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At least 199 records · Page 11

Reverse Energy Cascade in Turbulent Weakly Ionized Plasmas

For systems far from equilibrium, the neglect of a role for viscous effects in turbulence may be generally inappropriate when the relaxation time for the molecular process approaches the local flow time (Orou et al. (1996)). Furthermore, for stationary collisional plasmas, the conventional Reynolds number is irrelevant under circumstances where the standard features of turbulence in ordinary gases are observed in the plasma (Johnson et al. (1987)). The current theoretical understanding of these turbulent phenomenon is particularly inadequate for turbulence associated with ionizing shock waves; generally speaking, thermodynamic, acoustic and pressure fluctuations are all seen as amplified across the shock wave followed by a dramatic decay (relaminarization) usually attributed to a lack of importance of viscosity in the turbulent regions. This decay would be accelerated when the flow speed is also reduced due to the importance usually given to the conventional Reynolds number (which is directly proportional to velocity) as a quality of turbulence index. However, evidence supporting this consensus is lacking. By contrast, recent evidence of vanishing triple correlations form De Silva et al. (1996) provides strong support for early theoretical speculation of inherently molecular effects in macroscopic turbulence in Tsuge (1974). This specifically suggests that the role of compressive effects ordinarily associated with the shock wave could be significantly muted by the existence of a strongly turbulent local environment. There is also more recent theoretical speculation (Frisch et al. (1984)) of an inherently and previously unsuspected non-dissipative nature to turbulence, with energy conservation being nurtured by reverse energy cascades in the turbulent fluctuation spectra. Furthermore, the role which might be played by fluctuations on quantum mechanical phenomena and variations in molecular parameters is completely unknown, especially of the sort which might be found in optical spectra. A determination of the role which changing turbulent parameters might play on optical signatures behind a reflected shock wave should therefore provide a useful tool for the evolution of theoretical models for turbulence.

Williams, Kyron↗

Directional Solidification of a Binary Alloy into a Cellular Convective Flow: Localized Morphologies

A steady, two dimensional cellular convection modifies the morphological instability of a binary alloy that undergoes directional solidification. When the convection wavelength is far longer than that of the morphological cells, the behavior of the moving front is described by a slow, spatial-temporal dynamics obtained through a multiple-scale analysis. The resulting system has a "parametric-excitation" structure in space, with complex parameters characterizing the interactions between flow, solute diffusion, and rejection. The convection stabilizes two dimensional disturbances oriented with the flow, but destabilizes three dimensional disturbances in general. When the flow is weak, the morphological instability behaves incommensurably to the flow wavelength, but becomes quantized and forced to fit into the flow-box as the flow gets stronger. At large flow magnitudes the instability is localized, confined in narrow envelopes with cells traveling with the flow. In this case the solutions are discrete eigenstates in an unbounded space. Their stability boundary and asymptotics are obtained by the WKB analysis.

Chen, Y.- J.↗

Transpiration cooling in hypersonic flight

A preliminary numerical study of transpiration cooling applied to a hypersonic configuration is presented. Air transpiration is applied to the NASA all-body configuration flying at an altitude of 30500 m with a Mach number of 10.3. It was found that the amount of heat disposal by convection is determined primarily by the local geometry of the aircraft for moderate rates of transpiration. This property implies that different areas of the aircraft where transpiration occurs interact weakly with each other. A methodology for quick assessments of the transpiration requirements for a given flight configuration is presented.

Tavella, Domingo↗

Formaldehyde Column Density Measurements as a Suitable Pathway to Estimate Near-Surface Ozone Tendencies from Space

In support of future satellite missions that aim to address the current shortcomings in measuring air quality from space, NASA's Deriving Information on Surface Conditions from Column and Vertically Resolved Observations Relevant to Air Quality (DISCOVER-AQ) field campaign was designed to enable exploration of relationships between column measurements of trace species relevant to air quality at high spatial and temporal resolution. In the DISCOVER-AQ data set, a modest correlation (r2 = 0.45) between ozone (O3) and formaldehyde (CH2O) column densities was observed. Further analysis revealed regional variability in the O3-CH2O relationship, with Maryland having a strong relationship when data were viewed temporally and Houston having a strong relationship when data were viewed spatially. These differences in regional behavior are attributed to differences in volatile organic compound (VOC) emissions. In Maryland, biogenic VOCs were responsible for approx.28% of CH2O formation within the boundary layer column, causing CH2O to, in general, increase monotonically throughout the day. In Houston, persistent anthropogenic emissions dominated the local hydrocarbon environment, and no discernable diurnal trend in CH2O was observed. Box model simulations suggested that ambient CH2O mixing ratios have a weak diurnal trend (+/-20% throughout the day) due to photochemical effects, and that larger diurnal trends are associated with changes in hydrocarbon precursors. Finally, mathematical relationships were developed from first principles and were able to replicate the different behaviors seen in Maryland and Houston. While studies would be necessary to validate these results and determine the regional applicability of the O3-CH2O relationship, the results presented here provide compelling insight into the ability of future satellite missions to aid in monitoring near-surface air quality.

