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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Is coverage a factor in non-Gaussianity of IMF parameters?

Recently, Feynman and Ruzmaikin (1994) showed that IMF parameters for the 1973 to 1990 period are not log-normally distributed as previously suggested by Burlaga and King (1979) for the data obtained over a shorter time period (1963-75). They studied the first four moments, namely: mean, variance, skewness, and kurtosis. For a Gaussian distribution, moments higher than the variance should vanish. In particular, Feynman and Ruzmaikin obtained very high values of kurtosis during some periods of their analysis. We note that the coverage for IMF parameters is very uneven for the period analyzed by them, ranging from less than 40% to greater than 80%. So a question arises as to whether the amount of coverage is a factor in their analysis. We decided to test this for the B(sub z) component of IMF, since it is an effective geoactive parameter for short term disturbances. Like them, we used 1-hour averaged data available on the Omnitape. We studied the scatter plots of the annual mean values of B(sub z)(nT) and its kurtosis versus the percent coverage for the year. We obtain a correlation coefficient of 0.48 and 0.42 respectively for the 1973-90 period. The probability for a chance occurrence of these correlation coefficients for 18 pair of points is less than 8%. As a rough measure of skewness, we determined the percent asymmetry between the areas of the histograms representing the distributions of the positive and the negative values of B(sub z) and studied its correlation with the coverage for the year. This analysis yields a correlation coefficient of 0.41 When we extended the analysis for the whole period for which IMF data are available (1963-93) the corresponding correlation coefficients are 0.59, 0.14, and 0.42. Our findings will be presented and discussed

Ahluwalia, H. S.↗
NASA NTRS1996

Wake Geometry Measurements and Analytical Calculations on a Small-Scale Rotor Model

An experimental investigation was conducted in the Langley 14- by 22-Foot Subsonic Tunnel to quantify the rotor wake behind a scale model helicopter rotor in forward level flight at one thrust level. The rotor system in this test consisted of a four-bladed fully articulated hub with blades of rectangular planform and an NACA 0012 airfoil section. A laser light sheet, seeded with propylene glycol smoke, was used to visualize the vortex geometry in the flow in planes parallel and perpendicular to the free-stream flow. Quantitative measurements of wake geometric proper- ties, such as vortex location, vertical skew angle, and vortex particle void radius, were obtained as well as convective velocities for blade tip vortices. Comparisons were made between experimental data and four computational method predictions of experimental tip vortex locations, vortex vertical skew angles, and wake geometries. The results of these comparisons highlight difficulties of accurate wake geometry predictions.

Ghee, Terence A.↗
NASA NTRS1959

Effect of Contraction on Turbulence and Temperature Fluctuations Generated by a Warm Grid

Hot-wire anemometer measurements were made of several statistical properties of approximately homogeneous and isotropic fields of turbulence and temperature fluctuations generated by a warm grid in a uniform airstream sent through a 4-to-1 contraction. These measurements were made both in the contraction and in the axisymmetric domain farther downstream. In addition to confirming the well-known turbulence anisotropy induced by strain, the data show effects on the skewnesses of both longitudinal velocity fluctuation (which has zero skewness in isotropic turbulence) and its derivative. The concomitant anisotropy in the temperature field accelerates the decay of temperature fluctuations.

