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NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗

NASA NTRS1993

Eddy mixing coefficient values derived from simulations with the NASA Ames Mars GCM

Values of eddy mixing coefficients, especially that for vertical mixing, are of particular importance for various photochemical models of the Mars atmosphere, which are either globally or zonally averaged. These models represent atmospheric transport processes in terms of eddy diffusion. While this is not appropriate for the advective transport by the mean meridional circulation (in general, a part of the eddy diffusion tensor actually does represent advection--a 'correction' to the Eulerian-mean circulation), it can be applied to simulate both the small- and larger-scale eddy transports of an atmospheric constituent. An effort is underway to estimate values of the eddy mixing coefficients for the Mars atmosphere using circulation data generated with the NASA Ames Mars GCM. This model simulates the three-dimensional winds in the atmosphere, and these are then used as inputs for a tracer transport model. The latter model has previously been used in interactive dust transport experiments with the Ames GCM. Idealized tracer transport experiments, with a conservative or nearly conservative hypothetical tracer, are performed to generate data from which the eddy diffusion coefficients can be estimated. Carrying out matched pairs of tracer experiments, using two very different initial states, permits all four components of the diffusion tensor to be determined. A large number of GCM experiments have been conducted, spanning a range of seasons and atmospheric dust loading, allowing the eddy mixing coefficients to be estimated for a variety of atmospheric conditions.

Barnes, J. R.↗

NASA NTRS1993

Stationary eddies in the Mars general circulation as simulated by the NASA-Ames GCM

Quasistationary eddies are prominent in a large set of simulations of the Mars general circulation performed with the NASA-Ames GCM. Various spacecraft observations have at least hinted at the existence of such eddies in the Mars atmosphere. The GCM stationary eddies appear to be forced primarily by the large Mars topography, and (to a much lesser degree) by spatial variations in the surface albedo and thermal inertia. The stationary eddy circulations exhibit largest amplitudes at high altitudes (above 30-40 km) in the winter extratropical regions. In these regions they are of planetary scale, characterized largely by zonal wavenumbers 1 and 2. Southern Hemisphere winter appears to be dominated by a very strong wave 1 pattern, with both waves 1 and 2 being prominent in the Northern Hemisphere winter regime. This difference seems to be basically understandable in terms of differences in the topography in the two hemispheres. The stationary eddies in the northern winter extratropics are found to increase in amplitude with dust loading. This behavior appears to be at least partly associated with changes in the structure of the zonal-mean flow that favor a greater response to wave 1 topographic forcing. There are also strong stationary eddy circulations in the tropics and in the summer hemisphere. The eddies in the summer subtropics and extratropics arc substantially stronger in southern summer than in northern summer. The summer hemisphere stationary circulations are relatively shallow and are characterized by smaller zonal scales than those in the winter extratropics.

Barnes, J. R.↗

NASA NTRS1995

A preliminary attempt to use neural networks for turbulent eddy classification

This note describes an attempt to use standard neural network tools to fashion a means of detecting eddy patterns in the wall region of a turbulent flow. The research was motivated by the desire to formulate a means to use only flow parameters that can be sensed on the wall to describe the passing eddy structure. If a simple formulation can be obtained, it could conceivably be utilized to control actuators embedded in the wall. Such actuators have been developed by Jacobson and Reynolds (1993a), Blackwelder and Liu (1994), Tung et al. (1995), and others. These actuators have the common characteristics that they are small and are typically flush with the wall when not deployed. When they are activated, it is assumed that they will be able to interact constructively with the turbulent eddies near their location to either decrease the wall shear stress, enhance or reduce the mixing, etc. At present, there is only a nascent understanding of the interaction dynamics between the actuators and the eddies in the flow. Nevertheless, for such interaction to succeed, methods to couple the actuators to the oncoming flow must be obtained. General methods must be found that will detect the space and temporal location of the desired structure. In particular, it will be necessary to know when the eddies will arrive at the location of the actuator. This research attempted to use the shear stress measurements on the wall in the vicinity of an actuator location to predict when a particular eddy pattern would arrive and/or occur at the designated location. In this work the eddy pattern to be detected was identified by its velocity signature only.

