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NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗

NASA NTRS1993

The onset of electrohydrodynamic instability in isoelectric focusing

The onset of electrohydrodynamic motion associated with the imposition of an electric field across a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly over the depth of the layer. The variation of the conductivity is due to concentration gradients in the charge-carrying solutes and its spatio-temporal evolution is represented by a convective-diffusion equation. When the viscous relaxation time is long compared to the time for charge relaxation, the analysis reveals that the neutral stability curves for the layer can be characterized by three dimensionless parameters: Ra(sub e) is equivalent to d(epsilon)E(sup 2, sub 0) Delta sigma/mu K(sub eff) sigma(sub 0), an electrical Rayleigh number; delta sigma/sigma(sub 0), the relative conductivity increment; and alpha, the transverse wave number of the disturbance. Here d is the thickness, epsilon is the dielectric constant, and mu is the viscosity of layer, E(sub 0) is the applied field strength at the lower conductivity boundary, and K(sub eff) is an effective diffusivity associated with the Brownian motion of the charge-carrying solutes. With viscous-stress-free boundaries, at which the electrical conductivity and the normal component of the electric field are prescribed, the critical Ra(sub e) is 1.504 x 10(exp 4) at a critical transverse wave number of 1.97 when Delta sigma/sigma(sub 0) is 10. As Delta sigma/sigma(sub 0) increases, the critical Ra(sub e) increases and shifts to shorter wavelength disturbances; the critical imposed field strength, however, passes through a minimum because the lower-conductivity boundary exerts a considerable stabilizing influence in the presence of steep conductivity gradients. Similar trends were obtained for liquid layers with rigid boundaries.

Baygents, James C.↗

NASA NTRS1998

Bubble and Drop Nonlinear Dynamics (BDND)

Free drops and bubbles are weakly nonlinear mechanical systems that are relatively simple to characterize experimentally in 1-G as well as in microgravity. The understanding of the details of their motion contributes to the fundamental study of nonlinear phenomena and to the measurement of the thermophysical properties of freely levitated melts. The goal of this Glovebox-based experimental investigation is the low-gravity assessment of the capabilities of a modular apparatus based on ultrasonic resonators and on the pseudo- extinction optical method. The required experimental task is the accurate measurements of the large-amplitude dynamics of free drops and bubbles in the absence of large biasing influences such as gravity and levitation fields. A single-axis levitator used for the positioning of drops in air, and an ultrasonic water-filled resonator for the trapping of air bubbles have been evaluated in low-gravity and in 1-G. The basic feasibility of drop positioning and shape oscillations measurements has been verified by using a laptop-interfaced automated data acquisition and the optical extinction technique. The major purpose of the investigation was to identify the salient technical issues associated with the development of a full-scale Microgravity experiment on single drop and bubble dynamics.

Trinh, E. H.↗

NASA NTRS1973

The initiation, development, and decay of the secondary flow in a bounded jet

The secondary flow in a low aspect ratio incompressible turbulent bounded jet is described in terms of a near, middle, and far field in which the secondary motion is initiated, developed, and decayed, respectively. The initiation of the secondary flow is explained by the distortion of the planar vortex loops which bound the jet at the exit plane. In the region away from the bounding plates, the vortex loop distortion is similar to that found in rectangular free jets; however, the bounding plates cause an additional production of streamwise vorticity near the plates which has no counterpart in the free jet flow. Downstream of the jet core region, a large-scale secondary flow developes from this vorticity. Farther downstream the secondary flow decays; the resultant flow may be characterized as a combination of a plane jet and boundary layer flows. This explanation is supported by the vorticity and velocity data of this investigation.

