Tidal Displacement Research Articles

Prospect for Measuring Lunar Tidal Deformation and Displacement Love Numbers With Earth-Based Radar

Prospect for Measuring Lunar Tidal Deformation and Displacement Love Numbers With Earth-Based Radar

Evaluation of Tidal Effect in Long-Strip DInSAR Measurements Based on GPS Network and Tidal Models

A long-strip differential interferometric synthetic aperture radar (DInSAR) measurement based on multi-frame image mosaicking is currently the realizable approach to measure large-scale ground deformation. As the spatial range of the mosaicked images increases, the nonlinear variation of ground ocean tidal loading (OTL) displacements is more significant, and using plane fitting to remove the large-scale errors will produce large tidal displacement residuals in a region with a complex coastline. To conveniently evaluate the ground tidal effect on mosaic DInSAR interferograms along the west coast of the U.S., a three-dimensional ground OTL displacements grid is generated by integrating tidal constituents’ estimation of the GPS reference station network and global/regional ocean tidal models. Meanwhile, a solid earth tide (SET) model based on IERS conventions is used to estimate the high-precision SET displacements. Experimental results show that the OTL and SET in a long-strip interferogram can reach 77.5 mm, which corresponds to a 19.3% displacement component. Furthermore, the traditional bilinear ramp fitting methods will cause 7.2~20.3 mm residual tidal displacement in the mosaicked interferograms, and the integrated tidal constituents displacements calculation method can accurately eliminate the tendency of tidal displacement in the long-strip interferograms.

Effect of ion partitioning on an oscillatory electro-osmotic flow on solute transport process of fractional Jeffrey fluid through polyelectrolyte-coated nanopore with reversible wall reaction

The ion-partitioning effects on solute transport phenomena of time-periodic electro-osmotic flow in fractional Jeffrey fluid are investigated through a polyelectrolyte layer (PEL)-coated conical nanopore within a reactive wall whose ends are connected with two large reservoirs. By considering the ion-partitioning effects, analytical solutions for the induced potential and the axial velocity are presented, respectively, from the modified Poisson–Boltzmann equation and the Cauchy momentum equation with the proper constitutive equation of the fractional Jeffrey fluid model in the exterior and interior of the PEL. The analytic solution of the convection–diffusion for solute transport is established in the entire domain. The influence of the oscillating Reynolds number Rew, permittivity ratio εr between two mediums, relaxation time λ1ω, retardation time λ2ω, phase partitioning coefficient σp, PEL fixed charge density qfix, Debye–Hückel parameter κa, and softness parameter λs are investigated in this study. Asymptotic solution for the axial velocity was also presented for low-oscillating Reynolds numbers and validated. The maximum axial velocity occurs when the permittivity between the PEL and electrolyte is the same for all models. The volumetric flow rate decreases with the increase in the PEL thickness, positive PEL charge density, and softness parameter in our study. The volume flow rate of the Newtonian fluid increased 24.07% for Maxwell fluid (λ1ω=5, α = 1) and 11.56% for Jeffrey fluid (λ1ω=5, λ1ω=1, α = 1, and β=0.5), when κa=25, Rew = 10, qfix = 5, d = 0.2, εr=0.6, and λs=1.0. The mass transport rate increases with relaxation time, tidal displacement, and permittivity ratio between these layers.

Coastal wetland responses to a century of climate change in northern Sahara, Morocco