Blackwelder, Ron F.↗

NASA NTRS1999

Mesoscale Eddies, Satellite Altimetry, and New Production in the Sargasso Sea

Satellite altimetry and hydrographic observations are used to characterize the mesoscale eddy field in the Sargasso Sea near Bermuda and to address the role of physical processes on the supply of new nutrients to the euphotic zone. The observed sea level anomaly (SLA) field is dominated by the occurrence of westward propagating features with SLA signatures as large as 25 cm, Eulerian temporal scales of roughly a month, lifetimes of several months, spatial scales of approximately 200 km, and a propagation of approximately 5 cm/s. Hydrographic estimates of dynamic height anomaly (referenced to 4000 dbar) are well correlated with satellite SLA (r(exp 2) = 0.65), and at least 85% of the observed dynamic height variability is associated with the first baroclinic mode of motion. This allows us to apply the satellite observations to remotely sensed estimate isopycnal displacements and the flux of nutrients into the euphotic zone due to eddy pumping. Eddy pumping is the process by which mesoscale eddies induce isopycnal displacements that lift nutrient-replete waters into the euphotic zone, driving new primary production. A kinematic approach to the estimation of the eddy pumping results in a flux of 0.24 +/- 0.1 mol N/sq m (including a scale estimate for the small contribution due to 18 deg water eddies). This flux is more than an order of magnitude larger than the diapycnal diffusive flux as well as scale estimates for the vertical transport due to isopycnal mixing along sloping isopycnal surfaces. Eddy pumping and wintertime convection are the two dominant mechanisms transporting new nutrients into the euphotic zone, and the sum of all physical new nutrient supply fluxes effectively balances previous geochemical estimates of annual new production for this site. However, if biological transports (e.g., nitrogen fixation, etc.) are significant, the new nitrogen supply budget will be in excess of geochemical new production estimates. This suggests that the various physical and biological transport fluxes, as well as geochemical inferences of new production, still need to be reconciled and many outstanding questions remain.

Siegel, David A.↗

NASA NTRS1999

Mesoscale Eddies, Satellite Altimetry, and New Production in the Sargasso Sea

Satellite altimetry and hydrographic observations are used to characterize the mesoscale eddy field in the Sargasso Sea near Bermuda and to address the role of physical processes on the supply of new nutrients to the euphotic zone. The observed sea level anomaly (SLA) field is dominated by the occurrence of westward propagating features with SLA signatures as large as 25 cm, Eulerian temporal scales of roughly a month, lifetimes of several months, spatial scales of approximately 200 km, and a propagation of approximately 5 cm/s . Hydrographic estimates of dynamic height anomaly (referenced to 4000 dbar) are well correlated with satellite SLA (r(sup 2) = 0.65), and at least 85% of the observed dynamic height variability is associated with the first baroclinic mode of motion. This allows us to apply the satellite observations to remotely estimate isopycnal displacements and the flux of nutrients into the euphotic zone due to eddy pumping. Eddy pumping is the process by which mesoscale eddies induce isopycnal displacements that lift nutrient- replete waters into the euphotic zone, driving new primary production. A kinematic approach to the estimation of the eddy pumping results in a flux of 0.24+/-0.1 mol N/sq m/yr (including a scale estimate for the small contribution due to 18 deg water eddies). This flux is more than an order of magnitude larger than the diapycnal diffusive flux as well as scale estimates for the vertical transport due to isopycnal mixing along sloping isopycnal surfaces. Eddy pumping and wintertime convection are the two dominant mechanisms transporting new nutrients into the euphotic zone, and the sum of all physical new nutrient supply fluxes effectively balances previous geochemical estimates of annual new production for this site. However, if biological transports (e.g., nitrogen fixation, etc.) are significant, the new nitrogen supply budget will be in excess of geochemical new production estimates. This suggests that the various physical and biological transport fluxes, as well as geochemical inferences of new production, still need to be reconciled and many outstanding questions remain.

Siegel, David A.↗

NASA NTRS1994

Eddy current correction in volume-localized MR spectroscopy

The quality of volume-localized magnetic resonance spectroscopy is affected by eddy currents caused by gradient switching. Eddy currents can be reduced with improved gradient systems; however, it has been suggested that the distortion due to eddy currents can be compensated for during postprocessing with a single-frequency reference signal. The authors propose modifying current techniques for acquiring the single-frequency reference signal by using relaxation weighting to reduce interference from components that cannot be eliminated by digital filtering alone. Additional sequences with T1 or T2 weighting for reference signal acquisition are shown to have the same eddy current characteristics as the original signal without relaxation weighting. The authors also studied a new eddy current correction method that does not require a single-frequency reference signal. This method uses two free induction decays (FIDs) collected from the same volume with two sequences with opposite gradients. Phase errors caused by eddy currents are opposite in these two FIDs and can be canceled completely by combining the FIDs. These methods were tested in a phantom. Eddy current distortions were corrected, allowing quantitative measurement of structures such as the -CH = CH- component, which is otherwise undetectable.