Surface Conditions from Column and Vertically Reso↗

Inviscid vortex motions in weakly three-dimensional boundary layers and their relation with instabilities in stratified shear flows

We consider the inviscid instability of three-dimensional boundary-layer flows with a small crossflow over locally concave or convex walls, along with the inviscid instability of stratified shear flows. We show how these two problems are closely related through the forms of their governing equations. A proposed definition of a generalized Richardson number for the neutrally stable inviscid vortex motions is given. Implications of the similarity between the two problems are discussed.

Blackaby, Nicholas D.↗

Aeroelastic modal characteristics of mistuned blade assemblies: Mode localization and loss of eigenstructure

An investigation of the effects of small mistuning on the aeroelastic modes of bladed disk assemblies with aerodynamic coupling between blades is presented. The cornerstone of the approach is the use and development of perturbation methods that exhibit the crucial role of the interblade coupling and yield general findings regarding mistuning effects. It is shown that blade assemblies with weak aerodynamic interblade coupling are highly sensitive to small blade mistuning, and that their dynamics is quantitatively altered in the following ways: the regular pattern that characterizes the root locus of the tuned aeroelastic eigenvalues in the complex plane is totally lost; the aeroelastic mode shapes becomes severely localized to only a few blades of the assembly and lose their constant interblade phase angle feature; and curve veering phenomena take place when the eigenvalues are plotted versus a mistuning parameter.

Pierre, Christophe↗

Aeroelastic modal characteristics of mistuned blade assemblies - Mode localization and loss of eigenstructure

An investigation of the effects of small mistuning on the aeroelastic modes of bladed-disk assemblies with aerodynamic coupling between blades is presented. The cornerstone of the approach is the use and development of perturbation methods that exhibit the crucial role of the interblade coupling and yield general findings regarding mistuning effects. It is shown that blade assemblies with weak aerodynamic interblade coupling are highly sensitive to small blade mistuning, and that their dynamics is qualitatively altered in the following ways: the regular pattern that characterizes the root locus of the tuned aeroelastic eigenvalues in the complex plane is totally lost; the aeroelastic mode shapes become severely localized to only a few blades of the assembly and lose their constant interblade phase angle feature; curve veering phenomena take place when the eigenvalues are plotted versus a mistuning parameter.

Pierre, Christophe↗

Localization of Ad-Hoc Lunar Constellations in Communication Failure Modes for Distributed Spacecraft Autonomy

