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Near-planar TS waves and longitudinal vortices in channel flow - Nonlinear interaction and focussing

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an O(1) relative amount. All the types of nonlinear interaction, however, can result in the formation of focused responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Hall, Philip↗

The Dos and Don'ts of how to Build a Planet, Using the Moon as an Example

The bulk chemical compositions of planets may yield important clues concerning planetary origins. Failing that, bulk compositions are still important, in that they constrain calculation of planetary mineralogies and also constrain the petrogenesis of basaltic magmas. In the case of the Earth, there is little or no debate about the composition of the Earth's upper mantle. This is because our sample collections contain peridotitic xenoliths of that mantle. The most fertile of these are believed to have been little modified from their primary compositions. Using these samples and chondritic meteorites as a starting point, small perturbations on the compositions of existing samples allow useful reconstruction of the bulk silicate Earth (BSE). Elsewhere, I have argued that the next simplest case is the Eucrite Parent Body (EPB). Reconstructions based on Sc partitioning indicate that the EPB can be well approximated by a mixture of 20% eucrite and 80% equilibrium olivine. This leads to a parent body that is similar to CO (or devolatilized CM) chondrites. Partial melting experiments on CM chondrites confirm this model, because the residual solids in these experiments are dominated by olivine with minor pigonite [3]. The most difficult bodies to reconstruct are those that have undergone the most differentiation. Both the Moon and Mars may have passed through a magma ocean stage. In any event, lunar and martian basalts, unlike eucrites, were not derived from undifferentiated source regions. Reconstructions are primarily based on compositional trends within the basalts themselves with some critical assumptions: (i) Refractory lithophile elements (Ca, Al, REE, actinides) are presumed to be in chondritic relative abundances; and (ii) some major element ratio is believed to exist in a chondritic ratio (e.g., Mg/Si, Mg/Al). The most commonly used parameter is Mg/Si.

Jones, J. H.↗

Comparison of Land Skin Temperature from a Land Model, Remote Sensing, and In-situ Measurement

Land skin temperature (Ts) is an important parameter in the energy exchange between the land surface and atmosphere. Here hourly Ts from the Community Land Model Version 4.0, MODIS satellite observations, and in-situ observations in 2003 were compared. Compared with the in-situ observations over four semi-arid stations, both MODIS and modeled Ts show negative biases, but MODIS shows an overall better performance. Global distribution of differences between MODIS and modeled Ts shows diurnal, seasonal, and spatial variations. Over sparsely vegetated areas, the model Ts is generally lower than the MODIS observed Ts during the daytime, while the situation is opposite at nighttime. The revision of roughness length for heat and the constraint of minimum friction velocity from Zeng et al. [2012] bring the modeled Ts closer to MODIS during the day, and have little effect on Ts at night. Five factors contributing to the Ts differences between the model and MODIS are identified, including the difficulty in properly accounting for cloud cover information at the appropriate temporal and spatial resolutions, and uncertainties in surface energy balance computation, atmospheric forcing data, surface emissivity, and MODIS Ts data. These findings have implications for the cross-evaluation of modeled and remotely sensed Ts, as well as the data assimilation of Ts observations into Earth system models.

Modeling↗

An Analysis of Spatio-Temporal Relationship between Satellite-Based Land Surface Temperature and Station-Based Near-Surface Air Temperature over Brazil

A better understanding of the relationship between land surface temperature (Ts) and near-surface air temperature (Ta) is crucial for improving the simulation accuracy of climate models, developing retrieval schemes for soil and vegetation moisture, and estimating large-scale Ta from satellite-based Ts observations. In this study, we investigated the relationship between multiple satellite-based Ts products, derived from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Aqua satellite, and Ta from 204 meteorological stations over Brazil during 2003–2016. Monthly satellite-based Ts products used in this study include: (1) AIRS Version 6 with 1° spatial resolution, (2) AIRS Version 7 with 1° spatial resolution, (3) MODIS Collection 6 with 0.05° spatial resolution, and (4) MODIS Collection 6 with 1° spatial resolution re-sampled from (3) for a direct comparison with AIRS products. We found that satellite-based Ts is lower than Ta over the forest area, but higher than Ta over the non-forest area. Nevertheless, the correlation coefficients (R) between monthly Ta and four Ts products during 2003–2016 are greater than 0.8 over most stations. The long-term trend analysis shows a general warming trend in temperatures, particularly over the central and eastern parts of Brazil. The satellite products could also observe the increasing Ts over the deforestation region. Furthermore, we examined the temperature anomalies during three drought events in the dry season of 2005, 2010, and 2015. All products show similar spatio-temporal patterns, with positive temperature anomalies expanding in areal coverage and magnitude from the 2005 to 2015 event. The above results show that satellite-based Ts is sensitive in reflecting environmental changes such as deforestation and extreme climatic events, and can be used as an alternative to Ta for climatological studies. Moreover, the observed differences between Ts and Ta may inform how thermal assumptions can be improved in satellite-based retrievals of soil and vegetation moisture or evapotranspiration.

