Tidal studies from the perturbations in satellite orbits

1977 ◽  
Vol 284 (1326) ◽  
pp. 595-606 ◽  
Keyword(s):  
Numerical Models ◽  
Ocean Tide ◽  
Satellite Orbits ◽  
Phase Lag ◽  
Love Number ◽  
Orbital Theory ◽  
Long Wavelength ◽  
Orbital Perturbations ◽  
Tidal Potential ◽  
Tidal Perturbations

Tidal perturbations in the orbits of close Earth satellites permit the Love number K 2 and the phase lag ε 2 of the tidal effective Earth to be estimated. These parameters differ significantly from the nominal values of K 2 = 0.30 and ε 2 < 0.5° that would be expected if only the solid tide was important. This difference is due to the contribution of the oceans to the total tidal potential. This contribution is less well known than the solid tide potential and the study of the orbital perturbations permits an estimation of some of the long wavelength variations in the ocean tide. In this paper we discuss the method and the results obtained from two satellites for the S 2 and M 2 ocean tide. These tidal parameters are compared with and combined with numerical models of these tides to give improved parameters to be used in any orbital theory.

Effect of Spray-Wall Interaction On Thermoacoustic Instability Prediction by Flame Transfer Function and the Convective Time Delay Method

2021 ◽  
Author(s):  
Sheng Meng ◽  
Man Zhang
Keyword(s):  
Time Delay ◽  
Transfer Function ◽  
Numerical Models ◽  
Time Lag ◽  
Interaction Model ◽  
Phase Lag ◽  
Thermoacoustic Instability ◽  
Spray Flame ◽  
Wall Interaction ◽  
Definition Of

Abstract This study numerically investigates the effect of spray-wall interactions on thermoacoustic instability prediction. The LES-based flame transfer function (FTF) and the convective time delay methods are used by combining the Helmholtz acoustic solver to predict a single spray flame under the so-called slip and film spray-wall conditions. It is found that considering more realistic film liquid and a wall surface interaction model achieves a more accurate phase lag in both of the time lag evaluations compared to the experimental results. Additionally, the results show that a new time delay exists between the liquid film fluctuation and the unsteady heat release, which explains the larger phase value in the film spray-wall condition than in the slip condition. Moreover, the prediction capability of the FTF framework and the convective time delay methodology in the linear regime are also presented. In general, the instability frequency differences predicted using the FTF framework under the film condition are less than 10 Hz compared with the experimental data. However, an underestimation of the numerical gain value leads to requiring a change in the forcing position and an improvement in the numerical models. Due to the ambiguous definition of the gain value in the convective time delay method, this approach leads to arbitrary and uncertain thermoacoustic instability predictions.

scholarly journals Long secondary periods in luminous red giant variables

2019 ◽  
Vol 492 (1) ◽  
pp. 1348-1362 ◽  
Author(s):  
Masaki Takayama ◽  
Yoshifusa Ita
Keyword(s):  
Numerical Models ◽  
Colour Change ◽  
Light Curves ◽  
Red Giants ◽  
Radial Pulsation ◽  
Phase Lag ◽  
Dipole Mode ◽  
Near Ir ◽  
Stellar Pulsations ◽  
Red Giant

ABSTRACT The origin of long secondary periods (LSPs) in red giant variables is unknown. We investigate whether stellar pulsations in red giants can explain the properties of the LSP variability. VIJHKs light curves obtained by OGLE and the IRSF/SIRIUS survey in the Small Magellanic Cloud are examined. The sample of oxygen-rich LSP stars shows evidence of a phase lag between the light curves of optical and near-IR band. The change in radius contributes to the bolometric change roughly half as much as the change in temperature, implying that the change in effective temperature plays an important role in the luminosity change associated with the LSPs. We have created numerical models based on the spherical harmonics to calculate the light amplitudes of dipole mode variability and have found that the models can roughly reproduce the amplitude–amplitude relations (e.g. (ΔI, ΔH)). The LSP variability can be reproduced by the dipole mode oscillations with temperature amplitude of ≲100 and ≲150 K for oxygen-rich stars and most carbon stars, respectively. Radial pulsation models are also examined and can reproduce the observed colour change of the LSPs. However, there is still an inconsistency in length between the LSP and periods of radial fundamental mode. On the other hand, theoretical period–luminosity relations of the dipole mode corresponding to so-called oscillatory convective mode were roughly consistent with observation. Hence, our result suggests that the observations can be consistent with stellar pulsations corresponding to oscillatory convective modes.

