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NASA NTRS1988

Semi-Lagrangian integration of a grid-point shallow water model on the sphere

This paper describes a semi-Lagrangian technique for integrating the equations of motion on the global domain. The technique uses an auxiliary spherical coordinate system at each near-polar gridpoint of the latitude-longitude grid; the auxiliary system is obtained by a rotation such that the new equator passes through the gridpoint in question and the new coordinate directions coincide with those of the original system at that point. The technique was applied to the shallow water equations, incorporating a semiimplicit treatment of the adjustment terms on a C-grid, with two-time levels. A five day integration was successfully carried out for a situation involving strong cross-polar flow. No filtering or diffusion was required to maintain stability over a five day period.

Mcdonald, A.↗

NASA NTRS1999

Seasonal-to-Interannual Variability in Antarctic Sea-Ice Dynamics, and Its Impact on Surface Fluxes and Water Mass Production

Strong seasonal and interannual signals in Antarctic bottom-water outflow remain unexplained yet are highly correlated with anomalies in net sea-ice growth in coastal polynyas. The mechanisms responsible for driving salination and replenishment and rejuvenation of the dense shelf "source" waters likely also generate pulses of bottom water outflow. The objective of this research is to investigate time-scales of variability in the dynamics of sea-ice in the Southern Ocean in order to determine the primary sites for production of dense shelf waters. We are using a merged satellite/buoy sea-ice motion data set for the period 1978-present day to compute the dynamics of opening and closing of coastal polynyas over the continental shelf. The Ocean Circulation and Climate Advanced Model (OCCAM) ocean general circulation model with coupled sea-ice dynamics is presently forced using National Center for Environmental Prediction (NCEP) data to simulate fluxes and the salination impact of the ocean shelf regions. This work is relevant in the context of measuring the influence of polar sea-ice dynamics upon polar ocean characteristics, and thereby upon global thermohaline ocean circulation. Interannual variability in simulated net freezing rate in the Southern Weddell Sea is shown for the period 1986-1993. There is a pronounced maximum of ice production in 1988 and minimum in 1991 in response to anomalies in equatorward meridional wind velocity. This follows a similar approximate 8-year interannual cycle in Sea Surface Temperature (SST) and satellite-derived ice-edge anomalies reported elsewhere as the "Antarctic Circumpolar Wave." The amplitude of interannual fluctuations in annual net ice production are about 40% of the mean value, implying significant interannual variance in brine rejection and upper ocean heat loss. Southward anomalies in wind stress induce negative anomalies in open water production, which are observed in passive microwave satellite images. Thus, cycles of enhanced poleward wind stress reduce ice growth by compacting the ice along the coastline and closing open water in leads and polynyas. Model simulations confirm that years of low ice production, such as 1991, coincide with years of lower than normal bottom water outflow. Future plans include the assimilation of satellite ice concentrations and ice drift dynamics to more accurately constrain boundary conditions in the model.