Mills, Robert R., Jr.↗
NASA NTRS1998

RH1020 Single Event Clock Upset Summary Report

This report summarizes the testing and analysis of "single event clock upset' in the RH1020. Also included are SEU-rate predictions and design recommendations for risk analysis and reduction. The subject of "upsets" in the RH1020 is best understood by using a model consisting of a global clock buffer and a D-type flip-flop as the basic memory unit. The RH1020 is built on the ACT 1 family architecture. As such, it has one low-skew global clock buffer with a TTL-level input threshold that is accessed via a single dedicated pin. The clock signal is driven to full CMOS levels, buffered, and sent to individual row buffers with one buffer per channel. For low-skew performance, the outputs of all of the RH1020 row buffers are shorted together via metal lines, as is done in the A1020B. All storage in the RH1020 consists of routed flip-flops, constructed with multiplexors and feedback through the routing segments. A simple latch can be constructed from a single (combinatorial or C) module; an edge-triggered flip-flop is constructed using two concatenated latches. There is no storage in the I/O modules. The front end of the clock buffering circuitry, at a common point relative to the row buffer, is a sub-circuit that was determined to be the most susceptible to heavy ions. This is due, in part, to its smaller transistors compared to the rest of the circuitry. This conclusion is also supported by SPICE simulations and an analysis of the heavy ion data, described in this report. The edge triggered D flip-flop has two single-event-upset modes. Mode one, called C-module upset, is caused by a heavy ion striking the C-module's sensitive area on the silicon and produces a soft single bit error at the output of the flip-flop. Mode two, called clock upset, is caused by a heavy ion strike on the clock buffer, generating a runt pulse interpreted as a false clock signal and consequently producing errors at the flip-flop outputs. C-module upset sensitivity in the RH1020 is essentially the same as that of its ACT 1 siblings (A1020, A1020A and A1020B), which were well tested, analyzed, and documented in the literature.

Katz, Richard B.↗
NASA NTRS1999

A Three-Dimensional Coupled Internal/External Simulation of a Film-Cooled Turbine Vane

A three-dimensional Navier-Stokes simulation has been performed for a realistic film-cooled turbine vane using the LeRC-HT code. The simulation includes the flow regions inside the coolant plena and film cooling holes in addition to the external flow. The vane is the subject of an upcoming NASA Glenn Research Center experiment and has both circular cross-section and shaped film cooling holes. This complex geometry is modeled using a multi-block grid which accurately discretizes the actual vane geometry including shaped holes. The simulation matches operating conditions for the planned experiment and assumes periodicity in the spanwise direction on the scale of one pitch of the film cooling hole pattern. Two computations were performed for different isothermal wall temperatures, allowing independent determination of heat transfer coefficients and film effectiveness values. The results indicate separate localized regions of high heat transfer coefficient values, while the shaped holes provide a reduction in heat flux through both parameters. Hole exit data indicate rather simple skewed profiles for the round holes, but complex profiles for the shaped holes with mass fluxes skewed strongly toward their leading edges.

Heidmann, James D.↗
NASA NTRS2000

Interference Lattice-based Loop Nest Tilings for Stencil Computations

A common method for improving performance of stencil operations on structured multi-dimensional discretization grids is loop tiling. Tile shapes and sizes are usually determined heuristically, based on the size of the primary data cache. We provide a lower bound on the numbers of cache misses that must be incurred by any tiling, and a close achievable bound using a particular tiling based on the grid interference lattice. The latter tiling is used to derive highly efficient loop orderings. The total number of cache misses of a code is the sum of (necessary) cold misses and misses caused by elements being dropped from the cache between successive loads (replacement misses). Maximizing temporal locality is equivalent to minimizing replacement misses. Temporal locality of loop nests implementing stencil operations is optimized by tilings that avoid data conflicts. We divide the loop nest iteration space into conflict-free tiles, derived from the cache miss equation. The tiling involves the definition of the grid interference lattice an equivalence class of grid points whose images in main memory map to the same location in the cache-and the construction of a special basis for the lattice. Conflicts only occur on the boundaries of the tiles, unless the tiles are too thin. We show that the surface area of the tiles is bounded for grids of any dimensionality, and for caches of any associativity, provided the eccentricity of the fundamental parallelepiped (the tile spanned by the basis) of the lattice is bounded. Eccentricity is determined by two factors, aspect ratio and skewness. The aspect ratio of the parallelepiped can be bounded by appropriate array padding. The skewness can be bounded by the choice of a proper basis. Combining these two strategies ensures that pathologically thin tiles are avoided. They do not, however, minimize replacement misses per se. The reason is that tile visitation order influences the number of data conflicts on the tile boundaries. If two adjacent tiles are visited successively, there will be no replacement misses on the shared boundary. The iteration space may be covered with pencils larger than the size of the cache while avoiding data conflicts if the pencils are traversed by a scanning-face method. Replacement misses are incurred only on the boundaries of the pencils, and the number of misses is minimized by maximizing the volume of the scanning face, not the volume of the tile. We present an algorithm for constructing the most efficient scanning face for a given grid and stencil operator. In two dimensions it is based on a continued fraction algorithm. In three dimensions it follows Voronoi's successive minima algorithm. We show experimental results of using the scanning face, and compare with canonical loop orderings.