AbstractCoastal wetlands are highly sensitive to changes occurring at the coastline. It is critically important to determine region‐specific projections for these areas due to their specificities and vulnerabilities to climate change. This work aimed to value the impacts of recent climate changes at West Africa Sahara coastland, southern Morocco, at Khnifiss Lagoon. We have applied a combined approach using remote sensing techniques and environmental reconstructions based on high‐resolution analysis of sediment cores, covering the current warm period. Remote sensing highlighted changes to the lagoon inlet, accompanied by a greater meandering character of the tidal channels. As a response, the sediment cores have recorded a predominant vegetation substitution due to changes in the tidal limit, and an increase in organic carbon accumulation was observed. For the current climatology, during positive phases of the North Atlantic Oscillation, winds reaching the coast strengthen in an east‐to‐west direction. In the Khnifiss Lagoon, whose inlet is dominated by the ebb tide, the intensity and direction of the winds on the coast at surface level modifies its connection to the ocean by increasing sediment transport toward the interior of the lagoon. Locally biological responses to wind intensification, and possibly sea‐level rise, exemplify the lagoon sensitivity to large‐scale processes. Coastal vegetated wetlands are considered to be highly dynamic environments. However, we expect a loss of the upper tidal vegetation due to boundary conditions limiting the accommodation space in this arid environment in a possible future scenario of continuously inland tidal line displacement.

Comparison of GPS-derived ocean tide loading displacements with models in New Zealand

ABSTRACT We investigate the tidal displacement signals of two principle semidiurnal () and diurnal () tidal constituents in New Zealand. We calculate the predicted loading displacements using the latest ocean tide models and Earth models. The results show that, for the constituent, the tide models FES2014b and TPXO9-Atlas have subtle differences, and the vector differences between the Earth models shows that the regularity of the influence of the Earth model is weak. The vector difference of constituent have significant spatial coherence (about 0.2 mm). The residuals of constituent in the up component subtract about 0.2 mm across the entire areas after considering the anelastic dispersion. We find that the clear regional-scale spatial coherence of the residuals exists in both constituents in all models even if spatial water density and compressibility have been considered. However, the spatial coherence of residuals disappears when the network-mean value removed, and the reduction of RMS for constituent is close to the theoretical error of body tide (about 0.5 mm). We also find that for the different ocean tide models, part of the differences in residuals between the observations and predictions would be attributed to the choice of geocentric reference frame.

Global Drivers and Transport Mechanisms of Lunar Rockfalls

AbstractThe long‐ and short‐term drivers and transport mechanisms of lunar rockfalls are currently not well understood, but could provide valuable information about the geologic processes that still shape the surface of the Moon today. Here, we compare the global distribution of rockfalls with relevant geophysical data, such as seismic, topographic, thermal, gravity anomaly, and tidal displacement data sets. Rockfalls appear to predominantly occur (a) on equator‐facing slopes and thus in regions with large thermal amplitudes, (b) on slope angles well above‐average (Δ ∼ 10°), and (c) in regions with above‐average rock abundance. We do not observe a qualitatively or statistically relevant relation between rockfall abundance, monitored Apollo‐era shallow seismic activity, and the distribution of visible tectogenetic features. Informed by our global analysis, we conduct a targeted, in‐depth study of 687 rockfall boulders and trajectories in 13 sites across the Moon, including 7 craters, 2 volcanic vents, 2 tectonic structures, and 2 unclassified geomorphic regions. We identify four different source region types, where the type appears to control the occurrence of rockfalls. The source region type in turn is controlled by surface age rather than geomorphic context. We find that rockfall trajectories are mainly controlled by the trigger energy and the geometry of the slope. Our results suggest that erratic small‐scale impacts (mainly in old, Imbrian‐Nectarian, shallow terranes), aided by solar‐induced thermal fatigue of fractured bedrock (mainly in young, Copernican‐Eratosthenian steep terranes), were the dominant, global‐scale long‐ and short‐term drivers of rockfalls in the Moon's recent geologic past.

Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids.