The contraction of satellite orbits under the influence of air drag. VIII. Orbital lifetime in an oblate atmosphere, when perigee distance is perturbed by odd zonal harmonics in the geopotential

1987 ◽  
Vol 414 (1847) ◽  
pp. 271-295 ◽  
Keyword(s):  
Narrow Band ◽  
Great Majority ◽  
Satellite Orbits ◽  
Orbital Theory ◽  
Air Drag ◽  
Zonal Harmonics ◽  
The Earth ◽  
Upper Limits

This paper is devoted to developing the necessary orbital theory for predicting the lifetimes of satellites moving in an oblate atmosphere and subjected to the perturbations due to odd zonal harmonics in the geopotential. The effects of odd zonal harmonics and atmospheric oblateness are expressed as multiplying factors, F (oz) and F (ao), to be applied to the lifetime predictions calculated in the absence of the perturbations. The results are valid for the great majority of orbits about the Earth, and in particular for all orbital eccentricities between 0 and 1; but the limits set for the controlling parameters exclude ( a ) near-polar orbits with perigee heights lower than about 180 km, and ( b ) orbits having inclinations within a narrow band centred on 63.4°. The results show that, when the controlling parameters are at their upper limits, either F (oz) or F (ao) can change the lifetime by up to about 35%, and taken together they can produce changes of up to 60%, if the initial and final positions of perigee are at specified points on the orbit and the eccentricity exceeds 0.2. Such combinations of values rarely arise, however, and the effects are more often of order 10-20%. Even at these moderate levels, the effects need to be taken into account in order to make realistic estimates of the decay dates of satellites in the last few months of their lives.

New unconstrained global ocean tide solutions for satellite gravimetry including minor tides

2020 ◽  
Author(s):  
Roman Sulzbach ◽  
Henryk Dobslaw ◽  
Maik Thomas
Keyword(s):  
Numerical Models ◽  
Signal To Noise Ratio ◽  
Column Height ◽  
Global Ocean ◽  
Ocean Tide ◽  
Data Sets ◽  
Satellite Gravimetry ◽  
The North ◽  
The Individual ◽  
Ocean Tide Models

&lt;p&gt;The quality of global ocean tide models has increased drastically over the last decades due to the availability of dense open-ocean observations from satellite altimetry. In regions of poor altimetry coverage (e.g., polar seas and coastal areas) and for minor tides with a small signal-to-noise ratio, however, reliable estimates from unconstrained global numerical models are still (and will remain) critically important. We will present in this contribution recent results from the purely-hydrodynamic, barotropic tidal model TiME (Weis et al., 2008) that benefit from a newly introduced rotated grid avoiding the singularity at the North Pole; a revised scheme for dynamic feedbacks of self-attraction and loading; and revised bathymetry data-sets that also include water column height modifications in cavities underneath the Antarctic ice-shelves.&lt;/p&gt;&lt;p&gt;By focussing exemplarily on the M&lt;sub&gt;2&lt;/sub&gt; tide, we will demonstrate the individual impact of all those changes on the simulated water height variations. It will be shown that the effects of ice-shelf cavities extend well beyond the Southern Ocean and affect even amphidromic systems in the Northern Hemisphere. We will also emphasize the ability of unconstrained numerical models as TiME to explicitly simulate minor tidal lines, thereby allowing to thoroughly test (and subsequently improve) admittance-based methods currently employed for the processing of satellite gravimetry data from the GRACE and GRACE-FO missions.&lt;/p&gt;

scholarly journals The nodal dependence of long-period ocean tides in the Drake Passage

2018 ◽  
Author(s):  
Philip L. Woodworth ◽  
Angela Hibbert
Keyword(s):  
Tide Gauge ◽  
Drake Passage ◽  
Ocean Tide ◽  
Phase Lag ◽  
Tide Gauge Data ◽  
Long Period ◽  
The North ◽  
Ocean Tide Model ◽  
Gauge Data ◽  
Tidal Variability

