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At least 469 records · Page 26

Assimilation of Satellite-Derived Skin Temperature Observations into Land Surface Models

Land surface (or "skin") temperature (LST) lies at the heart of the surface energy balance and is a key variable in weather and climate models. Here we assimilate LST retrievals from the International Satellite Cloud Climatology Project (ISCCP) into the Noah and Catchment (CLSM) land surface models using an ensemble-based, off-line land data assimilation system. LST is described very differently in the two models. A priori scaling and dynamic bias estimation approaches are applied because satellite and model LST typically exhibit different mean values and variability. Performance is measured against 27 months of in situ measurements from the Coordinated Energy and Water Cycle Observations Project at 48 stations. LST estimates from Noah and CLSM without data assimilation ("open loop") are comparable to each other and superior to that of ISCCP retrievals. For LST, RMSE values are 4.9 K (CLSM), 5.6 K (Noah), and 7.6 K (ISCCP), and anomaly correlation coefficients (R) are 0.62 (CLSM), 0.61 (Noah), and 0.52 (ISCCP). Assimilation of ISCCP retrievals provides modest yet statistically significant improvements (over open loop) of up to 0.7 K in RMSE and 0.05 in anomaly R. The skill of surface turbulent flux estimates from the assimilation integrations is essentially identical to the corresponding open loop skill. Noah assimilation estimates of ground heat flux, however, can be significantly worse than open loop estimates. Provided the assimilation system is properly adapted to each land model, the benefits from the assimilation of LST retrievals are comparable for both models.

Reichle, Rolf H.↗

Simulation of Laser Cooling and Trapping in Engineering Applications

An advanced computer code is undergoing development for numerically simulating laser cooling and trapping of large numbers of atoms. The code is expected to be useful in practical engineering applications and to contribute to understanding of the roles that light, atomic collisions, background pressure, and numbers of particles play in experiments using laser-cooled and -trapped atoms. The code is based on semiclassical theories of the forces exerted on atoms by magnetic and optical fields. Whereas computer codes developed previously for the same purpose account for only a few physical mechanisms, this code incorporates many more physical mechanisms (including atomic collisions, sub-Doppler cooling mechanisms, Stark and Zeeman energy shifts, gravitation, and evanescent-wave phenomena) that affect laser-matter interactions and the cooling of atoms to submillikelvin temperatures. Moreover, whereas the prior codes can simulate the interactions of at most a few atoms with a resonant light field, the number of atoms that can be included in a simulation by the present code is limited only by computer memory. Hence, the present code represents more nearly completely the complex physics involved when using laser-cooled and -trapped atoms in engineering applications. Another advantage that the code incorporates is the possibility to analyze the interaction between cold atoms of different atomic number. Some properties that cold atoms of different atomic species have, like cross sections and the particular excited states they can occupy when interacting with each other and light fields, play important roles not yet completely understood in the new experiments that are under way in laboratories worldwide to form ultracold molecules. Other research efforts use cold atoms as holders of quantum information, and more recent developments in cavity quantum electrodynamics also use ultracold atoms to explore and expand new information-technology ideas. These experiments give a hint on the wide range of applications and technology developments that can be tackled using cold atoms and light fields. From more precise atomic clocks and gravity sensors to the development of quantum computers, there will be a need to completely understand the whole ensemble of physical mechanisms that play a role in the development of such technologies. The code also permits the study of the dynamic and steady-state operations of technologies that use cold atoms. The physical characteristics of lasers and fields can be time-controlled to give a realistic simulation of the processes involved such that the design process can determine the best control features to use. It is expected that with the features incorporated into the code it will become a tool for the useful application of ultracold atoms in engineering applications. Currently, the software is being used for the analysis and understanding of simple experiments using cold atoms, and for the design of a modular compact source of cold atoms to be used in future research and development projects. The results so far indicate that the code is a useful design instrument that shows good agreement with experimental measurements (see figure), and a Windows-based user-friendly interface is also under development.