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

Mathematical and numerical predictions for optimum perfect mixing by bulk convective oscillatory exchange

The mixing quality for bulk convective oscillatory exchange are analyzed, modeled, and simulated for 24 cases mathematically and numerically. A new mathematical model has been derived for heat and mass transfer between two reservoirs to predict the perfect and optimum mixing quality. Two-dimensional axisymmetric simulations are carried out for incompressible viscous oscillatory flows. The computations are run for two reservoirs that are connected by a short duct over a unique range of the fluid’s axial displacements. From the mathematical model, two new equations for the instantaneous temperature in each reservoir have been derived to predict the perfect mixing quality for any bulk convective oscillatory exchange. According to the computational predictions, the mass exchange between the two reservoirs has been classified into five different regions depending on their mixing quality. Optimum perfect mixing conditions were obtained at a normalized fluid’s axial tidal displacement S¯=4.9 with mixing ratio ranged from 97%to100%. A new correlation for predicting the rate of heat transfer enhancement by the bulk convective oscillatory exchange is suggested. It is observed that the effective thermal conductivity has been enhanced by up to O(106) compared with the molecular conductivity of the fluid. Also, the mixing quality for specific mass exchange conditions has enhanced up to160% compared with the perfect mixing case.

Hydrodynamics rheological impact of an oscillatory electroosmotic flow on a mass transfer process in a microcapillary with a reversible wall reaction

In this work, we carry out a theoretical analysis of the mass transport rate through a long microcapillary, with a reactive wall, connecting two reservoirs with different concentrations of some electro-neutral solute, caused by an oscillatory electroosmotic flow of a Jeffreys fluid. The mass transport enhancement relative to that caused only by molecular diffusion is found to be a function of the following dimensionless parameters: the angular Reynolds number Rω; the Deborah numbers De1 and De2, associated with the relaxation and retardation times, respectively; the Schmidt number Sc; the Damköhler number Da; the partition number σ̃; the tidal displacement ΔZ; and the ratio between the radius of the microcapillary and the Debye length κ̃. We find that for a viscoelastic fluid, there exists a resonant behavior of the mass transfer rate when the angular Reynolds number assumes specific values. In this context, we evidence that the interaction between the fluid elasticity and the oscillatory character of the flow enhances the mass transfer rate up to several orders of magnitude compared with that caused by an oscillatory electroosmotic flow of a Newtonian fluid. We also found that the microcapillary wall’s reactive characteristics, manifested through the Damköhler number and the dimensionless partitioning coefficient, could enhance or diminish the mass transfer rate depending on the interplay of the other dimensionless parameters involved in the analysis.

Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic (EMHD) flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflow systems. Through the theoretical analysis, we find that the effective diffusivity primarily depends on five dimensionless parameters, i.e., the curvature ratio of the curved channel, the Schmidt number, the tidal displacement, the angular Reynolds number, and the dimensionless electric field strength parameter. Based on the obtained results, we can precisely control the mass transfer characteristics of the EMHD flow in a curved rectangular microchannel by appropriately altering the corresponding parameter values.

Numerical Characterization of Viscous Heat Dissipation Rate in Oscillatory Air Flow

Abstract The effect of viscous heat dissipation (VHD) in raising the temperature field of incompressible oscillatory air flow is studied numerically. A threshold is established for when the viscous heat dissipation term in the thermal energy equation changes or does not change the temperature field for the case of oscillatory air flow in a tube connecting two reservoirs. This new criterion has not been specified clearly in earlier oscillatory flow research. According to the defined threshold and when VHD is important, the effect of dissipative bulk heating can be described by a proposed correlation in terms of Womersley number (Wo) and axial tidal displacement (ΔZ) of the oscillatory fluid. These results are determined using two-dimensional (2D) numerical simulations of laminar oscillatory air flow (Pr = 0.7) for different adiabatic unconductive tube-reservoirs' systems configurations over a wide range of oscillatory frequencies and tidal displacements. It is found that the low amount of fluid kinetic energy, which is converted into internal energy, is not sufficient to significantly heat up the fluid at a low rate of the viscous work. Therefore, the effect of viscous heat dissipation in oscillatory air flow can be ignored only below a specific limit of unsteadiness depending on Womersley number and axial tidal displacement. Also, the results showed that the VHD becomes more significant with increasing (Wo) and (ΔZ).