Holdeman, J. D.↗

NASA NTRS1993

The Effects of Gravity on Wrinkled Laminar Flames

The effects of gravity are significant to the dynamics of idealized unconfined open premixed flames. Moderate to low turbulence Reynolds number flames, i.e., wrinkled laminar flames, of various unconfined geometries have been used extensively for investigating fundamental processes of turbulent flame propagation and to validate theoretical models. Without the wall constraints, the flames are free to expand and interact with surrounding ambient air. The flow field in which the flame exists is determined by a coupling of burner geometry, flame orientation and the gravity field. These complex interactions raise serious questions regarding the validity of comparing the experimental data of open flames with current theoretical and numerical models that do not include the effects of gravity nor effects of the larger aerodynamic flowfield. Therefore, studies of wrinkled laminar flame in microgravity are needed for a better understanding of the role of gravity on flame characteristics such as the orientation, mean aerodynamics stretch, flame wrinkle size and burning rate. Our approach to characterize and quantify turbulent flame structures under microgravity is to exploit qualitative and quantitative flow visualization techniques coupled with video recording and computer controlled image analysis technologies. The experiments will be carried out in the 2.2 second drop tower at the NASA Lewis Research Center. The longest time scales of typical wrinkled laminar flames in the geometries considered here are in the order of 10 msec. Hence, the duration of the drop is sufficient to obtain the amount of statistical data necessary for characterize turbulent flame structures.

Kostiuk, Larry W.↗

NASA NTRS2011

Global Assimilation of Multi-Sensor Snow Observations for Improved Characterization of Snow Processes

Snow conditions on the land surface are recognized to be key components of the global hydrological cycle as they play a critical role in the determination of local and regional climate. In many mid-latitude and high-latitude regions, the seasonal water storage and associated spring snowmelt dominate the local hydrology. The contribution to the runoff and moisture conditions from snow is vital in supporting agriculture and in determining water resources management practices. Consequently, accurate characterization of snow properties becomes important for both end-use applications and weather and climate research. Recently a joint effort between the u.S. Air Force and NASA has enabled a blended, multi-sensor snow product known as the AFWA NASA Snow Algorithm (ANSA). This global snow dataset has been generated by utilizing the Earth Observation System (EOS) Moderate Resolution Imaging Spectroradiometer (MODIS) and Advanced Microwave Scanning Radiometer for EOS (AMSR-E) datasets. ANSA product includes estimates of snow cover extent, snow water equivalent (SWE) and SWE-derived snow depth fields. The MODIS-based products enable snow cover mappings under cloud-free conditions whereas the passive microwave data from AMSR-E provides measurements under cloudy conditions. These remotely-sensed snow observations are further augmented with the information from ground-based snow measurements through data fusion techniques. The resulting ANSA products are employed in the NASA Land Information System (LIS) data assimilation framework, which provides a comprehensive environment for integrating community land surface models, ground and satellite-based observations, and ensemble-based data assimilation tools. LIS incorporates the multisensor ANSA snow retrievals with the land surface model estimates to generate spatially and temporally continuous estimates of snow states, through data assimilation. A suite of experiments to assimilate ANSA snow cover, SWE and snow depth estimates with different land surface models in LIS are conducted and the resulting estimates of snow conditions are evaluated against a number of in-situ observational datasets, over several regions of the world. These evaluations are used to compare and contrast the advantages and disadvantages of these multi-sensor snow observations.

Kumar, Sujay↗

NASA NTRS1973

Development and characteristics of free convection in the clear air as seen by radar and aircraft

Observations of the development of a convective field in clear air were made simultaneously using radar and an instrumented aircraft. The growth of the field as seen by the radar was compared with the characteristics of the temperature and humidity measurements made by aircraft at various times and locations within the convective depth. Probability distributions of the temperature and mixing ratio fluctuations exhibit distinct, identifiable characteristics for different regions within the field. The altitude of the aircraft measurement, referenced to the maximum altitude of the convective field at the time of the measurement, was found to be a usable parameter in the comparison of aircraft data and in the characterization of convective field growth. Using the relative height parameter, it was found that the area covered by convective cells (modified air) varies linearly with height in the upper reaches of the convective field. The characteristics of individual cells as seen by the radar and as deduced from the aircraft measurements are also discussed.