VanderWijngaart, Rob F.↗
NASA NTRS1961

Method for Calculating Induced Velocities at the Blades of a Slightly Inclined Propeller with Constant Circulation

A method for calculating the induced velocities at the blades of an inclined propeller is presented. The calculations are based upon an assumed wake consisting of one skewed helical vortex per blade. The blade circulation is assumed constant with respect to both radial and azimuth positions. The restriction of uniform radial circulation can be removed by superposition; however, the assumption of constant azimuth-wise circulation restricts the analysis to small propeller inclinations. Numerical values have been obtained for one wake skew angle. These values indicate large effects due to wake vortex spacing and to the number of blades.

Heyson, Harry H.↗
NASA NTRS2002

The Arabidopsis SKU5 gene encodes an extracellular glycosyl phosphatidylinositol-anchored glycoprotein involved in directional root growth

To investigate how roots respond to directional cues, we characterized a T-DNA-tagged Arabidopsis mutant named sku5 in which the roots skewed and looped away from the normal downward direction of growth on inclined agar surfaces. sku5 roots and etiolated hypocotyls were slightly shorter than normal and exhibited a counterclockwise (left-handed) axial rotation bias. The surface-dependent skewing phenotype disappeared when the roots penetrated the agar surface, but the axial rotation defect persisted, revealing that these two directional growth processes are separable. The SKU5 gene belongs to a 19-member gene family designated SKS (SKU5 Similar) that is related structurally to the multiple-copper oxidases ascorbate oxidase and laccase. However, the SKS proteins lack several of the conserved copper binding motifs characteristic of copper oxidases, and no enzymatic function could be assigned to the SKU5 protein. Analysis of plants expressing SKU5 reporter constructs and protein gel blot analysis showed that SKU5 was expressed most strongly in expanding tissues. SKU5 was glycosylated and modified by glycosyl phosphatidylinositol and localized to both the plasma membrane and the cell wall. Our observations suggest that SKU5 affects two directional growth processes, possibly by participating in cell wall expansion.

NASA Discipline Plant Biology↗
NASA NTRS2006

Design Enhancements of the Two-Dimensional, Dual Throat Fluidic Thrust Vectoring Nozzle Concept

A Dual Throat Nozzle fluidic thrust vectoring technique that achieves higher thrust-vectoring efficiencies than other fluidic techniques, without sacrificing thrust efficiency has been developed at NASA Langley Research Center. The nozzle concept was designed with the aid of the structured-grid, Reynolds-averaged Navier-Stokes computational fluidic dynamics code PAB3D. This new concept combines the thrust efficiency of sonic-plane skewing with increased thrust-vectoring efficiencies obtained by maximizing pressure differentials in a separated cavity located downstream of the nozzle throat. By injecting secondary flow asymmetrically at the upstream minimum area, a new aerodynamic minimum area is formed downstream of the geometric minimum and the sonic line is skewed, thus vectoring the exhaust flow. The nozzle was tested in the NASA Langley Research Center Jet Exit Test Facility. Internal nozzle performance characteristics were defined for nozzle pressure ratios up to 10, with a range of secondary injection flow rates up to 10 percent of the primary flow rate. Most of the data included in this paper shows the effect of secondary injection rate at a nozzle pressure ratio of 4. The effects of modifying cavity divergence angle, convergence angle and cavity shape on internal nozzle performance were investigated, as were effects of injection geometry, hole or slot. In agreement with computationally predicted data, experimental data verified that decreasing cavity divergence angle had a negative impact and increasing cavity convergence angle had a positive impact on thrust vector angle and thrust efficiency. A curved cavity apex provided improved thrust ratios at some injection rates. However, overall nozzle performance suffered with no secondary injection. Injection holes were more efficient than the injection slot over the range of injection rates, but the slot generated larger thrust vector angles for injection rates less than 4 percent of the primary flow rate.