Augmenting NASA Europa Clipper by a small probe: Europa Tomography Probe (ETP) mission concept

The Jupiter's moon Europa is believed to be one of the few bodies in the Solar System able to host habitable environments. Compelling evidence for the existence of a subsurface ocean was provided by the magnetic field measurements carried out by the Galileo spacecraft.The NASA/JPL Europa Clipper mission is scheduled for launch in the early 2020s. Due to the harsh Jovian radiation environment and budget limitations, the initial concept of an orbiter was abandoned, and the spacecraft will perform only multiple flybys of the moon. Although Clipper will investigate the surface and subsurface properties with a powerful suite of instruments, such approach is not very favourable to a thorough investigation of Europa's deep interior structure.In 2015 the Europa Clipper project announced the possibility to carry an additional flight element with a mass of about 250 kg. We then started investigating a smallest mission aimed at regaining the original science objectives of Clipper for studying the deep interior structure of Europa. Although this additional mass is no longer available, we describe here a mission concept, based on a mothercraft-daughtercraft configuration, which could be of interest to future exploration missions. Our proposal is based on a small spacecraft, the Europa Tomography Probe (ETP), to be inserted in a polar orbit around Europa with a lifetime of a few months. ETP should carry only a magnetometer and a transponder for inter-satellite link, thus not foreseeing any direct link to ground. By exploiting the magnetic induction effect from Jupiter, the magnetometer will measure Europa's magnetic polarizability, thus providing information on the thickness and conductivity of the internal salty ocean, while the ETP transponder will enable a two-way relay link with the mother spacecraft during Europa flybys. The relay link will be used to transfer telemetry data and to carry out range rate measurements on board Clipper. This configuration minimizes the required power on ETP and provides high quality Doppler observables using an ultra-stable oscillator hosted on Clipper. The limiting noise in Doppler measurements will be the frequency stability of ETP and Clipper relay electronics. Doppler data allow the determination of Europa's static gravity field with high resolution along with its variable part due to eccentricity tides (Love number k2). Measurements of the moon's gravity also provide accurate data on its rotational state (e.g., Europa's obliquity and libration amplitude). Furthermore, the inter-satellite Doppler observables can improve the accuracy in the determination of Clipper's position relative to Europa at the level of a few meters in the radial direction. The precise positioning of the main spacecraft relative to Europa and the altimetric measurements from the radar REASON could be exploited to measure the tidal displacement (Love number h2) of the outer icy shell.The NASA's Europa Clipper is viewed as the first applicable study case for the mission concept presented in this paper, which is of general interest to a class of similar flyby missions that can be conceived not only for the Jovian system, but also for Saturn and the ice giants of the solar system, Uranus and Neptune. In the latter case, for example, a small orbiter of Triton could significantly boost the science return from a larger spacecraft focusing on the observation of the planet. In the case of Europa, we show that joint magnetic field, gravity, and possibly altimetric measurements, will place strong constraints on the deep interior structure of the moon and provide a good determination of the ice shell thickness and ocean depth.

Axial conduction and dissipation in oscillatory laminar pipe flow at low and high frequencies

The problem of fully developed laminar fluid flow in pipes, driven by an oscillatory pressure gradient, can be solved exactly for the time-dependent velocity field and related quantities such as flow rate and tidal displacement. When dissipation is neglected and the momentary axial variation of temperature is assumed to be linear, the corresponding thermal energy equation describing heat transfer along a pipe connecting two reservoirs at different temperatures can also be solved to yield exact solutions for the time-dependent temperature field, axial heat flux, and effective axial conductivity. In this paper, it is shown that these exact solutions for the unsteady temperature field are invalid at low Womersley numbers because the momentary axial variation of temperature is not linear. When the thermal energy equation is written in quasisteady form, approximate quasisteady analytical solutions can be found for the temperature field, which yield effective axial conductivities several orders of magnitude greater than those given by the low-Womersley-number, unsteady-flow solution. It is also shown that the conditions under which effects of dissipation on axial heat transfer become significant, at high Womersley numbers, can be determined by a simple criterion. When dissipation is significant, exact solutions for the unsteady temperature field are invalid at high Womersley numbers because the momentary axial variation of temperature is also nonlinear.