As lunar missions increase in complexity inspired by NASA’s Artemis Program, they will require reliable and sufficient capability of the Position, Navigation, and Timing (PNT) system to support their scientific objectives. In addition, NASA's Commercial Lunar Payload Services (CLPS) program initiates the proliferation of public and private exploration partnerships using small satellites from commercial and private organizations, expanding traditionally confined low Earth orbit to be used for missions beyond geosynchronous orbit (Zucherman et al., 2022). Therefore, the Lunar PNT system is also required to provide navigation services compatible with the smaller platforms being sent by the public and private sectors, like CubeSats. However, traditional approaches to deep space missions’ navigation based on ground radio facilities have difficulties in providing sufficient support for the increasing number of users and communication at a distance from the Earth (Kaplev et al., 2022). In particular, the existing Lunar navigation technologies such as weak signal global positioning system (GPS) and deep space network (DSN) are not able to ensure operations of the upcoming small-scale Lunar missions due to their limitations in localization performance as well as capacity aspects. Another way to provide Lunar PNT service is to create a dedicated Lunar global navigation satellite system (GNSS) constellation, like GNSS systems on Earth. Space agencies like NASA, ESA, and JAXA are now developing the lunar communications relay and navigation systems (LCRNS) and Lunar navigation satellite systems (LNSS). In their systems, satellites will be deployed in moon orbits to provide the communication, positioning, navigation, and timing (CPNT) service at the lunar south pole region where the Artemis base camp will be expected (Murata et al., 2022). Meanwhile, common challenges considered in lunar PNT research arise from poor geometry of the terrestrial GNSS satellites when seen from the lunar user, highly perturbed lunar orbits, and limitations in power, size, and cost of the equipment on lunar satellites (Iiyama et al., 2023). It is also not clear if there will be enough Lunar users to support the cost and resources this would require as the Low-cost surface missions may not be able to support the large power, mass, and weight requirements that these navigation solutions entail (Niemoeller et al., 2022). As an alternative, existing Lunar science and exploration assets could be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions (Hagenau et al., 2021). Introducing the non-dedicated and ad-hoc Lunar navigation constellation gives a way to provide PNT services on-demand. The non-dedicated swarm assets of Lunar constellations are designed to localize themselves with minimal interaction with Earth by adding cooperative autonomous localization to lunar missions, freeing up valuable bandwidth and ground segment resources. An autonomous localization of Lunar constellations is based on the concept of the decentralized PNT system with a distributed extended Kalman filter (DEKF) approach to state estimation for minimal onboard operating costs. In the distributed data processing algorithm, computation is broken down and assigned to each satellite, resulting in a considerably decreased computational amount while maintaining the accuracy of the orbit ephemeris and clock offsets as the result of centralized data processing (Wen et al., 2019). The DEKF requires spacecraft to perform two-way ranging operations with each other to communicate simultaneously, leveraging neighbor two-way intersatellite link (ISL) measurements such as pseudoranges to, and relative velocities between, visible satellites as sensor values (Frank et al., 2021). The Lunar autonomous PNT simulation (LAPS) demonstrated the feasibility of orbital asset localization among ad-hoc Lunar small-sat constellations based on the DEKF in Hagenau et al. (2021) and evaluated the matching algorithm proposed by Frank et al. (2021) in scheduling position estimation updates. In previous papers, all assets and measurements are assumed to be always available without consideration of the impact of intermittent and permanent communication failure. This study presents localization performance with increasing levels of network degradation for swarm assets and users to demonstrate the robustness of the decentralized Lunar PNT service in more realistic scenarios. Main issues arising from communication failure include spacecraft permanent or transient loss, antenna failures, message delays, etc. We tested four possible reasons for network degradation for 7 days in 21 satellites frozen with an altitude of 5500 km, evenly spaced around 3 circular, 40 inclination orbital planes where each spacecraft has two directional antennas. As anchor nodes with an independent estimate of their position are required in the DEKF approach, two ground nodes in each pole and one node in the gateway were implemented in the simulation. First, the most probable failure scenario involves the loss of a single spacecraft due to solar interference and technical malfunctions of the assets. Losing the availability of a single spacecraft means losing the two-way ISL measurement of the asset in the DEKF update. In order to provide the best possible quality of PNT service with limited time and resources, the distributed Lunar constellations must schedule the communication activities. The scheduler leverages mixed-integer linear programming (MILP) for the coordination and scheduling of the desired “as-needed” localization service (Niemoeller et al., 2022). We assume the scheduler has completely excluded the spacecraft information before the DEKF update in the failure scenario. When a random spacecraft has been turned off at a specific time, the robustness of the autonomous Lunar PNT system is evaluated. The simulation results give an 11.5% degradation in median position accuracy compared to the idealized performance excluding the asset loss. Second, a large number of assets may vanish due to major hardware problems or meteor strikes around the moon. A multiple spacecraft loss can degrade the localization performance very fast by losing the communication ability to do cross-plane measurements and in-plane measurements in a 3-plane constellation. When the matching-based scheduler is aware of ISL availability, we investigate a large number of in-plane and cross-plane asset vanishments both in close proximity and equally spaced throughout the orbital plane. According to the simulations, the loss of in-plane measurements gives 40.2% degradation while cross-plane measurements degrade 50.5% of asset localization performance among available assets. Therefore, it is concluded that cross-plane measurements are more important in improving the position estimation accuracy. Third, spacecraft failure information can be lost due to the internal message delay, resulting in the DEKF update scheduler to solve the matching problem with unavailable assets. The DEKF update cycle is comprised of network setup, communication, and computations where a global broadcast network and a 2-way ISL network setup take 6 minutes in total (Frank et al., 2021). Once the broadcast network successfully transmits and receives information, a random spacecraft may lose its availability right before solving the matching problem. This means the matching solution is no longer optimal, resulting in degradation in the localization performance. A numerical assessment shows the matching-based scheduler with knowing failure holds 11.5% of position accuracy degradation, whereas the scheduler without knowing failure gives 34% degraded localization performance without asset loss. Fourth, a transient loss of a single or multiple spacecraft may occur due to their antenna outages. After losing the two-way ISL availability for a few DEKF update cycles, the availability of spacecraft can easily be recovered as their states have been independently updated using measurements from anchor nodes. It is likely that the longer failure will result in worse localization performance. We have tested the transient failure of a random single asset for 30 min in the simulation, which is losing 3 update cycles in the DEKF system. From the simulation results, the position accuracy has been degraded to 4.84% which is better than the degraded localization performance of 11.5% from the permanent loss scenario among available assets. In conclusion, the autonomous Lunar PNT system based on the DEKF approach shows the ability to maintain resilience and robustness in the possible communication failure scenarios, ensuring that localization accuracy is preserved across various network degradation and outages. Future studies on investigating user localization performance near the South Pole and the broadcast network system will be continued in the following months.