Flamm, Jeffrey D.↗
NASA NTRS2005

Common Cause Case Study: An Estimated Probability of Four Solid Rocket Booster Hold-down Post Stud Hang-ups

Until Solid Rocket Motor ignition, the Space Shuttle is mated to the Mobil Launch Platform in part via eight (8) Solid Rocket Booster (SRB) hold-down bolts. The bolts are fractured using redundant pyrotechnics, and are designed to drop through a hold-down post on the Mobile Launch Platform before the Space Shuttle begins movement. The Space Shuttle program has experienced numerous failures where a bolt has "hung-up." That is, it did not clear the hold-down post before liftoff and was caught by the SRBs. This places an additional structural load on the vehicle that was not included in the original certification requirements. The Space Shuttle is currently being certified to withstand the loads induced by up to three (3) of eight (8) SRB hold-down post studs experiencing a "hang-up." The results af loads analyses performed for four (4) stud-hang ups indicate that the internal vehicle loads exceed current structural certification limits at several locations. To determine the risk to the vehicle from four (4) stud hang-ups, the likelihood of the scenario occurring must first be evaluated. Prior to the analysis discussed in this paper, the likelihood of occurrence had been estimated assuming that the stud hang-ups were completely independent events. That is, it was assumed that no common causes or factors existed between the individual stud hang-up events. A review of the data associated with the hang-up events, showed that a common factor (timing skew) was present. This paper summarizes a revised likelihood evaluation performed for the four (4) stud hang-ups case considering that there are common factors associated with the stud hang-ups. The results show that explicitly (i.e. not using standard common cause methodologies such as beta factor or Multiple Greek Letter modeling) taking into account the common factor of timing skew results in an increase in the estimated likelihood of four (4) stud hang-ups of an order of magnitude over the independent failure case.

Cross, Robert↗
NASA NTRS2005

Common Cause Case Study: An Estimated Probability of Four Solid Rocket Booster Hold-Down Post Stud Hang-ups

Until Solid Rocket Motor ignition, the Space Shuttle is mated to the Mobil Launch Platform in part via eight (8) Solid Rocket Booster (SRB) hold-down bolts. The bolts are fractured using redundant pyrotechnics, and are designed to drop through a hold-down post on the Mobile Launch Platform before the Space Shuttle begins movement. The Space Shuttle program has experienced numerous failures where a bolt has hung up. That is, it did not clear the hold-down post before liftoff and was caught by the SRBs. This places an additional structural load on the vehicle that was not included in the original certification requirements. The Space Shuttle is currently being certified to withstand the loads induced by up to three (3) of eight (8) SRB hold-down experiencing a "hang-up". The results of loads analyses performed for (4) stud hang-ups indicate that the internal vehicle loads exceed current structural certification limits at several locations. To determine the risk to the vehicle from four (4) stud hang-ups, the likelihood of the scenario occurring must first be evaluated. Prior to the analysis discussed in this paper, the likelihood of occurrence had been estimated assuming that the stud hang-ups were completely independent events. That is, it was assumed that no common causes or factors existed between the individual stud hang-up events. A review of the data associated with the hang-up events, showed that a common factor (timing skew) was present. This paper summarizes a revised likelihood evaluation performed for the four (4) stud hang-ups case considering that there are common factors associated with the stud hang-ups. The results show that explicitly (i.e. not using standard common cause methodologies such as beta factor or Multiple Greek Letter modeling) taking into account the common factor of timing skew results in an increase in the estimated likelihood of four (4) stud hang-ups of an order of magnitude over the independent failure case.

Cross, Robert↗
NASA NTRS1989

Nozzle fabrication technique

A block of electrically-conductive material which is to be formed into a body with internal and/or external surfaces that approximate hyperboloids of one sheet is placed so that its axis is set at a predetermined skew angle with relation to a travelling EDM electrode wire and the electrode wire is then moved into cutting proximity of the body. Thereafter, by revolving the body about its own axis, the external and/or internal surfaces of the body will be cut into an approximate hyperbolic surface of revolution depending upon whether the body is positioned with the cutting wire outside of the body or in a previously-formed longitudinal passage in the body. As an alternative technique, elongated channels can also be cut into the walls of the body by successively orienting the body to a selected number of angular positions with the electrode wire being either outside of the body or in a previously-formed passage in the body. At each of these angular positions, the electrode wire is moved orthogonally with respect to the axis of the wire while both the body axis skew angle and the rotational position about that axis are controlled for cutting a channel or groove in the body as required to relieve stresses in the material of the body or to convey a coolant fluid.