land surface temperature↗

Streaming Instability with Multiple Dust Species – I. Favourable Conditions for the Linear Growth

A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth time-scale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles tomutually validate and study the unstablemodes of the instability in more detail.We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution [Ts, min, Ts, max] and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary is not appreciably sensitive to q or Ts, min.With a wide range of dust sizes present in the disc (e.g. Ts, min  10−3), the growth rate in the slow-growth regime decreases as more dust species are considered.With a narrow range of dust sizes (e.g. Ts, max/Ts, min = 5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by ε  1 or Ts, max  1, which may represent the favourable conditions for planetesimal formation.

Zhaohuan Zhu↗

Accessing Recent Trend of Land Surface Temperature from Satellite Observations

Land surface temperature (Ts) is an important element to measure the state of terrestrial ecosystems and to study surface energy budgets. In support of the land cover/land use change-related international program MAIRS (Monsoon Asia Integrated Regional Study), we have collected global monthly Ts measured by MODIS since the beginning of the missions. The MODIS Ts time series have approximately 11 years of data from Terra since 2000 and approximately 9 years of data from Aqua since 2002, which makes possible to study the recent climate, such as trend. In this study, monthly climatology from two platforms are calculated and compared with that from AIRS. The spatial patterns of Ts trends are accessed, focusing on the Eurasia region. Furthermore, MODIS Ts trends are compared with those from AIRS and NASA's atmospheric assimilation model, MERRA (Modern Era Retrospective-analysis for Research and Applications). The preliminary results indicate that the recent 8-year Ts trend shows an oscillation-type spatial variation over Eurasia. The pattern is consistent for data from MODIS, AIRS, and MERRA, with the positive center over Eastern Europe, and the negative center over Central Siberia. The calculated climatology and anomaly of MODIS Ts will be integrated into the online visualization system, Giovanni, at NASA GES DISC for easy use by scientists and general public.

Shen, Suhung↗

Trajectory Specification Applied to Terminal Airspace

Despite major efforts to automate air traffic control (ATC), it is still performed by humans today. The complexity and safety-criticality of ATC makes it very difficult to safely automate, but it must be automated to increase airspace capacity (the density of traffic that can be safely managed) and airport throughput (the number of arrivals and departures that an airport can safely handle in a given period of time) beyond what is possible with human controllers. This paper presents the Trajectory Specification (TS) concept, which can help to safely automate ATC. TS is a method of specifying aircraft trajectories such that the position at any given time in flight is restricted to a precisely defined bounding space, removing all ambiguity as to where the flight is allowed to be. The bounding space or volume is determined by tolerances relative to a reference trajectory (position as a function of time). The tolerances are dynamic and are based on the aircraft navigation capabilities and the traffic situation. The tolerances can be a piecewise linear function of time or distance along the route, allowing the tolerances to vary as needed, typically increasing with time for departures and decreasing for arrivals. A Trajectory Specification Language (TSL) is proposed for communicating trajectories from aircraft to ATC as requests and from ATC to aircraft as assignments. The TS concept requires a new generation of airborne Flight Management Systems (FMS) that understand the TSL and can fly the assigned trajectories, but this paper focuses on the ATC functions and the prototype ATC algorithms and software that were developed to test the TS concept. Assuming conformance, TS can guarantee safe separation for an arbitrary length of time even in the event of an ATC system or communication outage. It can help to achieve the high level of safety and reliability needed for ATC automation, and it can also reduce the reliance on ATC backup systems for tactical conflict detection and resolution during normal operation. TS can be applied to any controlled airspace, including enroute, terminal, and urban airspace, but this paper presents algorithms and software for arrival spacing and conflict detection and resolution in the terminal airspace serving a major airport. In a fast-time simulation of a full day of traffic in a major terminal airspace, all conflicts were resolved in near real time, demonstrating the computational feasibility and the preliminary operational feasibility of the TS concept. This paper is a compilation of previous papers, and it adds significant information that was omitted from those papers due to length limitations. It also updates some of the results of those earlier papers due to algorithm refinements and corrections of minor software errors.

air traffic control, trajectory↗

On the interaction of stationary crossflow vortices and Tollmien-Schlichting waves in the boundary layer on a rotating disc