Yeji Kim↗

A Method to Retrieve Rainfall Rate over Land from TRMM Observations

Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) observations over mesoscale convective systems (MCSs) reveal that there are localized maxima in the rain rate with a scale of about 10 to 20 km that represent thunderstorms (Cbs). Some of these Cbs are developing or intense, while others are decaying or weak. These Cbs constitute only about 20 % of the rain area of a given MCS. Outside of Cbs, the average rain rate is much weaker than that within Cbs. From an analysis of the PR data, we find that the spatial distribution of rain and its character, convective or stratiform, is highly inhomogeneous. This complex nature of rain exists on a scale comparable to that of a Cb. The 85 GHz brightness temperature, T85, observations of the TRMM Microwave Imager (TMI) radiometer taken over an MCS reflect closely the PR rain rate pattern over land. Local maxima in rain rate shown by PR are observed as local minima in T85. Where there are no minima in T85, PR observations indicate there is light rain. However, the TMI brightness temperature measurements (Tbs) have poor ability to discriminate convective rain from stratiform rain. For this reason, a TMI rain retrieval procedure that depends primarily on the magnitude of Tbs performs poorly. In order to retrieve rain rate from TMI data on land one has to include the spatial distribution information deduced from the T85 data in the retrieval method. Then, quantitative estimation of rain rate can be accomplished. A TMI rain retrieval method developed along these lines can yield estimates of rain rate and its frequency distribution which agree closely with that given by PR. We find the current TRMM project TMI (Version 5) rain retrieval algorithm on land could be improved with the retrieval scheme developed here. To support the conceptual frame work of the rain retrieval method developed here, a theoretical analysis of the TMI brightness temperatures in convective and stratiform regions is presented.

Prabhakara, C.↗

Effect of suction and blowing on boundary-layer transition

The effects of wall blowing and suction on boundary-layer stability and transition are studied on a flat plate. Titanium panels, in which 0.063 mm diameter holes were drilled on 0.635 mm centers, are inserted on the plate. Suction level and distribution are variable. Disturbances are introduced by means of a vibrating ribbon and measurements of both mean-flow and disturbance-flow velocities are made with a hot wire. Disturbance amplitudes are measured as a function of Reynolds number, frequency, and suction characteristics and compared with the previous Dynapore results of Reynolds and Saric. Transition measurements under natural and forced conditions are also made. The stabilizing effects of suction are documented. It is also shown that very high local flow rates through the suction holes (which approach a hole Reynolds number of 300) do not destabilize the flow. On the other hand, weak blowing lowers the transition Reynolds number but is found not to cause serious problems.

Saric, W. S.↗

Electroless-plating technique for fabricating thin-wall convective heat-transfer models

A technique for fabricating uniform thin-wall metallic heat-transfer models and which simulates a Shuttle thermal protection system tile is described. Two 6- by 6- by 2.5-in. tiles were fabricated to obtain local heat transfer rates. The fabrication process is not limited to any particular geometry and results in a seamless thin-wall heat-transfer model which uses a one-wire thermocouple to obtain local cold-wall heat-transfer rates. The tile is relatively fragile because of the brittle nature of the material and the structural weakness of the flat-sided configuration; however, a method was developed and used for repairing a cracked tile.