Ramirez-Serrano, Jaime↗

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMD is a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

high-performance computing↗

Receiver Gain Modulation Circuit

A receiver gain modulation circuit (RGMC) was developed that modulates the power gain of the output of a radiometer receiver with a test signal. As the radiometer receiver switches between calibration noise references, the test signal is mixed with the calibrated noise and thus produces an ensemble set of measurements from which ensemble statistical analysis can be used to extract statistical information about the test signal. The RGMC is an enabling technology of the ensemble detector. As a key component for achieving ensemble detection and analysis, the RGMC has broad aeronautical and space applications. The RGMC can be used to test and develop new calibration algorithms, for example, to detect gain anomalies, and/or correct for slow drifts that affect climate-quality measurements over an accelerated time scale. A generalized approach to analyzing radiometer system designs yields a mathematical treatment of noise reference measurements in calibration algorithms. By treating the measurements from the different noise references as ensemble samples of the receiver state, i.e. receiver gain, a quantitative description of the non-stationary properties of the underlying receiver fluctuations can be derived. Excellent agreement has been obtained between model calculations and radiometric measurements. The mathematical formulation is equivalent to modulating the gain of a stable receiver with an externally generated signal and is the basis for ensemble detection and analysis (EDA). The concept of generating ensemble data sets using an ensemble detector is similar to the ensemble data sets generated as part of ensemble empirical mode decomposition (EEMD) with exception of a key distinguishing factor. EEMD adds noise to the signal under study whereas EDA mixes the signal with calibrated noise. It is mixing with calibrated noise that permits the measurement of temporal-functional variability of uncertainty in the underlying process. The RGMC permits the evaluation of EDA by modulating the receiver gain using an external signal. Without the RGMC, samples of calibrated references from radiometers form an ensemble data set of the natural occurring fluctuations within a receiver. By driving the gain of an otherwise stable receiver with an external signal, the conceptual framework and generalization of the mathematics of EDA can be tested. A series of measurements was conducted to evaluate and characterize the performance of the RGMC. Test signals stepped the RGMC across its dynamic range of performance using a radiometer that sampled four noise references; analysis indicates that the RGMC successfully modulated the receiver gain with an external signal. Calibration algorithms applied to four noise references demonstrate the RGMC produced ensemble data sets of the external signal.

Jones, Hollis↗

Regional climate change projections from NA-CORDEX and their relation to climate sensitivity

Abstract The climate sensitivity of global climate models (GCMs) strongly influences projected climate change due to increased atmospheric carbon dioxide. Reasonably, the climate sensitivity of a GCM may be expected to affect dynamically downscaled projections. However, there has been little examination of the effect of the climate sensitivity of GCMs on regional climate model (RCM) ensembles. Therefore, we present projections of temperature and precipitation from the ensemble of projections produced as a part of the North American branch of the international Coordinated Regional Downscaling Experiment (NA-CORDEX) in the context of their relationship to the climate sensitivity of their parent GCMs. NA-CORDEX simulations were produced at 50-km and 25-km resolutions with multiple RCMs which downscaled multiple GCMs that spanned nearly the full range of climate sensitivity available in the CMIP5 archive. We show that climate sensitivity is a very important source of spread in the NA-CORDEX ensemble, particularly for temperature. Temperature projections correlate with driving GCM climate sensitivity annually and seasonally across North America not only at a continental scale but also at a local-to-regional scale. Importantly, the spread in temperature projections would be reduced if only low, mid, or high climate sensitivity simulations were considered, or if only the ensemble mean were considered. Precipitation projections correlate with climate sensitivity, but only at a continental scale during the cold season, due to the increasing influence of other processes at finer scales. Additionally, it is shown that the RCMs do alter the projection space sampled by their driving GCMs.

54 ENVIRONMENTAL SCIENCES↗

Universal Size-Dependent Stokes Shifts in Lead Halide Perovskite Nanocrystals

Size-dependent photoluminescence Stokes shifts (Δ E s ) universally exist in CsPbX 3 (X = Cl – , Br – , or I – ) perovskite nanocrystals (NCs). Δ E s values, which range from ~15 to 100 meV for NCs with average edge lengths ( l ) from approximately 13 to 3 nm, are halide-dependent such that Δ E s (CsPbI 3 ) > Δ E s (CsPbBr 3 ) ≳ Δ E s (CsPbCl 3 ). Observed size-dependent Stokes shifts are not artifacts of ensemble size distributions as demonstrated through measurements of single CsPbBr 3 NC Stokes shifts ((Δ E s ) = 42 ± 5 meV), which are in near quantitative agreement with associated ensemble ( l = 6.8 ± 0.8 nm) Δ E s values (Δ E s ≈ 50 meV). Transient differential absorption measurements additionally illustrate no significant spectral dynamics on the picosecond time scale that would contribute to Δ E s . This excludes polaron formation as being responsible for Δ E s . Overall, the results point to an origin for Δ E s , intrinsic to the size-dependent electronic properties of individual perovskite NCs.