Abstract. Almost three decades of bottom pressure recorder (BPR) measurements at the Drake Passage, and 31 years of hourly tide gauge data from Vernadsky station on the Antarctic Peninsula, have been used to investigate the temporal and spatial variations in this region of the three main long-period tides Mf, Mm and Mt (in order of decreasing amplitude, with periods of a fortnight, a month and third of a month respectively). The amplitudes of Mf and Mt, and the phase lags for all three constituents, vary over the nodal cycle (18.61 years) in essentially the same way as in the equilibrium tide, so confirming the validity of Doodson's nodal factors for these constituents. The amplitude of Mm is found to be essentially constant, and so inconsistent at the three-sigma level from the ±13 % (or ~ ±0.15 mbar) anticipated variation over the nodal cycle, which can probably be explained by energetic non-tidal variability in the records at monthly timescales and longer. The north-south differences in amplitude for all three constituents are consistent with those in a modern ocean tide model (FES2014), as are those in phase lag for Mf and Mt, while the difference for Mm is smaller than in the model. BPR measurements are shown to be superior to conventional tide gauge data in such tidal studies, thanks to the lower proportion of non-tidal variability in the records.

scholarly journals The global distribution of the M1 ocean tide

Ocean Science ◽  
2019 ◽  
Vol 15 (2) ◽  
pp. 431-442
Author(s):  
Philip L. Woodworth
Keyword(s):  
Tide Gauge ◽  
Local Level ◽  
Small Degree ◽  
Ocean Tide ◽  
Tide Gauge Records ◽  
Data Set ◽  
Worldwide Distribution ◽  
Tidal Potential ◽  
The Uk ◽  
First Time

Abstract. The worldwide distribution of the small degree-3 M1 ocean tide is investigated using a quasi-global data set of over 800 tide gauge records and a global tide model. M1 is confirmed to have a geographical variation in the Atlantic consistent with the suggestion of Platzman (1984b) and Cartwright (1975) that M1 is generated in the ocean as a consequence of the spatial and temporal overlap of M1 in the tidal potential and one (or at least a small number of) diurnal ocean normal mode(s). As a consequence, it is particularly strong around the UK and on North Sea coasts (amplitudes ∼10 mm). This analysis shows that their suggestion is also consistent to a great extent with the observed small amplitudes in the Pacific and Indian oceans. However, there are differences at the regional and local level which require much further study via more sophisticated ocean tidal modelling. By contrast, what is called the M1' tide (a combination of several degree-2 lines in the tidal potential with frequencies close to that of M1) is shown to have a geographical distribution consistent with expectations from other degree-2 diurnal tides, apart from locations such as around the UK where tidal interactions introduce complications. As far as I know, this is the first time that these small tidal constituents have been mapped on a global basis and, in particular, the first time that the ocean response to the degree-3 component of the tidal potential has been investigated globally.

The earth's variable rate of rotation: a discussion of some meterological and oceanic causes and consequences

1977 ◽  
Vol 284 (1326) ◽  
pp. 495-506 ◽  
Keyword(s):  
Earth’S Rotation ◽  
Satellite Orbits ◽  
Length Of Day ◽  
Variable Speed ◽  
Earth's Rotation ◽  
Factors Affecting ◽  
Zonal Winds ◽  
Tidal Changes ◽  
Tidal Perturbations ◽  
Frequency Variations

Aspects of the Earth’s variable speed of rotation, or variations in the length of day, and their geophysical consequences and causes are reviewed. Emphasis is placed on those areas which may benefit most from improved observations of the rotation rate. Seasonal changes in the length of day are primarily of meteorological origin. Zonal winds, in particular, play an important role, and year-to-year variations in the magni­tude of the seasonal rotational characteristics provide information on the variability of the year-to-year atmospheric circulation. Changes observed since 1955 in the annual and semi-annual change in the length of day indicate a decreasing strength of the zonal circulation at these frequencies. Changes observed in the astronomical biennial term indicate that the biennial zonal winds propagate downwards to variable depths and that it is of variable period. Higher-frequency variations in length of day are also primarily of meteorological origin and will mask or interfere with other geophysical factors affecting the Earth’s rotation, such as tides or earthquake caused changes in the inertia tensor. Thus improved observations of the variable rotation will have to be accom­panied by improved global compilations of zonal winds so that the meteorological contribution can be evaluated with equal accuracy. Present compilations of wind data are inadequate for this. An area where satellite observations can make an important contribution to studies of the Earth’s rotation concerns the separation of the secular tidal and non-tidal changes in length of day by studying the tidal perturbations in satellite orbits.

scholarly journals The nodal dependence of long-period ocean tides in the Drake Passage

