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At least 199 records · Page 11

Precision X-ray Timing of RX J0806.3+1527 with CHANDRA: Evidence for Gravitational Radiation from an Ultracompact Binary

RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an $\approx 100 \%$ X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of $\dot\nu \sim 10(exp -16)$ Hi s$(exp -l}$. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with {\it Chandra) . We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of $3.77 \pm\ 0.8 \times l0(exp -16)$ Hz s$(exp -l)$. Using the ephemeris derived from the new data we are able to phase up all the earlier {\it Chandra) and ROSAT data and show they are consistent with a constant $\dot\nu = 3.63 \pm 0.06 \times 10(exp -16)$ Hz s$(exp -1)s over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable $\dot\nu$ over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed $\dot\nu$ requires an $\dot m \approx 2 \times 10(exp -8)$ $M-{\odot)$ yr$(exp -l)$, that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high $\dot m$ in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is

Strohmayer, Tod↗

Spitzer 24 Micron Observations of Optical/Near-Infrared-Selected Extremely Red Galaxies: Evidence for Assembly of Massive Galaxies at Z approximately equal to 1-2?

We carried out direct measurement of the fraction of dusty sources in a sample of extremely red galaxies with (R - Ks) >= 5.3 mag and Ks < 20:2 mag, using 24 micron data from the Spitzer Space Telescope. Combining deep 24 micron Ks- and R-band data over an area of ~64 arcmin(sup 2) in ELAIS N1 of the Spitzer First Look Survey (FLS), we find that 50% +/- 6% of our extremely red object (ERO) sample have measurable 24 micron flux above the 3 (sigma) flux limit of 40 (micro)Jy. This flux limit corresponds to a star formation rate (SFR) of 12 solar masses per year ~1, much more sensitive than any previous long-wavelength measurement. The 24 micron-detected EROs have 24 micron/2.2 micron and 24 micron/0.7 micron flux ratios consistent with infrared luminous, dusty sources at z >= 1, and are an order of magnitude too red to be explained by an infrared quiescent spiral or a pure old stellar population at any redshift. Some of these 24 micron-detected EROs could be active galactic nuclei; however, the fraction among the whole ERO sample is probably small, 10%-20%, as suggested by deep X-ray observations as well as optical spectroscopy. Keck optical spectroscopy of a sample of similarly selected EROs in the FLS field suggests that most of the EROs in ELAIS N1 are probably at z ~1. The mean 24 micron flux (167 (micro)Jy) of the 24 micron-detected ERO sample roughly corresponds to the rest-frame 12 micron luminosity, (nu)L(nu)(12 micron, of 3x10(exp 10)(deg) solar luminosities at z ~1. Using the c IRAS (nu)L(nu)(12 (micron) and infrared luminosity LIR(8-1000 (micron), we infer that the (LIR) of the 24 micron- detected EROs is 3 x 10(exp 11) and 1 x 10(exp 12) solar luminosities at z = 1.0 and similar to that of local luminous infrared galaxies (LIRGs) and ultraluminous infrared galaxies (ULIRGs). The corresponding SFR would be roughly 50-170 solar masses per year. If the timescale of this starbursting phase is on the order of 108 yr as inferred for the local LIRGs and ULIRGs, the lower limit on the masses of these 24 micron-detected EROs is 5 x 10(exp 9) to 2 x 10(exp 10) solar masses. It is plausible that some of the starburst EROs are in the midst of a violent transformation to become massive early type galaxies at the epoch of z ~1-2.