36 MATERIALS SCIENCE↗

Analysis of Narrow Bipolar Events Using Mode Decomposition Methods

Multi-resolution analysis methods can reveal the underlying physical dynamics of nonstationary signals, such as those from lightning. In this paper we demonstrate the application of two multi-resolution analysis methods: Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) in a comparative way in the analysis of electric field change waveforms from lightning. EEMD and VMD decompose signals into a set of Intrinsic Mode Functions (IMFs). The IMFs can be combined using distance and divergence metrics to obtain noise reduction or to obtain new waveforms that isolate the physical processes of interest while removing irrelevant components of the original signal. We apply the EEMD and VMD methods to the observations of three close Narrow Bipolar Events (NBEs) that were reported by Rison et al. The ΔE observations reveal the occurrence of complex oscillatory processes after the main NBE sferic. We show that both EEMD and VMD are able to isolate the oscillations from the main NBE, with VMD being more effective of the two methods since it requires the least user supervision. The oscillations are found to begin at the end of the NBEs' downward fast positive breakdown and appear to be produced by a half-wavelength standing wave within a weakly-conducting resonant ionization cavity left behind in the wake of the streamer-based NBE event. In conclusion, additional analysis shows that one of the NBEs was likely initiated by an energetic cosmic ray shower, and also corrects a misinterpretation in the literature that fast breakdown is an artifact of NBE-like events in interferometer observations.

54 ENVIRONMENTAL SCIENCES↗

Influence of solution phase environmental heterogeneity and fluctuations on vibronic spectra: Perylene diimide molecular chromophore complexes in solution

Ensembles of ab initio parameterized Frenkel-exciton model Hamiltonians for different perylene diimide dimer systems are used, together with various dissipative quantum dynamics approaches, to study the influence of the solvation environment and fluctuations in chromophore relative orientation and packing on the vibronic spectra of two different dimer systems: a π-stacked dimer in aqueous solution in which the relative chromophore geometry is strongly confined by a phosphate bridge and a side-by-side dimer in dichloromethane involving a more flexible alkyne bridge that allows quasi-free rotation of the chromophores relative to one another. These entirely first-principles calculations are found to accurately reproduce the main features of the experimental absorption spectra, providing a detailed mechanistic understanding of how the structural fluctuations and environmental interactions influence the vibronic dynamics and spectroscopy of solutions of these multi-chromophore complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Resolving turbulent magnetohydrodynamics: a hybrid operator-diffusion framework

We present a hybrid machine learning framework that combines physics-informed neural operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic turbulence across a broad range of Reynolds numbers (Re). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with Re ϵ {100, 250, 500, 750, 1000, 3000, 10000}, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At Re = 1000 and 3000, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (Re = 10 000), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

Diffusion-Integrated Neural Operators↗

Light storage, retrieval, and controllable interference in an atomic tripod system

Highly efficient quantum memories are essential for advancing quantum information processing technologies, including scalable quantum computing and quantum networks. We experimentally demonstrate a light storage and retrieval protocol in a tripod system using an ensemble of laser-cooled 87 Rb atoms. The tripod system, which consists of three ground states and an excited state, offers rich dynamics: its use to coherently store and retrieve a weak probe pulse in the 87 Rb 𝐹 = 1 ground-state manifold leads to the interference of two spin-wave excitations during storage time that translate to an interference in the peak intensity of the retrieved probe pulse. Our work shows that these interferences, which manifest when varying the pulse sequence or energy level structure, can be controlled experimentally by varying the storage time, optical phase, and magnetic field strength. Theoretical simulations exhibit excellent agreement with the experimental results. In conclusion, this work demonstrates the rich dynamics and versatile capabilities of atomic tripod systems for light storage and retrieval, with key advantages over conventional Λ systems, highlighting the potential of atomic tripod systems for applications in quantum information processing, quantum synchronization, and atomic memory protocols.