NASA Discipline Musculoskeletal↗

NASA NTRS1979

Horizontal eddy diffusivities in the Northern Hemispheric stratosphere and lower mesosphere

Meteorological rocket soundings, launched between 1969-74 at six locations representative of low, middle, and high altitudes, are employed with the use of the statistical theory of diffusion, to determine the zonal and meridional component of eddy diffusivity between 30 and 55 km as a function of season, latitude, and altitude. A comparison is also made between annually-averaged eddy diffusivities above and below 30 km. It is shown that the zonal component of eddy diffusivity is approximately three to five times as large as the meridional component, in most cases. Both components of eddy diffusivity vary greatly with season, latitude, and altitude. Highest eddy diffusivities, found in the vicinity of the winter westerly jet, are approximately one order of magnitude higher than those present during the summer. Tropical eddy diffusivities, however, remain relatively small throughout the year. Annually, a minimum is indicated near 25 km between maximums located at the stratopause and tropopause.

Kao, S. K.↗

NASA NTRS1985

Transient Eddies in the UCLA GCM

The simulation of transient eddies in the nine level UCLA general circulation model (GCM) was examined and compared to observations, with emphasis on the Northern Hemisphere winter. Qualitatively, the UCLA GCM reproduces many features of the observed circulation and the relationship between the time mean flow and transient eddies; however, the magnitudes of transient eddies in the UCLA GCM, particularly at frequencies lower than those associated with baroclinic instability, appear to be much less than those observed. The pattern of low level transient eddy heat fluxes were similar to observations and acted to dissipate the low level seasonal mean temperature field. The simulated transient eddy kinetic energy at 300 mb is given for eddies of all time scales shorter than a season.

White, G. H.↗

NASA NTRS1987

Multiple dipole eddies in the Alaska Coastal Current detected with Landsat thematic mapper data

Seventeen dipole eddies, including five large, well-formed ones, three second-generation eddies, and two double eddies, were observed in the Alaska Coastal Current near Kayak Island in one single scene of the Landsat thematic mapper (TM) on April 22, l985. The digital Landsat TM satellite data were computer analyzed to extract details in the near coastal circulation in the northern Gulf of Alaska. Enhancement techniques were applied to the visible and thermal IR bands. The features are evident only in the visible bands because of the ability of these bands to detect the distribution of sediments in the near surface. These eddies did not have a significant thermal signature.The sources of these sediments are the glacial streams found throughout the Gulf of Alaska coast. Eddies of this configuration and frequency have never been observed here previously. However, the oceanographic and meteorological conditions are typical for this time of year. These eddies should be important to the cross-shelf mixing processes in the Alaska Coastal Current and are an indicator that the flow here can be unstable at certain times of the year.

Ahlnas, Kristina↗

NASA NTRS1988

Relationships between persistent large-scale flow anomalies and variation in synoptic-scale eddy activity and cyclogenesis

Observational analyses to study the relationships between large-scale flow anomalies and variations in synoptic-scale eddy activity and cyclogenesis are presented. The way in which changes in the large-scale flow influence the behavior of synoptic-scale eddies and the way in which changes in eddies may feedback to influence the large-scale flow anomalies are examined. Situations characterized by differing large-scale flows are compared, showing well-defined diferences in synoptic-scale eddy activity. The net forcings of anomalous mean flows by eddies as deduced from tendency methods and E-vector analyses suggest that synoptic-scale eddies may play an important role in maintaining certain anomalous flow patterns such as blocking.

Dole, Randall M.↗

NASA NTRS1992

Observations of an arc-shaped cloud band over an oceanographic warm eddy

Observations on January 7 and 8, 1991, of an arc-shaped cloud band outlining an area in the eastern Mediterranean within a warm ocean eddy were made using the NOAA-11 AVHRR. Clouds formed at the edge of the warm eddy's internal boundary layer as the wind traveled at right angles from the colder Aegean water toward the warm eddy. No clouds formed on the southern side of the warm eddy where sea surface temperatures were warmer and where the winds may not have flowed at right angles toward the warm eddy. An upper limit of 24 h was determined for the length of time the arc-shaped cloud stayed over the eddy.