high redshift↗

MCM Polarimetric Radiometers for Planar Arrays

A polarimetric radiometer that operates at a frequency of 40 GHz has been designed and built as a prototype of multiple identical units that could be arranged in a planar array for scientific measurements. Such an array is planned for use in studying the cosmic microwave background (CMB). All of the subsystems and components of this polarimetric radiometer are integrated into a single multi-chip module (MCM) of substantially planar geometry. In comparison with traditional designs of polarimetric radiometers, the MCM design is expected to greatly reduce the cost per unit in an array of many such units. The design of the unit is dictated partly by a requirement, in the planned CMB application, to measure the Stokes parameters I, Q, and U of the CMB radiation with high sensitivity. (A complete definition of the Stokes parameters would exceed the scope of this article. In necessarily oversimplified terms, I is a measure of total intensity of radiation, while Q and U are measures of the relationships between the horizontally and vertically polarized components of radiation.) Because the sensitivity of a single polarimeter cannot be increased significantly, the only way to satisfy the high-sensitivity requirement is to make a large array of polarimeters that operate in parallel. The MCM includes contact pins that can be plugged into receptacles on a standard printed-circuit board (PCB). All of the required microwave functionality is implemented within the MCM; any required supporting non-microwave ("back-end") electronic functionality, including the provision of DC bias and control signals, can be implemented by standard PCB techniques. On the way from a microwave antenna to the MCM, the incoming microwave signal passes through an orthomode transducer (OMT), which splits the radiation into an h + i(nu) beam and an h - i(nu) beam (where, using complex-number notation, h denotes the horizontal component, nu denotes the vertical component, and +/-i denotes a +/-90deg phase shift). Each of these beams enters the MCM through one of two WR-22 waveguide input terminals in the lid of the MCM. The h + i(nu0 and h - i(nu) signals are amplified, then fed to a phase-discriminator hybrid designed specifically to fit the predominantly planar character of the MCM geometry and to enable determination of Q and U. The phase-discriminator hybrid generates four outputs, which are detected and used to calculate I, Q, and U.

Kangaslahti, Pekka↗

Performance Evaluation of an Actuator Dust Seal for Lunar Operation

Exploration of extraterrestrial surfaces (e.g. moon, Mars, asteroid) will require durable space mechanisms that will survive potentially dusty surface conditions in addition to the hard vacuum and extreme temperatures of space. Baseline tests with lunar simulant were recently completed at NASA GRC on a new Low-Temperature Mechanism (LTM) dust seal for space actuator application. Following are top-level findings of the tests completed to date in vacuum using NU-LHT-2M lunar-highlands simulant. A complete set of findings are found in the conclusions section.Tests were run at approximately 10-7 torr with unidirectional rotational speed of 39 RPM.Initial break-in runs were performed at atmospheric conditions with no simulant. During the break-in runs, the maximum torque observed was 16.7 lbf-in. while the maximum seal outer diameter temperature was 103F. Only 0.4 milligrams of NU-LHT-2M simulant passed through the sealshaft interface in the first 511,000 cycles while under vacuum despite a chip on the secondary sealing surface.Approximately 650,000 of a planned 1,000,000 cycles were completed in vacuum with NU-LHT-2M simulant.Upon test disassembly NU-LHT-2M was found on the secondary sealing surface.

lunar↗

Object-Based Comparison of Data-Driven and Physics-Driven Satellite Estimates of Extreme Rainfall

The Global Precipitation Measurement (GPM) constellation of spaceborne sensors provides a variety of direct and indirect measurements of precipitation processes. Such observations can be employed to derive spatially and temporally consistent gridded precipitation estimates either via data-driven retrieval algorithms or by assimilation into physically based numerical weather models. We compare the data-driven Integrated Multisatellite Retrievals for GPM (IMERG) and the assimilation-enabled NASA-Unified Weather Research and Forecasting (NU-WRF) model against Stage IV reference precipitation for four major extreme rainfall events in the southeastern United States using an object-based analysis framework that decomposes gridded precipitation fields into storm objects. As an alternative to conventional ‘‘grid-by-grid analysis,’’ the object-based approach provides a promising way to diagnose spatial properties of storms, trace them through space and time, and connect their accuracy to storm types and input data sources. The evolution of two tropical cyclones are generally captured by IMERG and NU-WRF, while the less organized spatial patterns of two mesoscale convective systems pose challenges for both. NU-WRF rain rates are generally more accurate, while IMERG better captures storm location and shape. Both show higher skill in detecting large, intense storms compared to smaller, weaker storms. IMERG’s accuracy depends on the input microwave and infrared data sources; NU-WRF does not appear to exhibit this dependence. Findings highlight that an object-oriented view can provide deeper insights into satellite precipitation performance and that the satellite precipitation community should further explore the potential for ‘‘hybrid’’ data-driven and physics-driven estimates in order to make optimal usage of satellite observations.

