke, E. N. Loomis, L. Welser-Sherrill, and K. A. Flippo, Phys. Plasmas 20, (2013).

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