Konrad, T. G.↗

NASA NTRS2009

Measurement and Characterization of Space Shuttle Solid Rocket Motor Plume Acoustics

Lift-off acoustic environments generated by the future Ares I launch vehicle are assessed by the NASA Marshall Space Flight Center (MSFC) acoustics team using several prediction tools. This acoustic environment is directly caused by the Ares I First Stage booster, powered by the five-segment Reusable Solid Rocket Motor (RSRMV). The RSRMV is a larger-thrust derivative design from the currently used Space Shuttle solid rocket motor, the Reusable Solid Rocket Motor (RSRM). Lift-off acoustics is an integral part of the composite launch vibration environment affecting the Ares launch vehicle and must be assessed to help generate hardware qualification levels and ensure structural integrity of the vehicle during launch and lift-off. Available prediction tools that use free field noise source spectrums as a starting point for generation of lift-off acoustic environments are described in the monograph NASA SP-8072: "Acoustic Loads Generated by the Propulsion System." This monograph uses a reference database for free field noise source spectrums which consist of subscale rocket motor firings, oriented in horizontal static configurations. The phrase "subscale" is appropriate, since the thrust levels of rockets in the reference database are orders of magnitude lower than the current design thrust for the Ares launch family. Thus, extrapolation is needed to extend the various reference curves to match Ares-scale acoustic levels. This extrapolation process yields a subsequent amount of uncertainty added upon the acoustic environment predictions. As the Ares launch vehicle design schedule progresses, it is important to take every opportunity to lower prediction uncertainty and subsequently increase prediction accuracy. Never before in NASA s history has plume acoustics been measured for large scale solid rocket motors. Approximately twice a year, the RSRM prime vendor, ATK Launch Systems, static fires an assembled RSRM motor in a horizontal configuration at their test facility in Utah. The remaining RSRM static firings will take place on elevated terrain, with the nozzle exit plume being mostly undeflected and the landscape allowing placement of microphones within direct line of sight to the exhaust plume. These measurements will help assess the current extrapolation process by direct comparison between subscale and full scale solid rocket motor data.

Kenny, Jeremy↗

NASA NTRS1991

Seed particle response and size characterization in high speed flows

The response of seed particles ranging between 0.7 and 8.7 micron is determined using a phase Doppler particle analyzer which simultaneously measures particle size and velocity. The stagnant seed particles are entrained into a high speed free jet at velocities ranging from 40 to 300 m/s. The size-mean axial velocity correlation and size-rms velocity correlations are used to determine the particle response to the sudden acceleration. It was determined that at the lower speeds, seed particles up to approximately 5 microns are adequate, but as velocities approach 300 m/s only particles on the order of one micron are suitable. The ability to determine size and velocity simultaneously is essential if seeding with polydispersions is used since it allows the rejection of data which will not accurately represent the flow field.

Rudoff, Roger C.↗

NASA NTRS1999

Electric Field Induced Interfacial Instabilities

The study of the interface in a charge-free, critical and near-critical binary fluid in the presence of an externally applied electric field is presented. At sufficiently large fields, the interface between the two phases of the binary fluid should become unstable and exhibit an undulation with a predefined wavelength on the order of the capillary length. As the critical point is approached, this wavelength is reduced, potentially approaching length-scales such as the correlation length or critical nucleation radius. At this point the critical properties of the system may be affected. In this paper, the flat interface of a marginally polar binary fluid mixture is stressed by a perpendicular alternating electric field and the resulting instability is characterized by the critical electric field E(sub c) and the pattern observed. The character of the surface dynamics at the onset of instability is found to be strongly dependent on the frequency f of the field applied. The plot of E(sub c) vs. f for a fixed temperature shows a sigmoidal shape, whose low and high frequency limits are well described by a power-law relationship, E(sub c) = epsilon(exp zeta) with zeta = 0.35 and zeta = 0.08, respectively. The low-limit exponent compares well with the value zeta = 4 for a system of conducting and non-conducting fluids. On the other hand, the high-limit exponent coincides with what was first predicted by Onuki. The instability manifests itself as the conducting phase penetrates the non-conducting phase. As the frequency increases, the shape of the pattern changes from an array of bifurcating strings to an array of column-like (or rod-like) protrusions, each of which spans the space between the plane interface and one of the electrodes. For an extremely high frequency, the disturbance quickly grows into a parabolic cone pointing toward the upper plate. As a result, the interface itself changes its shape from that of a plane to that of a high sloping pyramid.