Drinkwater, Mark R.↗

NASA NTRS2006

Exploring the Mineralogy of the Moon with M3

From the initial era or lunar exploration, we have learned that many processes active on the early Moon are common to most terrestrial planets, including the record of early and late impact bombardment. Since most major geologic activity ceased on the Moon approx. 3 Gy ago, the Moon's surface provides a record of the earliest era of terrestrial planet evolution. The type and composition of minerals that comprise a planetary surface are a direct result of the initial composition and subsequent thermal and physical processing. Lunar mineralogy seen today is thus a direct record of the early evolution of the lunar crust and subsequent geologic processes. Specifically, the distribution and concentration of specific minerals is closely tied to magma ocean products, lenses of intruded or remelted plutons, basaltic volcanism and fire-fountaining, and any process (e.g. cratering) that might redistribute or transform primary and secondary lunar crustal materials. The Moon Mineralogy Mapper (M3, or "m-cube") is a state-of-the-art imaging spectrometer that will fly on Chandrayaan-1, the Indian Space Research Organization (ISRO) mission to be launched late 2007 to early 2008. M3 is one of several foreign instruments chosen by ISRO to be flown on Chandrayaan-1 to complement the strong ISRO payload package. M3 was selected through a peer-review process as part of NASA s Discovery Program. It is under the oversight of PI Carle Pieters at Brown University and is being built by an experienced team at the Jet Propulsion Laboratory. Data analysis and calibration are carried out by a highly qualified and knowledgeable Science Team. To characterize diagnostic properties of lunar minerals, M3 acquires high spectral resolution reflectance data from 700 to 3000 nm (optional to 430 nm). M3 operates as a pushbroom spectrometer with a slit oriented orthogonal to the S/C orbital motion. Measurements are obtained simultaneously for 640 cross track spatial elements and 261 spectral elements. This translates to 70 m/pixel spatial resolution from a nominal 100 km polar orbit for Chandrayaan-1 . The primary science goal of M3 is to characterize and map lunar surface mineralogy in the context of its geologic evolution as outlined above. This translates into several sub-topics that focus on exploring the mineral character of the highland crust, characterizing the diversity basaltic volcanism, and identifying potential volatile concentrations near the poles. The primary exploration goal is to assess and map lunar mineral resources at high spatial resolution to support planning for future, targeted missions.

Pieters, C. M.↗

NASA NTRS2021

Organized kinetic energy backscatter in the hurricane boundary layer from radar measurements

The fluid mechanics of hurricanes strongly depends on boundary layer energetics due to the warm-core nature of the system with peak velocities located at lower levels. One barrier that has inhibited a more complete characterization of energy transfer in the boundary layer is a lack of observations that resolve large, turbulent eddies. In particular, the occurrence and structure of upscale energy transfer (backscatter) in the hurricane boundary layer as well as the effects of backscatter on the vortex intensity are unknown. The analysis presented here of very high-resolution, three-dimensional wind observations from Hurricane Rita (2005) at peak intensity reveals large regions of organized backscatter in the boundary layer associated with coherent, turbulent eddies. Strong forwardscatter is also found next to the backscatter regions due to the interaction between adjacent eddies. Two components of the stress tensor are primarily responsible for this alternating scatter structure, as shown by large correlation coefficients between the fields: the radial–vertical component (τ13) and the azimuthal–vertical component (τ23) with average correlations of 79% and 49 %, respectively. The Leonard, Reynolds and cross-term stress components are also provided. The impact of the sub-filter-scale energy transfer is estimated by computing the kinetic energy budget for the resolved-scale and eddy-scale motions. The results show that the sub-filter-scale energy transfer term is of the same order as the other terms in the eddy-scale budgets, contributing between 16% and 40% to the local time tendency with an average contribution of approximately 30 %. These results indicate that the coherent turbulent eddies can affect the vortex dynamics through wave–wave nonlinear interactions, which can subsequently influence the wave–mean flow interactions. This is the first study to examine the full sub-filter-scale

Sydney Sroka↗

DOE OSTI2021

The Stars Kepler Missed: Investigating the Kepler Target Selection Function Using Gaia DR2

The Kepler Mission revolutionized exoplanet science and stellar astrophysics by obtaining highly precise photometry of over 200,000 stars over 4 yr. A critical piece of information to exploit Kepler data is its selection function, since all targets had to be selected from a sample of half a million stars on the Kepler CCDs using limited information. Here we use Gaia DR2 to reconstruct the Kepler selection function and explore possible biases with respect to evolutionary state, stellar multiplicity, and kinematics. We find that the Kepler target selection is nearly complete for stars brighter than Kp < 14 mag and was effective at selecting main-sequence stars, with the fraction of observed stars decreasing from 95% to 60% between 14 < Kp < 16 mag. We find that the observed fraction for subgiant stars is only 10% lower, confirming that a significant number of subgiants selected for observation were believed to be main-sequence stars. Conversely we find a strong selection bias against low-luminosity red giant stars (R ≈ 3–5R {sub ⊙}, T {sub eff} ≈ 5500 K), dropping from 90% at Kp = 14 mag to below 30% at Kp = 16 mag, confirming that the target selection was efficient at distinguishing dwarfs from giants. We compare the Gaia Re-normalized Unit Weight Error (RUWE) values of the observed and nonobserved main-sequence stars and find a difference in elevated (>1.2) RUWE values at ∼σ significance, suggesting that the Kepler target selection shows some bias against either close or wide binaries. We furthermore use the Gaia proper motions to show that the Kepler selection function was unbiased with respect to kinematics.