extreme events↗

Qualitative Headspace GCMS Analysis of Lunar Regolith and Volatile Simulant Mixtures

Introduction: Future Artemis missions aim to return the volatile-bearing samples collected near lunar polar craters. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving the integrity of returned samples and the science value those samples contain. The extent to which that preservation is possible, and the trade-offs preservation requires (e.g. monetary costs, sample volume limitations) all must be considered. Even less-than pristine volatile-bearing samples will be of tremendous value to the scientific community seeking to unravel the history of lunar surface volatiles and, more broadly, volatiles in the solar system. A sample collected on the lunar surface will experience at least five distinctive periods during which any changes here referred to as “alteration” will certainly occur at some scale: collection on the lunar surface; transportation back to Earth; long-term storage; curatorial processing; and allocation/distribution. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on returned volatile samples by working with high-fidelity volatile-containing regolith simulants, setting the foundation for the future of cold curation. This abstract is focused on gas-surface interactions between LCROSS volatiles and readily available lunar regolith simulants. Experiments involved analyzing differences in headspace gas composition for various combinations of volatile and regolith simulants using gas chromatography/mass spectrometry (GC/MS). Experimental Procedure: The volatile simulants were chosen based on the molecules detected during the LCROSS mission.1 Stock solutions of condensed lunar volatile analytes were: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. The regolith simulants used were primarily JSC-1A and NU-LHT-4M. Additional regolith simulant control studies were conducted with <150 μm sieved sand and KBr. A nested vial sample preparation approach separated the liquid stock solutions from the regolith, eliminating potential matrix effects between liquid and solid phases. Fifteen microliter aliquots of liquid volatile simulants were added to a 2 mL liquid GC vial and capped in atmosphere. An 18G needle punctured the 2 mL GC vial immediately before being transferred and sealed in a 20 mL GC vial containing 0-0.3 g of regolith simulant, see Figure 1. Separating the analytes ensures any changes observed in the total headspace gases is a result of gas-surface and/or gas-gas interactions. Equipment and Method: Initial GC/MS method development for the separation and identification of relevant headspace gases can be found in Amick, et al. 2023.2 The only hardware change is a different column: a TG-1701MS 30 m × 0.25 mm × 1.00 μm column. The vials were sampled at 10°C, room temperature (~25°C) and 50°C. Low temperature samples were kept in a chilled autosampler stage for at least 1 hour prior to sampling. High temperature samples were agitated at 50°C for 5 minutes immediately prior to injection onto the column. Headspace chromatograms were collected for each combination of temperature, regolith, and volatile simulant, including controls without one or both types of analytes, in triplicate. The chromatogram elution window for each analyte or significant atmospheric gas was identified using the peak mass spectrum cross-referenced with Figure 1.Picture of the nested vial set-up. a NIST MS library search. Each analyte peak was integrated after filtering the mass spectrum trace for the parent or most unique mass-to-charge ratio. For example, the mass-to-charge ratio used to identify, filter for, and integrate the carbon dioxide peak was centered around 44 m/z. Results: Figure 2 shows the integrated peak area for hydrogen sulfide in all combinations of regolith simulants, temperatures, and the addition of ammonia in methanol solution. Multiple repeat experiments with H2S and regolith simulants have confirmed hydrogen sulfide is removed from the headspace within 1 hour when exposed to JSC-1A, NU-LHT-4M and sand (not pictured). The consumption of H2S by lunar regolith simulants at different temperatures indicates surface chemistry will be an integral component in sample integrity and preservation. It is important to note that while the effect of surface chemistry on gaseous hydrogen sulfide is intriguing, further investigation into more chemically accurate regolith simulants is necessary and ongoing. The sulfur in hydrogen sulfide is in its most reduced state while off-the-shelf, terrestrially sourced JSC-1A and NU-LHT-4M are more oxidized than most lunar materials,3which likely leads to different oxidation-reduction reactions than would be expected in lunar regolith. Figure 3 shows the integrated peak area of carbon dioxide for each sample combination that contained ammonia in methanol solution. The addition of ammonia to the GC vials results in a consistent and reproducible decrease in carbon dioxide gas, even at 50°C. The effect became more pronounced when JSC-1A or NU-LHT-4M were present. This set of experiments demonstrated that the sample composition will affect the chemical and physical state of each component present. Future spectroscopic and microscopy experiments will be geared towards identifying the cause for the CO2(g) concentration decrease and the consumption of hydrogen sulfide. As cold and volatile curation scientists, this information provides necessary insight on how to appropriately handle and analyze volatile bearing returned samples, as well as predict the effect chemical composition has on the various sample phases we will analyze upon return to Earth. Unlike traditional curation of geologic materials, the molecules in a sample cannot be identified or processed using the naked eye or even an optical microscope. Volatile curation will require a combination of analytical techniques, including but not limited to highly sensitive gas and solid/condensed phase spectroscopy. This set of experiments has demonstrated the need for more detailed studies of volatile mixtures with mineralogically and geochemically analogous lunar regolith simulants to prepare for the curation of volatile-rich lunar samples from the south polar region of the Moon. References: [1] Colaprete, A., et al. (2010) Science, 330, (463-468). [2] Amick, C. L., et al.(2023) Houston, Texas, [3] Heiken, G. H., et al.(1991) (778-778)