Accurate Evaluation of Vertical Tidal Displacement Determined by GPS Kinematic Precise Point Positioning: A Case Study of Hong Kong.

Global Positioning System (GPS) kinematic precise point positioning (KPPP) is an effective approach for estimating the Earth’s tidal deformation. The accuracy of KPPP is usually evaluated by comparing results with tidal models. However, because of the uncertainties of the tidal models, the accuracy of KPPP-estimated tidal displacement is difficult to accurately determine. In this paper, systematic vector differences between GPS estimates and tidal models were estimated by least squares methods in complex domain to analyze the uncertainties of tidal models and determine the accuracy of KPPP-estimated tidal displacements. Through the use of GPS data for 12 GPS reference stations in Hong Kong from 2008 to 2017, vertical ocean tide loading displacements (after removing the body tide effect) for eight semidiurnal and diurnal tidal constituents were obtained by GPS KPPP. By an in-depth analysis of the systematic and residual differences between the GPS estimates and nine tidal models, we demonstrate that the uncertainty of the tidal displacement determined by GPS KPPP for the M2, N2, O1, and Q1 tidal constituents is 0.2 mm, and for the S2 constituent it is 0.5 mm, while the accuracy of the GPS-estimated K1, P1, and K2 tidal constituents is weak because these three tidal constituents are affected by significant common-mode errors. These results suggest that GPS KPPP can be used to precisely constrain the Earth’s vertical tidal displacement in the M2, N2, O1, and Q1 tidal frequencies.

Physiological Validation of an Airborne Ultrasound Based Surface Motion Camera for a Contactless Characterization of Breathing Pattern in Humans.

Characterizing the breathing pattern in naturally breathing humans brings important information on respiratory mechanics, respiratory muscle, and breathing control. However, measuring breathing modifies breathing (observer effect) through the effects of instrumentation and awareness: measuring human breathing under true ecological conditions is currently impossible. This study tested the hypothesis that non-contact vibrometry using airborne ultrasound (SONAR) could measure breathing movements in a contactless and invisible manner. Thus, first, we evaluated the validity of SONAR measurements by testing their interchangeability with pneumotachograph (PNT) measurements obtained at the same time. We also aimed at evaluating the observer effect by comparing breathing variability obtained by SONAR versus SONAR-PNT measurements. Twenty-three healthy subjects (12 men and 11 women; mean age 33 years – range: 20–54) were studied during resting breathing while sitting on a chair. Breathing activity was described in terms of ventilatory flow measured using a PNT and, either simultaneously or sequentially, with a SONAR device measuring the velocity of the surface motion of the chest wall. SONAR was focused either anteriorly on the xiphoid process or posteriorly on the lower part of the costal margin. Discrete ventilatory temporal and volume variables and their coefficients of variability were calculated from the flow signal (PNT) and the velocity signal (SONAR) and tested for interchangeability (Passing-Bablok regression). Tidal volume (VT) and displacement were linearly related. Breathing frequency (BF), total cycle time (TT), inspiratory time (TI), and expiratory time (TE) met interchangeability criteria. Their coefficients of variation were not statistically significantly different with PNT and SONAR-only. This was true for both the anterior and the posterior SONAR measurements. Non-contact vibrometry using airborne ultrasound is a valid tool for measuring resting breathing pattern.

MRI Assessment of Global and Regional Diaphragmatic Motion in Critically Ill Patients Following Prolonged Ventilator Weaning.