47 OTHER INSTRUMENTATION↗

NASA NTRS1996

Monolithic Microwave Integrated Circuit (MMIC) Phased Array Demonstrated With ACTS

Monolithic Microwave Integrated Circuit (MMIC) arrays developed by the NASA Lewis Research Center and the Air Force Rome Laboratory were demonstrated in aeronautical terminals and in mobile or fixed Earth terminals linked with NASA's Advanced Communications Technology Satellite (ACTS). Four K/Ka-band experimental arrays were demonstrated between May 1994 and May 1995. Each array had GaAs MMIC devices at each radiating element for electronic beam steering and distributed power amplification. The 30-GHz transmit array used in uplinks to ACTS was developed by Lewis and Texas Instruments. The three 20-GHz receive arrays used in downlinks from ACTS were developed in cooperation with the Air Force Rome Laboratory, taking advantage of existing Air Force integrated-circuit, active-phased-array development contracts with the Boeing Company and Lockheed Martin Corporation. Four demonstrations, each related to an application of high interest to both commercial and Department of Defense organizations, were conducted. The location, type of link, and the data rate achieved for each of the applications is shown. In one demonstration-- an aeronautical terminal experiment called AERO-X--a duplex voice link between an aeronautical terminal on the Lewis Learjet and ACTS was achieved. Two others demonstrated duplex voice links (and in one case, interactive video links as well) between ACTS and an Army high-mobility, multipurpose wheeled vehicle (HMMWV, or "humvee"). In the fourth demonstration, the array was on a fixed mount and was electronically steered toward ACTS. Lewis served as project manager for all demonstrations and as overall system integrator. Lewis engineers developed the array system including a controller for open-loop tracking of ACTS during flight and HMMWV motion, as well as a laptop data display and recording system used in all demonstrations. The Jet Propulsion Laboratory supported the AERO-X program, providing elements of the ACTS Mobile Terminal. The successful performance of experimental, proof-of-concept MMIC K/Ka-band arrays developed with U.S. industry in field demonstrations with ACTS indicates that high density MMIC integration at 20 and 30 GHz is indeed feasible. The successful development and demonstration of the MMIC array systems was possible only because of significant intergovernmental and Government/industry cooperation and the high level of teamwork within Lewis. The results provide a strong incentive for continuing the focused development of MMIC-array technology for satellite communications applications, with emphasis on packaging and cost issues, and for continuing the planning and conducting of other appropriate demonstrations or experiments of phased-array technology with ACTS. Given the present pressures on reducing funding for research and development in Government and industry, the extent to which this can be continued in a cooperative manner will determine whether MMIC array technology will make the transition from the proof-of-concept level to the operational system level.

Source record↗

DOE OSTI2023

Theoretical framework for new magnetic materials for quantum computing and information storage. Final report for the Award No. DE-SC0018910

The focus of this grant was on molecular magnetic materials for information storage and quantum computing. We have been developing robust, first-principle methods for computing relevant electronic and magnetic properties of molecular building blocks (SMMs) of novel magnetic materials and quantum computers. These tools enable theoretical modeling of SMMs’ behavior, facilitating the interpretation of experimental studies and aiding the design of novel magnetic materials. Our strategy is based on the spin-flip (SF) approach, which extends the hierarchy of black-box single-reference methods to strongly correlated systems. Specifically, we developed general scalable algorithms and computer codes for calculating molecular properties, with an emphasis on spin-related properties, such as zero-field splittings, hyperfine couplings, and g-tensors. While our primary focus was on SF wave functions and SF-TDDFT, the underlying theory and computer codes were formulated using reduced density matrices, such that these tools are applicable to a broader class of methods. To extend the scope of applicability of wave-function-based SF methods to larger systems, we developed reduced-scaling approaches for the equation-of-motion coupled-cluster (EOM-CC) methods and continue developing libtensor (our open-source general tensor contraction library for many-body methods). We carried out extensive benchmarks and also carried out several applications.