Coherent control↗

Exascale Dislocation Simulator

ExaDiS, or Exascale Dislocation Simulator, is a set of software modules written to enable numerical simulations of large groups of moving and interacting dislocations, line defects in crystals responsible for crystal plasticity. By tracking time evolution of sufficiently large dislocation ensembles, ExaDiS predicts plasticity response and plastic strength of crystalline materials. ExaDiS is built around a library of core functions for Discrete Dislocation Dynamics method specifically written to perform efficient computations on GPUs.

Bertin, Nicolas↗

The tropical water and energy cycles in a cumulus ensemble model. Part 1: Equilibrium climate

A cumulus ensemble model is used to study the tropical water and energy cycles and their role in the climate system. The model includes cloud dynamics, radiative processes, and microphysics that incorporate all important production and conversion processes among water vapor and five species of hydrometeors. Radiative transfer in clouds is parameterized based on cloud contents and size distributions of each bulk hydrometeor. Several model integrations have been carried out under a variety of imposed boundary and large-scale conditions. In Part 1 of this paper, the primary focus is on the water and heat budgets of the control experiment, which is designed to simulate the convective - radiative equilibrium response of the model to an imposed vertical velocity and a fixed sea surface temperature at 28 C. The simulated atmosphere is conditionally unstable below the freezing level and close to neutral above the freezing level. The equilibrium water budget shows that the total moisture source, M(sub s), which is contributed by surface evaporation (0.24 M(sub s)) and the large-scale advection (0.76 M(sub s)), all converts to mean surface precipitation bar-P(sub s). Most of M(sub s) is transported verticaly in convective regions where much of the condensate is generated and falls to surface (0.68 bar-P(sub s)). The remaining condensate detrains at a rate of 0.48 bar-P(sub s) and constitutes 65% of the source for stratiform clouds above the melting level. The upper-level stratiform cloud dissipates into clear environment at a rate of 0.14 bar-P(sub s), which is a significant moisture source comparable to the detrained water vapor (0.15 bar-P(sub s)) to the upper troposphere from convective clouds. In the lower troposphere, stratiform clouds evaporate at a rate of 0.41 bar-P(sub s), which is a more dominant moisture source than surface evaporation (0.22 bar-P(sub s)). The precipitation falling to the surface in the stratiform region is about 0.32 bar-P(sub s). The associated latent heating in the water cycle is the dominant source in the heat budget that generates a net upward motion in convective regions, upper stratiform regions (above the freezing level), and a downward motion in the lower stratiform regions. The budgets reveal a cycle of water and energy resulted from radiation-dynamic-convection interactions that maintain equilibrium of the atmosphere.

Sui, C. H.↗

Comments on "The Sensitivity Study of Radiative-Convective Equilibrium in the Tropics with a Convective Resolving Model"

In general, there are two broad scientific objectives when using cloud resolving models (CRMs or cloud ensemble models-CEMs) to study tropical convection. The first one is to use them as a physics resolving models to understand the dynamic and microphysical processes associated with the tropical water and energy cycles and their role in the climate system. The second approach is to use the CRMs to improve the representation of moist processes and their interaction with radiation in large-scale models. In order to improve the credibility of the CRMs and achieve the above goals, CRMs using identical initial conditions and large-scale influences need to produce very similar results. Two CRMs produced different statistical equilibrium (SE) states even though both used the same initial thermodynamic and wind conditions. Sensitivity tests to identify the major physical processes that determine the SE states for the different CRM simulations were performed. Their results indicated that atmospheric horizontal wind is treated quite differently in these two CRMs. The model that had stronger surface winds and consequently larger latent and sensible heat fluxes from the ocean produced a warmer and more humid modeled thermodynamic SE state. In addition, the domain mean thermodynamic state is more unstable for those experiments that produced a warmer and more humid SE state. Their simulated wet (warm and humid) SE states are thermally more stable in the lower troposphere (from the surface to 4-5 km in altitude). The large-scale horizontal advective effects on temperature and water vapor mixing ratio are needed when using CRMs to perform long-term integrations to study convective feedback under specified large-scale environments. In addition, it is suggested that the dry and cold SE state simulated was caused by enhanced precipitation but not enough surface evaporation. We find some problems with the interpretation of these three phenomena.