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete among themselves. The interaction is considered of two types of instability mode (at an asymptotically large Reynolds number) which can occur in the flow above a rotating disc. In particular, the interaction is examined between lower branch Tollmien-Schlichting (TS) waves and the upper branch, stationary, inviscid crossflow vortex whose asymptotic structure has been described by Hall (1986). This problem is studied in the context of investigating the effect of the vortex on the stability characteristics of a small TS wave. Essentially, it is found that the primary effect is felt through the modification to the mean flow induced by the presence of the vortex. Initially, the TS wave is taken to be linear in character and it is shown (for the cases of both a linear and a nonlinear stationary vortex) that the vortex can exhibit both stabilizing and destabilizing effects on the TS wave and the nature of this influence is wholly dependent upon the orientation of this latter instability. Further, the problem is examined with a larger TS wave, whose size is chosen so as to ensure that this mode is nonlinear in its own right. An amplitude equation for the evolution of the TS wave is derived which admits solutions corresponding to finite amplitude, stable, traveling waves.

Bassom, Andrew P.↗

On the interaction of stationary crossflow vortices and Tollmien-Schlichting waves in the boundary layer on a rotating disc

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete among themselves. The interaction is considered of two types of instability mode (at an asymptotically large Reynolds number) which can occur in the flow above a rotating disc. In particular, the interaction is examined between lower branch Tollmien-Schlichting (TS) waves and the upper branch, stationary, inviscid crossflow vortex whose asymptotic structure has been described by Hall (1986). This problem is studied in the context of investigating the effect of the vortex on the stability characteristics of a small TS wave. Essentially, it is found that the primary effect is felt through the modification to the mean flow induced by the presence of the vortex. Initially, the TS wave is taken to be linear in character and it is shown (for the cases of both a linear and a nonlinear stationary vortex) that the vortex can exhibit both stabilizing and destabilizing effects on the TS wave and the nature of this influence is wholly dependent upon the orientation of this latter instability. Further, the problem is examined with a larger TS wave, whose size is chosen so as to ensure that this mode is nonlinear in its own right. An amplitude equation for the evolution of the TS wave is derived which admits solutions corresponding to finite amplitude, stable, traveling waves.

Bassom, Andrew P.↗

Skeletal unloading and dietary copper depletion are detrimental to bone quality of mature rats

This study was designed to examine the skeletal response to copper depletion and mechanical unloading in mature animals. In a 2 x 2 experimental design, 5.5-mo-old male Sprague-Dawley rats (n = 36) consumed either the control (AIN-93M) or Cu-depletion ((-)Cu) diet beginning 21 d before suspension and throughout the remainder of the study. Half of the rats in each dietary treatment group were either tail-suspended (TS) or kept ambulatory (AMB) for 28 d. Lower bone mineral densities (BMD) of 5th lumbar vertebra (L5) (P < 0.05) and femur were observed with (-)Cu and TS, but no differences were noted in the BMD of the humerus. Mechanical strength in the femur and vertebra decreased in response to TS, but were unaffected by copper depletion. Urinary deoxypyridinoline, an index of bone resorption, was significantly greater in TS rats, but unaltered by (-)Cu. No changes in serum or bone alkaline phosphatase activity, an indicator of bone formation, were observed. Our findings suggest that TS and (-)Cu decreased BMD in unloaded femur and vertebra but had no effect on normally loaded humerus. Bone loss with TS appeared to be related to accelerated bone resorption. Alterations in bone metabolism and bone mechanical properties in the mature skeleton resulting from (-)Cu warrant further investigation.

NASA Discipline Musculoskeletal↗

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body gravitation with the J2 spherical harmonic, other body gravitation, thrust, constant atmospheric drag from Earth's atmosphere, and solar radiation pressure for a sphere under constant illumination. The purpose of this Engineering Note is to demonstrate the performance of TS integration in an operational trajectory analysis code and to compare it with a standard method, eighth-order RKF. Results show that TS is 16.6 times faster on average and is more accurate in 87.5% of the cases presented.