36 MATERIALS SCIENCE↗

NASA NTRS1986

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

NASA NTRS1989

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

NASA NTRS1961

Experimental Study of Combined Forced and Free Laminar Convection in a Vertical Tube

An apparatus was built to verify an analysis of combined forced and free convection in a vertical tube with uniform wall heat flux and to determine the limits of the analysis. The test section was electrically heated by resistance heating of the tube wall and was instrumented with thermocouples in such a way that detailed thermal entrance heat-transfer coefficients could be obtained for both upflow and downflow and any asymmetry in wall temperature could be detected. The experiments showed that fully developed heat-transfer results, predicted by a previous analysis, were confirmed over the range of Rayleigh numbers investigated. The concept of "locally fully developed" heat transfer was established. This concept involves the assumption that the fully developed heat-transfer analysis can be applied locally even though the Rayleigh number is varying along the tube because of physical-property variations with temperature. Thermal entrance region data were obtained for pure forced convection and for combined forced and free convection. The analysis of laminar pure forced convection in the thermal entrance region conducted by Siegel, Sparrow, and Hallman was experimentally confirmed. A transition to an eddy motion, indicated by a fluctuation in wall temperature was found in many of the upflow runs. A stability correlation was found. The fully developed Nusselt numbers in downflow were below those for pure forced convection but fell about 10 percent above the analytical curve. Quite large circumferential variations in wall temperature were observed in downflow as compaired with those encountered in upflow, and the fully developed Nussalt numbers reported are based on average wall temperatures determined by averaging the readings of two diametrically opposite wall thermocouples at each axial position. With larger heating rates in downflow the wall temperature distributions strongly suggested a cell flow near the bottom. At still larger heating rates the wall temperatures varied in a periodic way.

Hallman, Theodore M.↗

NASA NTRS2003

The Deflection Plate Analyzer: A Technique for Space Plasma Measurements Under Highly Disturbed Conditions

A technique has been developed to measure the characteristics of space plasmas under highly disturbed conditions; e.g., non-Maxwellian plasmas with strong drifting populations and plasmas contaminated by spacecraft outgassing. The present method is an extension of the capabilities of the Differential Ion Flux Probe (DIFP) to include a mass measurement that does not include either high voltage or contamination sensitive devices such as channeltron electron multipliers or microchannel plates. This reduces the complexity and expense of instrument fabrication, testing, and integration of flight hardware as compared to classical mass analyzers. The new instrument design is called the Deflection Plate Analyzer (DPA) and can deconvolve multiple ion streams and analyze each stream for ion flux intensity (density), velocity (including direction of motion), mass, and temperature (or energy distribution). The basic functionality of the DPA is discussed. The performance characteristics of a flight instrument as built for an electrodynamic tether mission, the Propulsive Small Expendable Deployer System (ProSEDS), and the instrument s role in measuring key experimental conditions are also discussed.

Wright, Kenneth H., Jr.↗

NASA NTRS2004

The Deflection Plate Analyzer: A Technique for Space Plasma Measurements Under Highly Disturbed Conditions

Wright, Kenneth H., Jr.↗

NASA NTRS1993

Effects of discrete-source outgassing on motions of periodic comets and discontinuous orbital anomalies

Isoline maps of the Style II nongravitational parameters A1 and A2 of periodic comets are presented for a baseline model as functions of the parameters of the inertially fixed spin vector and the source's location-dependent thrust angle. The parameters A1 and A2 for a collection of sources are equal to the sum of their values for the individual contributors, thus depending on the source distribution. The model is consistent with even the most extreme among detected perturbations, including instances of rapid temporal changes in A2 and the discontinuous orbital anomalies, which are interpreted as products of a sudden redistribution of the transferred momentum due to episodic activation of short-lived sources. It is argued that the lifetimes of active regions vary considerably from case to case, and forced precession of the nucleus strongly influences the comet's activity pattern.