Tao, W.-K.↗

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗

Representative Phenomena of Cyclic Turbulent Combustion in High-Pressure Fuel Sprays

Abstract Cyclic variations in conventional diesel combustion engines can lead to large differences in engine out emissions even at steady operation. This study uses an optically accessible constant-pressure flow chamber to acquire fuel injections in quick succession to analyze mixing, auto-ignition, and combustion of diesel-surrogate n-heptane using multiple high-speed optical diagnostics. Prior studies have utilized fewer injections and/or they rely on analysis of ensemble average behavior. These approaches do not yield information on injection-to-injection variation or provide confidence in utilizing individual injection measurements for high-fidelity computational fluid dynamics(CFD) model validation. In this study, a large set of 500 injections is used to obtain global parameters including liquid length, vapor penetration length, ignition delay time, and lift-off length. Results for multiple injections are presented to illustrate large injection to injection variations. Potential sources for these variations are analyzed to conclude localized, small scale turbulence and rate of injection variations as the likely sources. Then, a statistical method based on z-scores is proposed and implemented to identify instantaneous injections that best represent the bulk data-set of jet boundaries measured independently by three different diagnostics. This synthesis of statistics-guided screening of data set and ensemble-average analysis offers higher confidence for CFD model validation relying upon both a representative single and average injection results.

42 ENGINEERING↗

Understanding the Cascade: Removing GCM Biases Improves Dynamically Downscaled Climate Projections

Polarization surrounding bias correction (BC) in creating climate projections arises from its lack of physicality. Here, we perform and analyze 18 dynamical downscaling simulations (with and without BC) to better understand the physical impacts of BC, applied before downscaling, on regional climate output across the western United States. Without BC, downscaled precipitation is systematically and unrealistically wet biased compared to a hierarchy of observationally based datasets over the 1980–2014 period due to cascading mean–state Global Climate Model (GCM) biases: (a) overly strong lower–tropospheric lapse rates (5 K/km), (b) overly cold (2 K) tropospheric temperatures, and (c) anomalous mid–tropospheric cyclonic vorticity advection. With BC, downscaled precipitation (snow) biases are virtually eliminated (halved). Identified GCM biases are common to the broader Coupled Model Intercomparison Project ensemble. Physical effects of BC on the quality of the regionalized projections, pending an evaluation of BC's distortion of the downscaled climate response, may motivate its broader application by dynamical downscalers.

54 ENVIRONMENTAL SCIENCES↗

Engineering long-lived entanglement through dissipation in quantum hybrid solid-state platforms

Spin squeezing, a form of many-body entanglement, is a crucial resource in quantum metrology and information processing. While experimentally viable protocols for generating stable spin squeezing have been proposed in quantum optics setups, there is growing interest in quantum hybrid solid-state systems as alternative platforms for both engineering and exploring many-body quantum phenomena. In this work, we propose a scheme to generate long-lived spin squeezing in an ensemble of solid-state qubits interacting with electromagnetic noise emitted by a squeezed solid-state bath. We identify the conditions under which quantum correlations within the bath can be transferred to the qubit array, driving it into an entangled state independently of its initial configuration. To assess the experimental feasibility of our approach, we analyze the dynamics of an array of solid-state spin defects coupled to a common ferromagnetic bath, which is driven into a non-equilibrium squeezed state through its interaction with a surface acoustic wave mode. Our results demonstrate that the ensemble can exhibit steady-state spin squeezing under suitable conditions, opening new pathways for the generation of robust many-body entanglement in solid-state spin ensembles.

NV centers↗

Flowfield dynamics in blunt fin-induced shock wave/turbulent boundary layer interactions

Fluctuating wall pressure measurements were made on centerline upstream of a blunt fin in a Much 5 turbulent boundary layer. By examining the ensemble average wall pressure distributions for different fixed shock foot positions, it was shown that local fluctuating wall pressure measurements are due to a distinct pressure distribution, P(i), which undergoes a stretching and flattening effect as its upstream boundary translates aperiodically between the upstream influence and separation lines. The locations of the maxima and minima in the centerline wall standard deviation distribution can be accurately predicted using this distribution, providing quantitative confirmation of the model. This model also explains the observed cross-correlations and ensemble average measurements within the interaction. Using the P(i) model, wall pressure signals from under the separated flow region were able to reproduce the position-time history of the separation shock foot. The negative time delay peak in the cross-correlation between the predicted and actual shock foot histories shows that the separated region fluctuations precede shock foot motion.

Brusniak, L.↗