Cecilia L Amick↗

Fundamental bands of S(32)O2(16)

The infrared-active vibration-rotation fundamentals of sulfur dioxide were measured with moderately high spectral resolution. Quantum number assignments were made for spectral lines from J = O to 57, by comparison with theoretically computed spectra which include the effects of centrifugal distortion. The following values for the band centers were determined: nu sub 1 = 1151.65 + or - 0.10/cm, nu sub 2 = 517.75 + or - 0.10/cm, and nu sub 3 = 1362.00 + or - 0.10/cm. Intensities of the observed lines have also been computed. Dipole moment derivatives were obtained.

Fox, K.↗

Ethane and acetylene abundances in the Jovian atmosphere

The paper reports spectra of Jupiter in the spectral region from 755 to 850 kaysers, which covers the nu-9 fundamental of ethane and contains lines from the R branch of the nu-5 fundamental of acetylene. The monochromatic absorption coefficient of the central Q branch of the nu-9 fundamental of ethane, which was determined in the laboratory, is applied in a radiative-transfer calculation to evaluate the ethane mixing ratio in the Jovian atmosphere; the present data are also used to place an upper limit on the acetylene mixing ratio. For the radiative-transfer calculation, emission intensity is computed for the region above the 0.02-atm level assuming both an isothermal inversion layer and a previously reported temperature profile. The resulting maximum mixing ratios consistent with the observations are 0.00003 for ethane and 7.5 by 10 to the -8th power for acetylene.

Tokunaga, A.↗

Semiclassical study of reactive scattering in a laser field - F + H2 + barred-h times omega times /1.06 microns/ system

Semiclassical calculations of collinear F+H2(nu = 0) reactive and inelastic scattering in an Nd-glass laser field of various intensities are described. The decoupling approximation developed for the Miller-George theory is used for nonadiabatic transitions between the electronic-field surfaces, and special attention is paid to the choice of a proper coordinate system for applying the decoupling approximation. An increase in the total reaction probability and population ratio of the nu = 3 over nu = 2 vibrational state of HF occurs suddenly as the field intensity increases beyond 10 TW/sq cm. It is found that in a laser field the H2 molecule can be vibrationally excited while the F atom is electronically excited.

Yuan, J.-M.↗

Identification of HgO/x/ species by matrix isolation spectroscopy

The condensation of Hg atoms in an ozone-doped argon matrix gas with irradiation from a medium-pressure mercury arc lamp at 10 K resulted in the formation of several trapped HgO(x) species. Tentative identification of HgO has been made from absorption bands appearing in the visible and IR regions of the spectrum based on (O-16)2 and (O-18)2 isotope studies. The following spectroscopic constants were obtained: nu(00) = 14634 cm, nu(1) = 548 cm, and nu(11) = 676 cm. Some qualitative evidence was obtained for the existence of HgO2.