Sekanina, Zdenek↗

DOE OSTI2020

Lightwave terahertz quantum manipulation of nonequilibrium superconductor phases and their collective modes

In this work, we present a gauge-invariant density matrix description of nonequilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch-Maxwell equations of motion that extend Anderson pseudospin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasiparticle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relates to our recent experiments. Coherent photogeneration of a nonlinear supercurrent with a dc component, achieved via condensate acceleration by an effective lightwave field, dynamically breaks the equilibrium inversion symmetry. Experimental signatures include high harmonic light emission at equilibrium-symmetry-forbidden frequencies, Rabi-Higgs collective modes and quasiparticle coherence, and nonequilibrium moving condensate states tuned by few-cycle THz fields. We use such lightwaves as an oscillating accelerating force that drives strong nonlinearities and anisotropic quasiparticle populations to control and amplify different classes of collective modes, e.g., damped oscillations, persistent oscillations, and overdamped dynamics via Rabi flopping. Recent phase-coherent nonlinear spectroscopy experiments can be modeled by solving the full nonlinear quantum dynamics including self-consistent light-matter coupling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Collective dynamics and defect generation for Wigner crystal ratchets

Here we consider a two-dimensional Wigner crystal coupled to a quasi-one-dimensional asymmetric potential under ac or dc driving. As a function of electron density, substrate strength, and ac amplitude, we find that the system exhibits ordered and disordered pinned and dynamical states. Ratchet effects can appear under an applied ac drive and can be associated with pronounced structural changes from a disordered state to a one-dimensional smecticlike state. We observe a pinned phase, a diodelike ratchet where motion only occurs along the easy direction of the substrate asymmetry, a plastic ratchet where motion occurs in both directions but there is only a net drift in the easy direction, and an elastic ratchet where the system forms a crystal without plastic deformation that can still undergo ratcheting. At high filling, we find that there can be a ratchet reversal in which the net drift is along the hard direction of the substrate asymmetry. For weak disorder, there is an Aubry transition to a floating phase where the ratchet effects are lost. We map out the different dynamical phases as a function of substrate strength, filling, ac amplitude, and ac frequency. The ratchet effect on strong substrates is enhanced by thermal fluctuations, but is destroyed when the fluctuations become too large. Based on our results, we suggest other ways to detect Wigner crystals as well as methods for creating different types of devices to control disordered charge flow.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1982

Phase resolved optical spectroscopy of the compact X-ray binary 2A1822-371

The optical, X-ray, and ultraviolet emissions of the X-ray system 2A1822-371 are modulated with a period of 5.57 hr. The 5.57 hr modulation is believed to reflect orbital motion about a mass donating companion star. The modulation at high energies is caused by the combined effects of an occultation by the companion and by a bulge on the accretion disk. The present investigation is concerned with an extension of the study of 2A1822-371, taking into account medium resolution optical spectroscopy of the system covering the 5.57 hr cycle. Broad shallow absorption lines are observed in the optical spectrum of 2A1822-371. These lines are similar to the rotationally broadened lines which are found in the spectra of disk accreting cataclysmic variables. Their presence in 2A1822-371 is, therefore, strong confirmation that it is a disk accreting star. The He II 4686 A and H-alpha emission lines have a breadth comparable to the absorption lines at all phases in the 5.57 hr cycle.