Burnett, William H.↗

NASA NTRS1995

A new non-eddy viscosity subgrid-scale model and its application to channel flow

To date, most large-eddy simulations (LES) have been carried out with eddy viscosity subgrid scale (SGS) models, with only a few exceptions that used the mixed model. Even though the assumptions behind Smagorinsky's model are rather stringent, it has been applied successfully to a variety of turbulent flows. This success is attributed to the ability of eddy viscosity models to drain energy from large scales, thus simulating the dissipative nature of turbulence. Most SGS models are absolutely dissipative, i.e. they remove energy from the large scales at every instant. However, SGS stresses may transfer energy back to the large scales intermittently; this reverse transfer or backscatter is especially important in geophysical flows and in transition. In a fully developed channel flow, there is reverse flow of energy from small to large scales near the walls, but eddy viscosity models are unable to account for this important feature. The dynamic localization eddy viscosity model of Ghosal et al. (1995) allows backscatter by co-evolving an auxiliary equation for the SGS energy; however, the computational cost is considerably larger than for conventional SGS models (Cabot 1994). In this report, a new non-eddy viscosity model based on local approximation of total quantities in terms of filtered ones is introduced; the scale similarity model of Bardina (1983) is a special case of this model. This procedure does not require the assumption of homogeneity, permits backscatter of energy from small to large scales, and is readily implemented in finite difference codes. The results of applying the proposed model to second order finite volume simulation of plane channel flow at high Reynolds numbers (Re(sub b) = 38,000) is described in this report. Greater emphasis is placed on the high Reynolds number flow since it provides a more rigorous test of the SGS model and its potential application. The results are compared to ones produced by the conventional and dynamic Smagorinsky models and the spectral LES of Piomelli (1993).

Shah, K. B.↗

NASA NTRS1996

Analysis of Subgrid Eddy Diffusivity in Turbulence Using Direct Numerical Simulation Databases

Direct numerical simulation data in isotropic turbulence at Taylor-scale Reynolds number 90 are used to compute subgrid transfer and spectral eddy diffusivities for passive scalars at Schmidt numbers 1 and 1/8. The results are consistent with spectral transfer processes dominated by a local forward cascade in wavenumber space which is a consequence of moderately nonlocal interactions in the scalar fields. Data decompositions show that resolvable-subgrid interactions make (in general) substantially stronger contributions than fully-subgrid interactions to the eddy diffusivity, which has a non-negligible inverse cascade, or backscatter, component. The eddy diffusivity has a strong cusp at wavenumbers close to the cutoff value separating resolvable and subgrid ranges. At low wavenumbers the eddy diffusivity is generally small, but there the details depend on Schmidt number. The behavior of the subgrid turbulent Schmidt number (the ratio of effective eddy viscosity to eddy diffusivity) is observed to depend strongly on Schmidt number. In interpreting the results at a given spectral cutoff it is important to note that the spectrum of less diffusive scalars (of higher Schmidt number) has more high-wavenumber content.

Yeung, P. K.↗

NASA NTRS1999

New Chemical, Bio-Optical and Physical Observations of Upper Ocean Response to the Passage of a Mesoscale Eddy Off Bermuda

A mesoscale eddy advected across the Bermuda Testbed Mooring site over a 30-day period centered on July 14, 1995. Temperature and current measurements along with biogeochemical measurements were used to characterize the biological response of the upper ocean associated with the introduction of nitrate into the euphotic layer due to the doming of isotherms associated with the eddy. Complementary shipboard data showed an anomalous water mass, which extended from a depth of approximately 50 to 1000 m, manifesting as a cold surface expression and warm anomaly at depth. Although mesoscale eddies are frequently observed in the Sargasso Sea, the present observations are particularly unique because of the high-temporal-resolution measurements of the new instrumentation deployed on the mooring. Analyzers that measure nitrate plus nitrite were placed at depths of 80 and 200 m and bio-optical sensors were located at depths of 20, 35, 45, 71, and 86 m. Peak nitrate values of nearly 3.0 micro-M at 80 m and chlorophyll a values of 1.4 mg/cubic m at 71 m were observed, a well as a 25- to 30-meter shoaling of the 1% light level depth. A Doppler shift from the inertial period (22.8 hours) to 25.2 hours was observed in several time series records due to the movement of the eddy across the mooring. Inertial pumping brought cold, nutrient-rich waters farther into the euphotic zone than would occur solely by isothermal lifting. Silicic acid was depleted to undetectable levels owing to the growth of diatoms within the eddy. The chlorophyll a values associated with the eddy appear to be the largest recorded during the eight years of the ongoing US JGOFS Bermuda Atlantic Time Series Study program.