Avery, D. E.↗

Experiments to verify nonparallel stability theory at Virginia Polytechnic Institute and State University, Blacksburg, Virginia

The effects of normal mass injection and suction on boundary-layer stability and transition are studied on a flat plate. Titanium panels, in which 0.063 mm diameter holes were drilled on 0.635 mm centers, are inserted in the plate. Suction level and distribution are variable. Disturbances are introduced by means of a vibrating ribbon and measurements of both mean- and disturbance-flow velocities are made with a hot wire. Disturbance amplitudes are measured as a function of Reynolds number, frequency, and suction characteristics, and are compared with the previous results obtained over a Dynapore surface. Transition measurements under natural and forced conditions are also made. The stabilizing effects of suction are documented. It is also shown that very high local flow rates through the suction holes (which approach a hole Reynolds number of 300) do not destabilize the flow. On the other hand, weak blowing lowers the transition Reynolds number, but is found not to cause serious problems.

Saric, William S.↗

'Direct' Gas-Phase Metallicities, Stellar Properties, and Local Environments of Emission-Line Galaxies at Redshifts Below 0.90

Using deep narrow-band (NB) imaging and optical spectroscopy from the Keck telescope and the Multi Mirror Telescope (MMT), we identify a sample of 20 emission-line galaxies (ELGs) at z = 0.065-0.90 where the weak auroral emission line, [O iii] lambda4363, is detected at >=3sigma. These detections allow us to determine the gas-phase metallicity using the "direct" method. With electron temperature measurements, and dust attenuation corrections from Balmer decrements, we find that 4 of these low-mass galaxies are extremely metal-poor with 12+log(O/H) <= 7.65 or one-tenth solar. Our most metal-deficient galaxy has 12+log(O/H)= 7.24(+0.45 / −0.30) (95% confidence), similar to some of the lowest metallicity galaxies identified in the local universe. We find that our galaxies are all undergoing significant star formation with average specific star formation rate (SFR) of (100 Myra)(exp −1), and that they have high central SFR surface densities (average of 0.5 Solar M / yr/ sq. kpc). In addition, more than two-thirds of our galaxies have between one and four nearby companions within a projected radius of 100 kpc, which we find is an excess among star-forming galaxies at z =0.4 -- 0.85. We also find that the gas-phase metallicities for a given stellar mass and SFR lie systematically lower than the local stellar M-Z-(SFR) relation by approx. = 0.2 dex (2 sigma significance). These results are partly due to selection effects, since galaxies with strong star formation and low metallicity are more likely to yield [O iii] lambda4363 detections. Finally, the observed higher ionization parameter and high electron density suggest that they are lower redshift analogs to typical z approx. > 1 galaxies.

Direct↗

Large-area multi-crystal NaI/Tl/ detectors for X-ray and gamma-ray astronomy

An array of large multicrystal NaI(Tl) detectors was constructed and used in a balloon-borne experiment to observe weak transient bursts of cosmic origin. The array had an active area of about 1 sq m and was sensitive to photons above 50 keV. Localized bursts which were observed are attributed to long-lived phosphorescence following large energy deposits by cosmic rays in the crystals.

Fishman, G. J.↗

A theory for chorus generation by energetic electrons during substorms

Previous observations during magnetospheric substorms reveal the existence of relatively narrow band electromagnetic emissions occurring slightly above and below one half of the electron cyclotron frequency in the equatorial magnetosphere beyond the plasmapause. Between these two bands of emission there exists a gap of much lower emission intensity. In this paper an interpretation is presented for these chorus observations wherein the lower emission band is represented by whistler noise and the upper emission band is described by the lowest harmonic of the ordinary mode. These emissions are assumed to be locally generated at the observation point. Both emission bands are excited by power law-distributed energetic electrons with a variable spectral index and a weak loss cone feature. The form of these energetic electrons is similar to the forms observed simultaneously with the chorus emissions. The calculated growth rates show a frequency distribution similar to that of the measured emissions. In addition, the same energetic electron distribution can also produce the electrostatic gyroharmonic emissions often seen by observers in conjunction with chorus emissions during substorms.