Butler, R.↗

A High Resolution Spectroscopic Study of the Nu2 Band of Hydrogen Sulfide and the 1-0 Band of Hydrogen Iodide

A tunable diode laser spectrometer was constructed and used to study: (1) the effects of centrifugal distortion on the transition frequencies and strengths of the nu sub 2 band of H2S, and (2) nuclear quadrupole hyperfine structure in the 1-0 band of HI. A total of 126 line frequencies and 94 line strengths in the nu sub 2 band of H2S were measured. The average accuracy of the line frequency measurements was + or - 0.0016 cm. The line strengths were measured to an average accuracy of about 3 percent. The effect of the finite spectral width of the diode laser on the measurement of line strengths is discussed. The observed H2S line frequencies were fit to Watson's AS and NS reduced Hamiltonian in both the Ir and IIIr coordinate representations in order to determine the best set of rotation distortion constants for the upper state of the nu sub 2 band. Comparisons of the observed line strengths in this band to rigid rotor line strengths are also presented. Nuclear quadrupole hyperfine structure in the low J lines of the 1-0 band of HI was observed. The upper vibrational state nuclear quadrupole coupling constant, determined from the observed splittings, was -1850 MHz + or - 12 MHz or 1.2 percent + or - 0.7 percent larger than the ground state coupling constant.

Strow, L. L.↗

A measurement of the vibrational band strength for the upsilon sub 3 band of the HO2 radical

The HO2 radicals generated in a discharge-flow system were observed with tunable diode laser absorption in the P-branch of the nu(3) vibrationall band at 1080/cm. The observed line positions agree with those calculated from the molecular constants for the nu(3) bland obtained from a previous study using laser magnetic resonance spectroscopy. The band strength was determined by observing line center absoptions when HO2 is produced in the reaction F + H2O2 yields HO2 + HF (k1) with a measured concentration of atomic fluorine and excess hydrogen peroxide. F-atom concentrations are measured by diode laser absorption of the spin-orbit transition at 404/cm. The analysis accounts for HO2 losses due to the reactions of HO2 + HO2 yields H2O2 + O2 (k3) and F + HO2 yields HF + O2 (k4). The line strength for the 6(15) 7(16) F(1) transition is 2.9 x 10 to the 21st power sq cm/molecule/cm which corresponds to a nu(3) band strength of 34 +/- 9 sq/cm(STP atm). This value is a factor of 6 lower than previous ab initio calculations. These results will be useful in assessing the feasibility of atmospheric measurements of HO2 using infrared absorption techniques.

Zahniser, M. S.↗

Neutrino production from the solar atmosphere

When the high energy primary cosmic rays enter near the solar surface, they pass through a thick matter but having a low density. If the density and path length satisfy an appropriate condition, the primaries collide with the constituents near the solar sphere (almost protons) and produce pions and kaons, most of which decay into mu plus nu sub mu without successive hadron collisions. Muons also decay into NU sub mu and NU sub e before reaching the Earth. The neutrino flux of which the producer is matter near the solar surface is computed by solving cascade diffusion equations. The calculated differential flux of muon neutrino at 1 TeV is 1 X 10 to the minus 13 power (GeV. cm square centimeters 2.s.ster)(-1) which is rather difficult to be observed in the present apparatuses or DUMAND.

Inazawa, H.↗

Hydrogen cyanide in comets - Excitation conditions and radio observations of comet IRAS-Araki-Alcock 1983d

The HCN emission of the pure rotation and rotation/vibration lines in comet IRAS-Araki-Alcock 1983d is examined. The prevailing excitation mechanism for the emissions was the excitation of the nu-2, 2 nu-2, and nu-3 vibrational bands by the solar infrared field. For the description of inner coma, a dynamical excitation model is presented which includes collisions. It is predicted on the basis of the model that HCN molecules in rotation and rotation vibration lines of IRAS-Araki-Alcock 1983d would be detectable with a large-millimeter wave telescope, and that the strongest infrared lines would be observable from space observatories. Subsequent searches for the J = 1-0 HCN radio lines in comet 1983d with the Five College Radio Astronomy Observatory (FCRAO) proved unsuccessful. An extremely low upper limit was found for HCN production which suggests that HCN might not be the only parent of planetary cometary CN.