Wells, Dennis L.↗
NASA NTRS2005

Hematite Spherules in Basaltic Tephra Altered Under Aqueous, Acid-Sulfate Conditions on Mauna Kea Volcano, Hawaii: Possible Clues for the Occurrence of Hematite-Rich Spherules in the Burns Formation at Meridiani Planum, Mars

Iron-rich spherules (>90% Fe2O3 from electron microprobe analyses) approx.10-100 microns in diameter are found within sulfate-rich rocks formed by aqueous, acid-sulfate alteration of basaltic tephra on Mauna Kea volcano, Hawaii. Although some spherules are nearly pure Fe, most have two concentric compositional zones, with the core having a higher Fe/Al ratio than the rim. Oxide totals less than 100% (93-99%) suggest structural H2O and/or /OH. The transmission Moessbauer spectrum of a spherule-rich separate is dominated by a hematite (alpha-Fe2O3) sextet whose peaks are skewed toward zero velocity. Skewing is consistent with Al(3+) for Fe(3+) substitution and structural H2O and/or /OH. The grey color of the spherules implies specular hematite. Whole-rock powder X-ray diffraction spectra are dominated by peaks from smectite and the hydroxy sulfate mineral natroalunite as alteration products and plagioclase feldspar that was present in the precursor basaltic tephra. Whether spherule formation proceeded directly from basaltic material in one event (dissolution of basaltic material and precipitation of hematite spherules) or whether spherule formation required more than one event (formation of Fe-bearing sulfate rock and subsequent hydrolysis to hematite) is not currently constrained. By analogy, a formation pathway for the hematite spherules in sulfate-rich outcrops at Meridiani Planum on Mars (the Burns formation) is aqueous alteration of basaltic precursor material under acid-sulfate conditions. Although hydrothermal conditions are present on Mauna Kea, such conditions may not be required for spherule formation on Mars if the time interval for hydrolysis at lower temperatures is sufficiently long.

Morris, R. V.↗
NASA NTRS2007

The Chaotic Light Curves of Accreting Black Holes

We present model light curves for accreting Black Hole Candidates (BHC) based on a recently developed model of these sources. According to this model, the observed light curves and aperiodic variability of BHC are due to a series of soft photon injections at random (Poisson) intervals and the stochastic nature of the Comptonization process in converting these soft photons to the observed high energy radiation. The additional assumption of our model is that the Comptonization process takes place in an extended but non-uniform hot plasma corona surrounding the compact object. We compute the corresponding Power Spectral Densities (PSD), autocorrelation functions, time skewness of the light curves and time lags between the light curves of the sources at different photon energies and compare our results to observation. Our model reproduces the observed light curves well, in that it provides good fits to their overall morphology (as manifest by the autocorrelation and time skewness) and also to their PSDs and time lags, by producing most of the variability power at time scales 2 a few seconds, while at the same time allowing for shots of a few msec in duration, in accordance with observation. We suggest that refinement of this type of model along with spectral and phase lag information can be used to probe the structure of this class of high energy sources.

Kazanas, Demosthenes↗
NASA NTRS2010

Relating Convective and Stratiform Rain to Latent Heating

The relationship among surface rainfall, its intensity, and its associated stratiform amount is established by examining observed precipitation data from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR). The results show that for moderate-high stratiform fractions, rain probabilities are strongly skewed toward light rain intensities. For convective-type rain, the peak probability of occurrence shifts to higher intensities but is still significantly skewed toward weaker rain rates. The main differences between the distributions for oceanic and continental rain are for heavily convective rain. The peak occurrence, as well as the tail of the distribution containing the extreme events, is shifted to higher intensities for continental rain. For rainy areas sampled at 0.58 horizontal resolution, the occurrence of conditional rain rates over 100 mm/day is significantly higher over land. Distributions of rain intensity versus stratiform fraction for simulated precipitation data obtained from cloud-resolving model (CRM) simulations are quite similar to those from the satellite, providing a basis for mapping simulated cloud quantities to the satellite observations. An improved convective-stratiform heating (CSH) algorithm is developed based on two sources of information: gridded rainfall quantities (i.e., the conditional intensity and the stratiform fraction) observed from the TRMM PR and synthetic cloud process data (i.e., latent heating, eddy heat flux convergence, and radiative heating/cooling) obtained from CRM simulations of convective cloud systems. The new CSH algorithm-derived heating has a noticeably different heating structure over both ocean and land regions compared to the previous CSH algorithm. Major differences between the new and old algorithms include a significant increase in the amount of low- and midlevel heating, a downward emphasis in the level of maximum cloud heating by about 1 km, and a larger variance between land and ocean in the new CSH algorithm.