Curtis, S. A.↗

More accurate predictions with transonic Navier-Stokes methods through improved turbulence modeling

Significant improvements in predictive accuracies for off-design conditions are achievable through better turbulence modeling; and, without necessarily adding any significant complication to the numerics. One well established fact about turbulence is it is slow to respond to changes in the mean strain field. With the 'equilibrium' algebraic turbulence models no attempt is made to model this characteristic and as a consequence these turbulence models exaggerate the turbulent boundary layer's ability to produce turbulent Reynolds shear stresses in regions of adverse pressure gradient. As a consequence, too little momentum loss within the boundary layer is predicted in the region of the shock wave and along the aft part of the airfoil where the surface pressure undergoes further increases. Recently, a 'nonequilibrium' algebraic turbulence model was formulated which attempts to capture this important characteristic of turbulence. This 'nonequilibrium' algebraic model employs an ordinary differential equation to model the slow response of the turbulence to changes in local flow conditions. In its original form, there was some question as to whether this 'nonequilibrium' model performed as well as the 'equilibrium' models for weak interaction cases. However, this turbulence model has since been further improved wherein it now appears that this turbulence model performs at least as well as the 'equilibrium' models for weak interaction cases and for strong interaction cases represents a very significant improvement. The performance of this turbulence model relative to popular 'equilibrium' models is illustrated for three airfoil test cases of the 1987 AIAA Viscous Transonic Airfoil Workshop, Reno, Nevada. A form of this 'nonequilibrium' turbulence model is currently being applied to wing flows for which similar improvements in predictive accuracy are being realized.

Johnson, Dennis A.↗

The physical mechanism of comet outbursts: An experiment

During a series of impact experiments into regolith-like powders at the NASA Ames Research Center Vertical Gun Facility in 1976, I observed and filmed a unique anomalous event that may illuminate outburst mechanisms in comets. During one test, a new batch of basalt powder (half the mass in particles less than 800 microns in diameter) retained some air pressure while the vacuum chamber was being evacuated. As a result, the projectile impacted into gas-charged regolith. Instead of ejecting the normal, relatively negligible amount of debris, the disturbance triggered a major eruption that lasted at least 18 seconds. The experimental results have been recently re-analyzed with reference to cometary phenomena. A series of frames from this eruption experiment are shown. The ejecta velocities of 150 to 300 cm/s would have been sufficient to drive debris into the coma of a comet nucleus smaller than a few kilometers diameter. The event suggests a mechanism for comet outbursts, discussed briefly by Hartmann et al.: the pore space in a layer of regolith, possibly with weak effective tensile strength, becomes gas charged as ice slowly sublimates. Once the effective tensile strength is exceeded by the gas pressure, the surface fails locally, triggering an eruption such as photographed here. This model is consistent with the emerging view of regolith materials on comets and is closest to the recent model of Rickman et al. The earlier models generally picture a more uniform flow of debris off the comet, not outbursts. Rickman et al. allow gas pressure to build until it matches the overburden pressure, followed by 'instantaneous blow-off'. They note that as soon as the mantle is found to be unstable, we consider it to be instantaneously swept away by the gas pressure. The main new points made here are that the experiment gives a more realistic view of the blow-off process after surface failure occurs, and the present model gives a recharge mechanism that can explain recurrent outbursts on comets such as P/Schwassmann-Wachmann 1 and 2060 Chiron. In fact, the resulting jets resemble distinct jet structures in high-resolution comet comae.

Hartmann, William K.↗

Warming of the Global Ocean: Spatial Structure and Water-Mass Trends

This study investigates the multidecadal warming and interannual-to-decadal heat content changes in the upper ocean (0-700 m), focusing on vertical and horizontal patterns of variability. These results support a nearly monotonic warming over much of the World Ocean, with a shift toward Southern Hemisphere warming during the well-observed past decade. This is based on objectively analyzed gridded observational datasets and on a modeled state estimate. Besides the surface warming, a warming climate also has a subsurface effect manifesting as a strong deepening of the midthermocline isopycnals, which can be diagnosed directly from hydrographic data. This deepening appears to be a result of heat entering via subduction and spreading laterally from the high-latitude ventilation regions of subtropical mode waters. The basin-average multidecadal warming mainly expands the subtropical mode water volume, with weak changes in the temperature-salinity (u-S) relationship (known as ''spice'' variability). However, the spice contribution to the heat content can be locally large, for example in Southern Hemisphere. Multidecadal isopycnal sinking has been strongest over the southern basins and weaker elsewhere with the exception of the Gulf Stream/North Atlantic Current/subtropical recirculation gyre. At interannual to decadal time scales, wind-driven sinking and shoaling of density surfaces still dominate ocean heat content changes, while the contribution from temperature changes along density surfaces tends to decrease as time scales shorten.

Global Ocean↗