Scott, James R.↗

The Effect of Acoustic Forcing on Instabilities and Breakdown in Swept-Wing Flow over a Backward-Facing Step

Instability interaction and breakdown were experimentally investigated in the flow over a swept backward-facing step. Acoustic forcing was used to excite the Tollmien-Schlichting (TS) instability and to acquire phase-locked results. The phase-averaged results illustrate the complex nature of the interaction between the TS and stationary cross flow instabilities. The weak stationary cross flow disturbance causes a distortion of the TS wavefront. The breakdown process is characterized by large positive and negative spikes in velocity. The positive spikes occur near the same time and location as the positive part of the TS wave. Higher-order spectral analysis was used to further investigate the nonlinear interactions between the TS instability and the traveling cross flow disturbances. The results reveal that a likely cause for the generation of the spikes corresponds to nonlinear interactions between the TS, traveling cross flow, and stationary cross flow disturbances. The spikes begin at low amplitudes of the unsteady and steady disturbances (2-4% U (sub e) (i.e. boundary layer edge velocity)) but can achieve very large amplitudes (20-30 percent U (sub e) (i.e. boundary layer edge velocity)) that initiate an early, though highly intermittent, breakdown to turbulence.

Eppink, Jenna L.↗

Constraints on Climate and Habitability for Earth-like Exoplanets Determined from a General Circulation Model

Conventional definitions of habitability require abundant liquid surface water to exist continuously over geologic timescales. Water in each of its thermodynamic phases interacts with solar and thermal radiation and is the cause for strong climatic feedbacks. Thus, assessments of the habitable zone require models to include a complete treatment of the hydrological cycle over geologic time. Here, we use the Community Atmosphere Model from the National Center for Atmospheric Research to study the evolution of climate for an Earth-like planet at constant CO2, under a wide range of stellar fluxes from F-, G-, and K-dwarf main sequence stars. Around each star we find four stable climate states defined by mutually exclusive global mean surface temperatures (Ts); snowball (Ts ≤ 235 K), waterbelt (235 K ≤ Ts ≤ 250 K), temperate (275 K ≤ Ts ≤ 315 K), and moist greenhouse (Ts ≥ 330 K). Each is separated by abrupt climatic transitions. Waterbelt, temperate, and cooler moist greenhouse climates can maintain open-ocean against both sea ice albedo and hydrogen escape processes respectively, and thus constitute habitable worlds. We consider the warmest possible habitable planet as having Ts ∼ 355 K, at which point diffusion limited water-loss could remove an Earth ocean in ∼1 Gyr. Without long timescale regulation of non-condensable greenhouse species at Earth-like temperatures and pressures, such as CO2, habitability can be maintained for an upper limit of ∼2.2, ∼2.4, and ∼4.7 Gyr around F-, G-, and K-dwarf stars respectively, due to main sequence brightening.

Eric T Wolf↗

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Thermal Expansion (DTE) Thermal Switch (TS) for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the TS operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center (MSFC) including the vibration (vibe) test, pre-vibe thermal vacuum (t-vac) cycle test, post-vibe t-vac cycle test, and long duration t-vac cycle test. The data collected from the pre- and post-vibe tests are compared to show the impact of the vibe test on performance. The data collected from the long duration test is used to calculate the total thermal contact conductance through the TS interfaces for both ‘on’ (TS closed, during hot plateau) and ‘off’ (TS open, during cold plateau) configurations, and the turndown ratio is also calculated. Challenges experienced throughout testing are also discussed.

Thermal control technology↗

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Expansion Thermal Switch for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the thermal switch (TS) operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center including the pre-vibe thermal vacuum cycle test, vibration test, post-vibe thermal vacuum cycle test, and long duration thermal vacuum cycle test. The pre- and post-vibe thermal cycle and the long duration cycle test tested to hot and cold plateau initial temperatures of 40 °C, and -173 °C, respectively. The pre- and post-vibe tests required plateau holds of at least 2 hours, whereas the long duration cycle test required plateau holds of at least 20 hours. The tests each used a rate of temperature change of < 2 °C/min when transitioning between plateaus. The data collected from each thermal test is compared to show the operation of the TS both before and after the vibration test to GEVS levels, and throughout the long duration cycle test. From the data collected, the total conductance through the TS interfaces is calculated for both on (TS closed – during hot plateau) and off (TS open – during cold plateau) configurations, and the turndown ratio is also calculated. Challenges and lessons learned from the testing are also discussed.

thermal control technology↗

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Thermal Expansion (DTE) Thermal Switch (TS) for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the TS operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center (MSFC) including the vibration (vibe) test, pre-vibe thermal vacuum (t-vac) cycle test, post-vibe t-vac cycle test, and long duration t-vac cycle test. The data collected from the pre- and post-vibe tests are compared to show the impact of the vibe test on performance. The data collected from the long duration test is used to calculate the total thermal contact conductance through the TS interfaces for both ‘on’ (TS closed, during hot plateau) and ‘off’ (TS open, during cold plateau) configurations, and the turndown ratio is also calculated. Challenges experienced throughout testing are also discussed.

Thermal control technology↗