Kusner, Robert E.↗

NASA NTRS2000

Coupling, Q-Factor, and Integration Aspects of Microsphere Applications

With suggested applications varying from microlaser and cavity QED through optical locking of diode lasers to modulators and sensors, high-Q silica microspheres with whispering-gallery (WG) modes so far remain the subject of tabletop feasibility demonstrations. Despite the uniquely high quality-factor and submillimeter dimensions suitable for tight packaging, this novel type of high-finesse cavity still has to be adapted to fiber- and integrated-optic hardware. In the visible and near infrared-band experiments (633-850nm) measuring the ringdown time tau of free oscillations, Q = (0.6 to 0.8 ) x 10(exp 10) has been obtained in silica spheres of diameter -800 microns (corresponding tau = 3 to 4 microseconds). It was proved that under normal laboratory conditions, quality-factor is subject to deterioration within several-minute scale down to (2 ... 3 ) x 10(exp 9). The responsible mechanism was identified as adsorption of a monolayer of atmospheric water, so that preservation of the ultimate Q requires manipulation in dry environment, or fast packaging into sealed devices. Larger Q can be expected closer to minimum of attenuation in fused silica alpha = 0.2 dB/km; Q greater than or equal to 1 x 10(exp 11) at lambda=1.55 microns, with corresponding energy storage time tau approx. 0.1ms. Experiments are currently underway to determine whether this high Q can be realized experimentally. The evident difficulty is that OH-related optical absorption has its peaks located near the reported minimum of attenuation in silica. We can also mention here that some of proposed fiber materials, yet not ready for fiber drawing, have been predicted to have smaller attenuation than fused silica and may be suitable for microsphere fabrication (sodium-magnesium silicate glass, alpha = 0.06dB/km). WG modes possess very small radiative loss (it does not prevent Q-10(exp 20) and more) and therefore are electromagnetically isolated and cannot be excited by free-space beams. If no modification (such as grating) is made on the sphere surface, the coupling has to he provided by an appropriate near-field device. A systematic theoretical approach has been recently developed to quantify the performance of near-field couplers for WG modes. Efficient coupling can be obtained upon fulfillment of two main conditions: (1) mode matching and (2) sufficient coupling strength to provide the buildup of a WG mode with a given intrinsic loss. In other words, the wave in the coupler has to be phase-matched and sufficiently overlapped with the WG mode to provide enough buildup in the cavity. If the coupling efficiency is characterized by the fractional depth K(sup 2) of the resonance dip in intensity transmittance observed upon varying the frequency of the exciting wave in the coupler.

Ilchenko, V. S.↗

NASA NTRS1983

Coherent structures - Reality and myth

Large-scale coherent structures (CS) in turbulent shear flows are characterized, reviewing recent theoretical and experimental investigations. The use of computers as a research tool and the flow-visualization experimental technique are introduced, CS are defined, the history of their discovery is traced, and their main characteristics are listed. Topics discussed and illustrated include the initial condition of the free shear layer, triple and double decomposition, topological features of CS, detection and eduction of CS, phase alignment via cross correlation, induced versus natural structures, the bursting phenomenon, turbulent spot, streaks, bursting frequency, the axisymmetric mixing layer, vortex pairing in an axisymmetric jet, CS and jet noise, broadband noise amplification via pure-tone excitation, CS interaction in a plane-jet near field, the Taylor hypothesis applied to CS, negative production, and the validity of the Reynolds-number similarity hypothesis. It is found that the coherent Reynolds stress, vorticity, and production are not much greater than the time-averaged values for fully developed flows with significant incoherent turbulence, suggesting that the importance of CS may have been exaggerated in some recent studies.