McNeil, J. D.↗

NASA NTRS1999

New Chemical, Bio-Optical and Physical Observations of Upper Ocean Response to the Passage of a Mesoscale Eddy off Bermuda

A mesoscale eddy advected across the Bermuda Testbed Mooring site over a 30-day period centered on July 14, 1995. Temperature and current measurements along with biogeochemical measurements were used to characterize the biological response of the upper ocean associated with the introduction of nitrate into the euphoric layer due to the doming of isotherms associated with the eddy. Complementary shipboard data showed an anomalous water mass, which extended from a depth of approximately 50 to 1000 m, manifesting as a cold surface expression and warm anomaly at depth. Although mesoscale eddies are frequently observed in the Sargasso Sea, the present observations are particularly unique because of the high-temporal-resolution measurements of the new instrumentation deployed on the mooring. Analyzers that measure nitrate plus nitrite were placed at depths of 80 and 200 m and bio-optical sensors were located at depths of 20, 35, 45, 71, and 86 m. Peak nitrate values of nearly 3.0 microns at 80 m and chlorophyll alpha values of 1.4 mg/cu m at 71 m were observed, as well as a 25- to 30-meter shoaling of the 1% light level depth. A Doppler shift from the inertial period (22.8 hours) to 25.2 hours was observed in several time series records due to the movement of the eddy across the mooring. Inertial pumping brought cold, nutrient-rich waters farther into the euphotic zone than would occur solely by isothermal lifting. Silicic acid was depleted to undetectable levels owing to the growth of diatoms within the eddy. The chlorophyll alpha values associated with the eddy appear to be the largest recorded during the 8 years of the ongoing U.S. JGOFS Bermuda Atlantic Time Series Study (BATS) program.

McNeil, J. D.↗

NASA NTRS1994

Corrosion Detection in Airframes Using a New Flux-Focusing Eddy Current Probe

A new flux-focusing eddy current probe was recently developed at NASA Langley Research Center. The new probe is similar in design to a reflection type eddy current probe, but is unique in that it does not require the use of an impedance bridge for balancing. The device monitors the RMS output voltage of a pickup coil and, as a result, is easier to operate and interpret than traditional eddy current instruments. The unique design feature of the probe is a ferromagnetic cylinder, typically 1020 steel, which separates a concentrically positioned drive and pickup coil. The increased permeability of the steel causes the magnetic flux produced by the drive coil to be focused in a ring around the pickup coil. At high frequencies the eddy currents induced in both the sample and the cylinder allow little or no flux to link with the pickup coil. This results in a self-nulling condition which has been shown to be useful for the unambiguous detection of cracks in conducting materials. As the frequency is lowered the flux produced by the drive coil begins to link with the pickup coil causing an output which, among other things, is proportional to the thickness of the test specimen. This enables highly accurate measurements of the thickness of conducting materials and helps to facilitate the monitoring of thickness variations in a conducting structure such as an aircraft fuselage. Under ideal laboratory conditions the probe can sense thickness changes on the order of 1% as illustrated. However, this is highly dependent upon the thickness, and the geometric complexity of the sample being tested and for practical problems the sensitivity is usually much less. In this presentation we highlight some of the advantages and limitations in using the probe to inspect aircraft panels for corrosion and other types of material nonuniformities. In particular, we present preliminary results which illustrate the probes capabilities for detecting first and second layer corrosion in aircraft panels which may contain air gaps between the layers. Since the probe utilized eddy currents its corrosion detection capabilities are similar to convectional eddy current techniques, but the new probe is much easier to use.

Fulton, James P.↗

NASA NTRS2007

Eddies Enhance Biological Production in the Weddell-Scotia Confluence of the Southern Ocean

Satellite data show that oceanic eddies generated in the Southern Antarctic Circumpolar Current Front (SACCF) are associated with increased phytoplankton biomass. Cyclonic eddies with high chlorophyll a concentration (Chl-a) retain phytoplankton within the eddy cores and increase the light available for photosynthesis in the upper mixed layer by limiting vertical mixing and lifting of the isopycnal surfaces. Anticyclonic eddies have low Chl-a in the core but increased Chl-a in the periphery. Cross-frontal mixing mediated by eddies transports nutrients (e.g., Fe and Si) to the north and contributes to the increased Chl-a in the frontal zone. Interannual variations in the cyclonic eddy activity are positively correlated with variations in Chl-a during the spring bloom in regions of the Antarctic Circumpolar Current around South Georgia.

Kahru, M.↗