Introduction: diaphragmatic dysfunction is a common cause of slow weaning in mechanically ventilated patients. Diaphragmatic dysfunction in ventilated patients can be global or regional. The aim of our study was to evaluate the motion of the entire diaphragm in patients who were ventilated for a protracted period in comparison with healthy controls by using Magnetic Resonance Imaging (MRI). Methods: Intensive care patients who had a prolonged ventilator wean and required tracheostomies were enrolled based on extensive exclusion criteria. MRI dynamic sequence and subtraction images were used to measure vertical displacement at five different points on each hemi-diaphragm during normal tidal breathing. Tidal displacement of each point on the right and left hemi-diaphragms of the patients were compared to the precise respective points on the right and left hemi-diaphragms of enrolled controls. Results: Eight intensive care patients and eight controls were enrolled. There were observed significant differences in the displacements of the left hemi-diaphragm between the two groups (median 6.4 mm [Interquartile range (IQR), 4.6–12.5]) vs. 11.6 mm [IQR, 9.5–14.5], p = 0.02). There were also observed significant differences in the displacements at five evaluated study points on the left hemi-diaphragms of the patients when compared to the precise respective points in controls, especially at the dome (median 6.7 mm [IQR, 5.0–11.4] vs. 13.5 mm [IQR 11.5-18], p value = 0.005) and the anterior zone of apposition (median 5.0 mm [IQR, 3.3–7.1] vs. 7.8mm [IQR, 7.1–10.5], p value = 0.01). The intensive care patients showed lower minimal and maximal values of displacement of right hemi-diaphragms compared to the controls, suggesting that the differences in the displacement of right hemi-diaphragm are possible; however, the differences in the mean values of displacement of right hemi-diaphragm between the intensive care patient group and the control group (median 9.8 mm [IQR (Interquartile range), 5.0–12.3] vs. 10.1 mm [IQR 8.3–18.5], p = 0.12) did not reach the level of significance. Conclusion: Although frequently global, diaphragm dysfunction in ventilated patients after prolonged ventilation can also be regional or focal when assessed by MRI dynamic sequence. The vertical displacement of both right and left hemi-diaphragms at various anatomical locations had different values in both controls, and patients. There were significant focal variations in the movement of diaphragm in patients with ventilator-induced diaphragmatic dysfunction.

基于云计算的潮汐桩智能变位系统车流量阈值及轨道设计

基于云计算的潮汐桩智能变位系统车流量阈值及轨道设计

X-ray and optical monitoring of the December 2017 outburst of the Be/X-ray binary AXJ0049.4–7323

AXJ0049.4–7323 (SXP 756) is a Be/X-ray binary that shows an unusual and poorly understood optical variability that consists of periodic and bright optical outbursts, simultaneous with X-ray outbursts, characterised by a highly asymmetric profile. The periodicity of the outbursts is thought to correspond to the orbital period of the neutron star. To understand the peculiar behaviour shown by this source, we performed the first multi-wavelength monitoring campaign during the periastron passage of December 2017. The monitoring lasted for about 37 days and consisted of X-ray, near-ultraviolet, and optical data from the Neil Gehrels Swift Observatory, the optical I band from the OGLE survey, and spectroscopic observations of the Hα line performed with the 3.9 m Anglo-Australian Telescope. These observations revealed AXJ0049.4–7323 during an anomalous outburst having remarkably different properties compared to the previous ones. In the I band, it showed a longer rise timescale (∼60 days instead of 1–5 days) and a longer decay timescale. At the peak of the outburst, it showed a sudden increase in luminosity in the I band, corresponding to the onset of the X-ray outburst. The monitoring of the Hα emission line showed a fast and highly variable profile composed of three peaks with variable reciprocal brightness. To our knowledge, this is the second observation of a variable three-peak Hα profile of a Be/X-ray binary, after A0535+26. We interpreted these results as a circumstellar disc warped by tidal interactions with the neutron star in a high eccentricity orbit during its periastron passage. The fast jump in optical luminosity at the peak of the outburst and the previous asymmetric outbursts might be caused by the reprocessing of the X-ray photons in the circumstellar disc or the tidal displacement of a large amount of material from the circumstellar disc or the outer layers of the donor star during the periastron passage of the neutron star, which led to an increase in size of the region emitting in the I band. Further multi-wavelength observations are necessary to discriminate among the different scenarios proposed to explain the puzzling optical and X-ray properties of AXJ0049.4–7323.