Hussain, A. K. M. F.↗

NASA NTRS2010

An Assessment of the Surface Longwave Direct Radiative Effect of Airborne Saharan Dust During the NAMMA Field Campaign

In September 2006, NASA Goddard s mobile ground-based laboratories were deployed to Sal Island in Cape Verde (16.73degN, 22.93degW) to support the NASA African Monsoon Multidisciplinary Analysis (NAMMA) field study. The Atmospheric Emitted Radiance Interferometer (AERI), a key instrument for spectrally characterizing the thermal IR, was used to retrieve the dust IR aerosol optical depths (AOTs) in order to examine the diurnal variability of airborne dust with emphasis on three separate dust events. AERI retrievals of dust AOT are compared with those from the coincident/collocated multifilter rotating shadow-band radiometer (MFRSR), micropulse lidar (MPL), and NASA Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) sensors. The retrieved AOTs are then inputted into the Fu-Liou 1D radiative transfer model to evaluate local instantaneous direct longwave radiative effects (DRE(sub LW)) of dust at the surface in cloud-free atmospheres and its sensitivity to dust microphysical parameters. The top-of-atmosphere DRE(sub LW) and longwave heating rate profiles are also evaluated. Instantaneous surface DRE(sub LW) ranges from 2 to 10 W/sq m and exhibits a strong linear dependence with dust AOT yielding a DRE(sub LW) of 16 W/sq m per unit dust AOT. The DRE(sub LW) is estimated to be approx.42% of the diurnally averaged direct shortwave radiative effect at the surface but of opposite sign, partly compensating for the shortwave losses. Certainly nonnegligible, the authors conclude that DRE(sub LW) can significantly impact the atmospheric energetics, representing an important component in the study of regional climate variation.

Hansell, R. A.↗

NASA NTRS1989

X-ray/EUV optics for astronomy and microscopy; Proceedings of the Meeting, San Diego, CA, Aug. 7-11, 1989

Topics included in these proceedings are on X-ray/EUV zone plates, filters, and windows; X-ray/EUV microscopes, telescopes, and monochromators; the design, characterization, and test of multilayer optics; the fabrication of X-ray/EUV multilayer optics; and the design, characterization, and test of grazing incidence X-ray optics. Other topics are on the fabrication of grazing incidence X-ray optics, X-ray/EUV space observatories and missions, the test and calibration of X-ray/EUV instruments, X-ray polarimetry, and X-ray/EUV spectroscopy and instruments. Papers are presented on 8-keV X-ray zone plates, a cylindrical X-ray multilayer monochromator, multilayer mirrors for 182 A, advanced flow polishing of exotic optical materials, and optical analysis of grazing incidence ring resonators for free-electron lasers. Attention is also given to X-ray mirrors for the European Synchrotron Radiation Facility, the XUV wide-field camera for Rosat, an optical test and alignment method for the XMM mirror module, Bragg crystal polarimeters, and a liftoff process for multilayer phase gratings.

Hoover, Richard B.↗

NASA NTRS2005

Analysis of a Free Surface Film from a Controlled Liquid Impinging Jet over a Rotating Disk Including Conjugate Effects, with and without Evaporation

A detailed analysis of the liquid film characteristics and the accompanying heat transfer of a free surface controlled liquid impinging jet onto a rotating disk are presented. The computations were run on a two-dimensional axi-symmetric Eulerian mesh while the free surface was calculated with the volume of fluid method. Flow rates between 3 and 15 1pm with rotational speeds between 50 and 200 rpm are analyzed. The effects of inlet temperature on the film thickness and heat transfer are characterized as well as evaporative effects. The conjugate heating effect is modeled, and was found to effect the heat transfer results the most at both the inner and outer edges of the heated surface. The heat transfer was enhanced with both increasing flow rate and increasing rotational speeds. When evaporative effects were modeled, the evaporation was found to increase the heat transfer at the lower flow rates the most because of a fully developed thermal field that was achieved. The evaporative effects did not significantly enhance the heat transfer at the higher flow rates.