Ocean Science ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 711-730 ◽  
Author(s):  
Philip L. Woodworth ◽  
Angela Hibbert
Keyword(s):  
Tide Gauge ◽  
Drake Passage ◽  
Ocean Tide ◽  
Phase Lag ◽  
Tide Gauge Data ◽  
Tide Gauge Records ◽  
Long Period ◽  
Ocean Tide Model ◽  
Gauge Data ◽  
Tidal Variability

Abstract. Almost three decades of bottom pressure recorder (BPR) measurements at the Drake Passage, and 31 years of hourly tide gauge data from the Vernadsky Research Base on the Antarctic Peninsula, have been used to investigate the temporal and spatial variations in this region of the three main long-period tides Mf, Mm and Mt (in order of decreasing amplitude, with periods of a fortnight, a month and one-third of a month, respectively). The amplitudes of Mf and Mt, and the phase lags for all three constituents, vary over the nodal cycle (18.61 years) in essentially the same way as in the equilibrium tide, so confirming the validity of Doodson's “nodal factors” for these constituents. The amplitude of Mm is found to be essentially constant, and so inconsistent at the 3σ level from the ±13 % (or ∼±0.15 mbar) anticipated variation over the nodal cycle, which can probably be explained by energetic non-tidal variability in the records at monthly timescales and longer. The north–south differences in amplitude for all three constituents are consistent with those in a modern ocean tide model (FES2014), as are those in phase lag for Mf and Mt, while the phase difference for Mm is smaller than in the model. BPR measurements are shown to be considerably superior to coastal tide gauge data in such studies, due to the larger proportion of non-tidal variability in the latter. However, correction of the tide gauge records for non-tidal variability results in the uncertainties in nodal parameters being reduced by a factor of 2 (for Mf at least) to a magnitude comparable (approximately twice) to those obtained from the BPR data.

Tidal loading in Nova Scotia: results from improved ocean tide models

1978 ◽  
Vol 15 (6) ◽  
pp. 981-993 ◽  
Author(s):  
Christopher Beaumont ◽  
Ross Boutilier
Keyword(s):  
Nova Scotia ◽  
Atlantic Ocean ◽  
North Atlantic ◽  
North Atlantic Ocean ◽  
Numerical Models ◽  
Ocean Tide ◽  
Ocean Tide Model ◽  
Phase Calibration ◽  
Tidal Loading ◽  
Ocean Tide Models

A re-examination of tilt and gravity observations from Nova Scotia in light of recent ocean tide studies confirms previous assertions that the M2 tide in the western North Atlantic Ocean is intermediate between the numerical models of Tiron, Sergeev, and Michurin, and of Zahel.Tilt calculations, using a new M2 ocean tide model, reinforce the conclusion that the crust beneath Nova Scotia is of a transitional type between oceanic and thickened continental and is more easily deformed than most other crustal types.The tilt observations are in poor agreement with the Jachens–Kuo model, JK25, of the O1 tide in the western North Atlantic Ocean. It is suggested that the gravity observations, from which JK25 was inferred, were subject to amplitude and phase calibration errors. These errors are estimated from a comparison with the M2 results.

scholarly journals The global distribution of the M1 ocean tide

2019 ◽  
Author(s):  
Philip L. Woodworth
Keyword(s):  
Tide Gauge ◽  
Local Level ◽  
Normal Modes ◽  
Small Degree ◽  
Ocean Tide ◽  
Tide Gauge Records ◽  
Data Set ◽  
Tidal Potential ◽  
The Uk ◽  
First Time

Abstract. The worldwide distribution of the small degree-3 M1 ocean tide is investigated using a quasi-global data set of over 800 tide gauge records and a global tide model. M1 is confirmed to have a geographical variation in the Atlantic consistent with the suggestion of Platzman and Cartwright that M1 is generated in the ocean as a consequence of the spatial and temporal overlap of M1 in the tidal potential and one (or at least a small number) of diurnal ocean normal modes. As a consequence, it is particularly strong around the UK and on North Sea coasts. This analysis shows that their suggestion is also consistent to a great extent with the observed small amplitudes in the Pacific and Indian Oceans. However, there are differences at the regional and local level which require much further study via more sophisticated ocean tidal modelling. By contrast, the M1' tide is shown to have a geographical distribution consistent with expectations from other degree-2 diurnal tides, apart from locations such as around the UK where tidal interactions introduce complications. As far as we know, this is the first time that these small tidal constituents have been mapped on a global basis and, in particular, the first time that the ocean response to the degree-3 component of the tidal potential has been investigated globally.

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