Tao, Wei-Kuo↗
NASA NTRS2011

Constraining the Physical Properties of Meteor Stream Particles by Light Curve Shapes Using the Virtual Meteor Observatory

Different authors have produced models for the physical properties of meteoroids based on the shape of a meteor's light curve, typically from short observing campaigns. We here analyze the height profiles and light curves of approx.200 double-station meteors from the Leonids and Perseids using data from the Virtual Meteor Observatory, to demonstrate that with this web-based meteor database it is possible to analyze very large datasets from different authors in a consistent way. We compute the average heights for begin point, maximum luminosity, and end heights for Perseids and Leonids. We also compute the skew of the light curve, usually called the F-parameter. The results compare well with other author's data. We display the average light curve in a novel way to assess the light curve shape in addition to using the F-parameter. While the Perseids show a peaked light curve, the average Leonid light curve has a more flat peak. This indicates that the particle distribution of Leonid meteors can be described by a Gaussian distribution; the Perseids can be described with a power law. The skew for Leonids is smaller than for Perseids, indicating that the Leonids are more fragile than the Perseids.

Koschny, D.↗
NASA NTRS2012

An "Inefficient Fin" Non-Dimensional Parameter to Measure Gas Temperatures Efficiently

A gas containment vessel that is not in thermal equilibrium with the bulk gas can affect its temperature measurement. The physical nature of many gas dynamics experiments often makes the accurate measurement of temperature a challenge. The environment itself typically requires that the thermocouple be sheathed, both to protect the wires and hot junction of the instrument from their environment, and to provide a smooth, rigid surface for pressure sealing of the enclosure. However, that enclosure may also be much colder than the gas to be sensed, or vice-versa. Either way, the effect of such gradients is to potentially skew the temperature measurements themselves, since heat may then be conducted by the instrument. Thermocouple designers traditionally address this problem by insulating the sheath from the thermocouple leads and hot junction as much as possible. The thermocouple leads are typically packed in a ceramic powder inside the sheath, protecting them somewhat from temperature gradients along the sheath, but there is no effective mechanism to shield the sheath from the enclosure body itself. Standard practice dictates that thermocouples be used in installations that do not present large thermal gradients along the probe. If this conduction dominates heat transfer near the tip of the probe, then temperature measurements may be expected to be skewed. While the same problem may be experienced in the measurement of temperature at various points within a solid in a gradient, it tends to be aggravated in the measurements of gas temperature, since heat transfer dependent on convection is often less efficient than conduction along the thermocouple. The proposed solution is an inefficient fin thermocouple probe. Conventional wisdom suggests that in many experiments where gas flows through an enclosure (e.g., flow in pipe, manifold, nozzle, etc.), the thermocouple be introduced flush to the surface, so as not to interfere with the flow. In practice, however, many such experiments take place where the flow is already turbulent, so that a protruding thermocouple probe has a negligible effect on the flow characteristics. The key question then becomes just how far into the flow should a thermocouple protrude in order to properly sense the gas temperature at that point. Modeling the thermocouple as an "inefficient fin" directly addresses this question. The appropriate assumptions in this case are: one-dimensional conduction along the fin; steady-state, constant, and homogeneous thermal conductivity; negligible radiation; and a uniform, constant heat transfer coefficient over the probe surface. It is noted that the nature of the ceramic-filled probe makes the key assumption of homogeneous thermal conductivity that much more conservative.

Lemieux, Patrick↗
NASA NTRS2011

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Canuto, V. M.↗