Mason, K. O.↗

NASA NTRS1994

Shock propagation and the generation of magnetohydrodynamic wave fields in inhomogeneous molecular clouds

We develop a simple one-dimensional model for the interaction of a steady, thin, planar shock wave with a nonrigid cloud which may be in motion relative to the surrounding medium, and we apply the model to shocks impinging on, and propagating through, molecular clouds. Both 'adiabatic' (gamma = 5/3) and radiative (gamma = 1) shocks are considered and we allow for the presence of a uniform magnetic field directed either parallel or perpendicular to the shock normal. The former field orientation is equivalent to the hydrodynamic case, and the latter involves only fast MHD shocks. We focus on the manner in which such shocks can generate internal kinetic motions in the cloud on a range of size and density scales through the direct acceleration of cores and clumps by shocks transmitted into them and through the generation of an MHD wavefield via the reflection of the incident shock at clump boundaries. We find that stronger incident Mach numbers and smaller density contrasts lead to more efficient cloud acceleration, as do isothermal intercloud shocks and small intercloud magnetic field strengths. The acceleration efficiency is insensitive to the adiabatic index and the magnetic field strength in the cloud itself. For typical parameter choices, the direct acceleration of clouds and clumps by strong shocks is found to be substantial and could at least in part account for their observed velocity dispersions. If the shocks are moderately weak, the final velocity of the cloud is linearly related to its initial velocity, with higher acceleration giving shallower slopes (i.e., final velocity distributions which are less sensitive to the initial distribution). Compared to the kinetic energy of the postshock cloud, the energy given to the wavefield at each encounter is small, and the heating of the interclump medium by the dissipation of this wavefield is found to be insufficient to balance the cooling rate in the cloud as a whole (although it may be important in particular regions), even if this medium is warm, unless it is also extremely tenuous (n approximately less than 0.1/cu cm). Nevertheless, the correction for the velocity imparted to the cloud leads to a substantial increase in the critical incident Mach numner for wave emission over that reported by Spitzer for the rigid case. The implications of our model for shock-induced star formation are discussed briefly.

Miesch, Mark S.↗

NASA NTRS1997

The Spectral and Statistical Properties of Turbulence Generated by a Vortex/Blade-Tip Interaction

The perpendicular interaction of a streamwise vortex with the tip of a lifting blade was studied in incompressible flow to provide information useful to the accurate prediction of helicopter rotor noise and the understanding of vortex dominated turbulent flows. The vortex passed 0.3 chord lengths to the suction side of the blade tip, providing a weak interaction. Single and two-point turbulence measurements were made using sub-miniature four sensor hot-wire probes 15 chord lengths downstream of the blade trailing edge; revealing the mean velocity and Reynolds stress tensor distributions of the turbulence, as well as its spanwise length scales as a function of frequency. The single point measurements show the flow downstream of the blade to be dominated by the interaction of the original tip vortex and the vortex shed by the blade. These vortices rotate about each other under their mutual induction, winding up the turbulent wakes of the blades. This interaction between the vortices appears to be the source of new turbulence in their cores and in the region between them. This turbulence appears to be responsible for some decay in the core of the original vortex, not seen when the blade is removed. The region between the vortices is not only a region of comparatively large stresses, but also one of intense turbulence production. Velocity autospectra measured near its center suggests the presence quasi-periodic large eddies with axes roughly parallel to a line joining the vortex cores. Detailed two-point measurements were made on a series of spanwise cuts through the flow so as to reveal the turbulence scales as they would be seen along the span of an intersecting airfoil. The measurements were made over a range of probe separations that enabled them to be analyzed not only in terms of coherence and phase spectra but also in terms of wave-number frequency (kappa-omega) spectra, computed by transforming the measured cross-spectra with respect to the spanwise separation of the probes. These data clearly show the influence of the coherent eddies in the spiral wake and the turbulent region between the cores. These eddies produce distinct peaks in the upwash velocity kappa-omega spectra, and strong anisotropy manifested both in the decay of the kappa-omega spectrum at larger wave-numbers and in differences between the kappa-omega spectra of different components. None of these features are represented in the von Karman spectrum for isotropic turbulence that is often used in broadband noise computations. Wave-number frequency spectra measured in the cores appear to show some evidence that the turbulence outside sets tip core waves, as has previously been hypothesized. These spectra also provide for the first time a truly objective method for distinguishing velocity fluctuations produced by core wandering from other motions.

Devenport, William J.↗