Experimental and numerical investigation of axial heat transfer enhancement by oscillatory flows

In the current study, axial heat transfer enhancements by laminar oscillatory flow between cold and hot reservoirs connected by a bundle of tubes are examined experimentally and numerically. The dimensionless frequency parameter, Womersley number Wo, ranged from 0.1 to 100 with different tidal displacements. Exceeding its molecular counterpart by about five orders of magnitude, the oscillatory thermal conductivity was enhanced with quadratic scaling on the tidal displacement or pressure-gradient amplitude, and the square root of the frequency of oscillation. Two correlations were suggested for the oscillatory thermal conductivity enhancement as a function of Wo and tidal displacement. The correlations showed that the axial heat transfer rate scaled in proportion to Wo1.62 for Wo > 3 and behaves exponentially for low Wo with different scales depending on pressure gradient amplitude. The study has proposed a classification for the oscillatory flow by partitioning the flow into four different regions varying from low tidal displacement to bulk convective exchange. The results also showed that for unsteady flow the unsteady axial conduction is negligible for Wo > 3, but becomes significant as it goes below Wo = 3. This criterion invalidates the previous studies’ assumption for Wo < 3 by ignoring the unsteady axial conduction. Finally, more than ten times of enhancement in axial heat transfer rate was observed in tubes with sufficient wall thickness. This non-zero thermal diffusivity at the interface between the fluid and the tube wall has improved the storage-release process through the Stokes layer.

Effects of unmodelled tidal displacements in GPS and GLONASS coordinate time-series

This study demonstrates the effect of unmodelled (sub-)daily tidal displacement on GLONASS (GLObalnaya NAvigatsionnaya Sputnikovaya Sistema) coordinate time series in comparison with GPS (Global Positioning System). More than two propagated periodic signals appear in GPS and GLONASS coordinate time series in the presence of an unmodelled M2 /O1 tidal displacements. The propagation mechanism of Stewart et al. (2005) explains well most of the periodic signals. At a fortnightly period, an unmodeled M2 tidal displacement propagates into two long-period signals at 13.6x (x is a positive integer) and 14.76 days for GPS, while only a significant propagated periodic signal at 14.76-day is discernible for GLONASS. Similarly, significant propagated periodic signals at 13.6x and 14.19 days for GPS and only at 14.19-day for GLONASS are evident as a result of an unmodeled O1 tidal displacement. However, an unmodeled Mf (long-period) results in a strong power of similar magnitude at 13.6x-day (∼13.66-day) for both GPS and GLONASS solutions. The appearance of different periodic signals but as a result of the same unmodelled tidal displacement is attributed to the different ground repeat periods of the constellations, which is one of the factors of the propagation mechanism from Stewart et al. (2005). The latter explains the reason why the 13.6x-day fortnightly is present only for GPS solutions. Comparing the powers of the M2 aliased periodic signals at 13.6x-day and 14.76-day from a stacked spectra over all stations, the amplitude of the former is larger than the latter by an order of magnitude. The results of this study may infer that the 13.6x-day periodic signal in GPS/GNSS (Global Navigation Satellite System) derived products of the IGS (International GNSS Service) is a joint contribution of the propagation of unmodelled (sub-)daily tidal displacements and errors at longer periods with the former appearing to contribute more. We also demonstrated that significant reduction of the propagated periodic signals can be achieved from combined-system solutions.