Bockelee-Morvan, D.↗

Infrared emission from desorbed NO2(*) and NO(*)

Infrared photons from the radiative cascade accompany both the gas phase NO2 continuum chemiluminescence (which originates from its 2B2 and 2B1 states) and the NO beta bands. When these upper electronic states are excited by recombination/desorption at surfaces of low Earth orbiting spacecraft, similar IR emission spectrums will be observed. The principal NO2 features (other than the long wavelength tail of its electronic transitions) are the nu sub 3 fundamental sequence near 6.2 microns and nu sub 1 + nu sub 3 intercombination bands near 3.6 microns; NO would emit the delta v=1 and delta v=2 systems above 5.3 and 2.7 microns. Because of the long radiative lifetimes of the upper vibrational states, the infrared radiances in projections parallel to the vehicle surface (which we estimate) are substantially less than those of the visible and ultraviolet glows.

Kofsky, I. L.↗

Analytic theory of the selection mechanism in the Saffman-Taylor problem

An analytic approach to the problem of predicting the widths of fingers in a Hele-Shaw cell is presented. The analysis is based on the WKB technique developed recently for dealing with the effects of surface tension in the problem of dendritic solidification. It is found that the relation between the dimensionless width lambda and the dimensionless group of parameters containing the surface tension, nu, has the form lambda - 1/2 = nu exp 2/3 in the limit of small nu.

Hong, D. C.↗

Spectral evolution of young stellar objects

An evolutionary sequence, from protostars to pre-main-sequence stars, is suggested for the classification of young stellar objects. This sequence is derived by comparing the predictions of the theoretical models of Adams and Shu with the morphological classification scheme of Lada and Wilking. We first define the spectral index in the near- and mid-infrared, n is identical to d log(nu F sub nu)/d log nu, and then interpret the class of sources with negative spectral indices as protostars. The inferred mass infall rates for these objects are generally consistent with the measured gas temperatures of approx. 35 K in Ophiuchus, and of approx. 10 K in Taurus. Fitting the data requires us to adopt cloud rotation rates in Ophiuchus which are typically an order of magnitude greater than in Taurus, and we speculate on the mechanistic origin for this difference. Next, we consider a subclass of T Tauri stars with near- and mid-infrared excesses and positive or zero spectral indices. We find that the objects with the steeper indices can be understood as the post-infall products from the collapse of rotating cloud cores, where the infrared excesses arise from the simple reprocessing of visible stellar photons in optically thick but spatially thin disks. The sources with flatter spectra may require massive accretion disks. Given the existence of protostars and naked star/disk systems, there is a natural interpretation of another subclass of T Tauri stars, those with two peaks in their emergent spectral energy distributions. These are readily explained as intermediate cases in which dust envelopes still surround the stars and disks. Finally, we find that the theory can be extended to explain the spectral energy distribution of FU Orionis, a famous outburst source. Our model suggests that FU Orionis has a disk, but it offers no discrimination between the competing ideas that the outburst took place on the star or in the disk.

Adams, F. C.↗

An experimental study using flow visualization on the effect of an acoustic field on heat transfer from spheres

The physical mechanisms responsible for the heat transfer process in a thermal-acoustic field were investigated using the technique of holographic interferometry for flow visualization. Experimental results were obtained with sound pressure levels in the range of 120 to 150 decibels, relative to a pressure of 0.0002 dynes/sq cm. Steady state laminar flow was observed when the vibrational Reynolds number was below 400; separated flow was observed when it was above 400. In the presence of a horizontal sound field, the data indicate that the relation between the vibrational Nusselt number, Nu(v) and the vibrational Reynolds number, Re(v) is given by Nu(v) = Re(v) exp 0.22. In the presence of a vertical sound field, the corresponding relation is Nu(v) = Re(v) exp 0.15.

Leung, W. W.↗