Sankaran, Subramanian↗

NASA NTRS2010

Photon Counting Using Edge-Detection Algorithm

New applications such as high-datarate, photon-starved, free-space optical communications require photon counting at flux rates into gigaphoton-per-second regimes coupled with subnanosecond timing accuracy. Current single-photon detectors that are capable of handling such operating conditions are designed in an array format and produce output pulses that span multiple sample times. In order to discern one pulse from another and not to overcount the number of incoming photons, a detection algorithm must be applied to the sampled detector output pulses. As flux rates increase, the ability to implement such a detection algorithm becomes difficult within a digital processor that may reside within a field-programmable gate array (FPGA). Systems have been developed and implemented to both characterize gigahertz bandwidth single-photon detectors, as well as process photon count signals at rates into gigaphotons per second in order to implement communications links at SCPPM (serial concatenated pulse position modulation) encoded data rates exceeding 100 megabits per second with efficiencies greater than two bits per detected photon. A hardware edge-detection algorithm and corresponding signal combining and deserialization hardware were developed to meet these requirements at sample rates up to 10 GHz. The photon discriminator deserializer hardware board accepts four inputs, which allows for the ability to take inputs from a quadphoton counting detector, to support requirements for optical tracking with a reduced number of hardware components. The four inputs are hardware leading-edge detected independently. After leading-edge detection, the resultant samples are ORed together prior to deserialization. The deserialization is performed to reduce the rate at which data is passed to a digital signal processor, perhaps residing within an FPGA. The hardware implements four separate analog inputs that are connected through RF connectors. Each analog input is fed to a high-speed 1-bit comparator, which digitizes the input referenced to an adjustable threshold value. This results in four independent serial sample streams of binary 1s and 0s, which are ORed together at rates up to 10 GHz. This single serial stream is then deserialized by a factor of 16 to create 16 signal lines at a rate of 622.5 MHz or lower for input to a high-speed digital processor assembly. The new design and corresponding hardware can be employed with a quad-photon counting detector capable of handling photon rates on the order of multi-gigaphotons per second, whereas prior art was only capable of handling a single input at 1/4 the flux rate. Additionally, the hardware edge-detection algorithm has provided the ability to process 3-10 higher photon flux rates than previously possible by removing the limitation that photoncounting detector output pulses on multiple channels being ORed not overlap. Now, only the leading edges of the pulses are required to not overlap. This new photon counting digitizer hardware architecture supports a universal front end for an optical communications receiver operating at data rates from kilobits to over one gigabit per second to meet increased mission data volume requirements.

Gin, Jonathan W.↗

NASA NTRS1985

Interstellar turbulence, random density variations, and scintillation measurements

The presence of random electron variations suggests that the ionized interstellar medium is turbulent. In the interstellar plasma the presence of power spectra of such variations extending to spatial scales much less than a Coulomb mean free path, Lambda sub c, is required by analyses of measurements of scintillation and angular broadening of pulsar radio signals. The existence of corresponding variations in magnetic field strength could efficiently scatter cosmic rays and thus constrain cosmic-ray propagation. Unfortunately both the origin of the electron density variations and mechanisms by which these variations couple to fluctuations in magnetic field strength are unknown. It is conjectured that the small-scale density variations are generated by the convective distortion of initially large-scale isobaric entropy structures in the turbulent interstellar plasma. An investigation of the spectra of turbulent entropy structures, velocity, and magnetic fields at small spatial scales is made. The modifier small is employed to characterize length scales much less than the dimension, L, containing the bulk of the turbulent energy.

Higdon, J. C.↗

NASA NTRS1980

Thermal Pollution Math Model. Volume 1. Thermal Pollution Model Package Verification and Transfer

Two three dimensional, time dependent models, one free surface, the other rigid lid, were verified at Anclote Anchorage and Lake Keowee respectively. The first site is a coastal site in northern Florida; the other is a man-made lake in South Carolina. These models describe the dispersion of heated discharges from power plants under the action of ambient conditions. A one dimensional, horizontally-averaged model was also developed and verified at Lake Keowee. The data base consisted of archival in situ measurements and data collected during field missions. The field missions were conducted during winter and summer conditions at each site. Each mission consisted of four infrared scanner flights with supporting ground truth and in situ measurements. At Anclote, special care was taken to characterize the complete tidal cycle. The three dimensional model results compared with IR data for thermal plumes on an average within 1 C root mean square difference. The one dimensional model performed satisfactorily in simulating the 1971-1979 period.

Lee, S. S.↗