On some properties of Venedikov's method of tidal analysis

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On the tidal heating of Enceladus

Enceladus, one of Saturn's moons, shows significant volcanic activity identified by the Cassini spacecraft. The aim of the present study is to investigate – with the adaptation of mathematical tools used in geodynamics – the extent of tidal heating due to the mean motion resonance with Dione. For the purpose of calculations a two-layer model of Enceladus was used. The inner part of the model is a “rocky core” with a relative radius 0.55, while the outer part is composed of water ice. The results of model calculations show that the effective tidal heating is not uniformly distributed within Enceladus. It was found for the selected model of Enceladus, that the tidal heating is maximum within the depth interval (25–75) km. Due to the inhomogeneity within Enceladus, 85% of the tidal energy is generated in a volume that contains just 39% of its mass. In time intervals of 3.0 × 10⁸ and 5.3 × 10⁸ years the temperature increase in the relative depth range 0.70 ≤ r/a_E ≤ 0.90 is approximately 270 and 370 K, respectively.     

On the comparison of tidal gravity parameters with tidal models in central Europe

Two accurately calibrated superconducting gravimeters (SGs) provide high quality tidal gravity records in three central European stations: C025 in Vienna and at Conrad observatory (A) and OSG050 in Pecný (CZ). To correct the tidal gravity factors from ocean loading effects we compared the load vectors from different ocean tides models (OTMs) computed with different software: OLFG/OLMP by the Free Ocean Tides Loading Provider (FLP), ICET and NLOADF. Even with the recent OTMs the mass conservation is critical but the methods used to correct the mass imbalance agree within 0.1 nm/s². Although the different software agrees, FLP probably provides more accurate computations as this software has been optimised. For our final computation we used the mean load vector computed by FLP for 8 OTMs (CSR4, NAO99, GOT00, TPX07, FES04, DTU10, EOT11a and HAMTIDE). The corrected tidal factors of the 3 stations agree better than 0.04% in amplitude and 0.02° in phase. Considering the weighted mean of the three stations we get for O1 δ_c = 1.1535 ± 0.0001, for K1 δ_c = 1.1352 ± 0.0003 and for M2 δ_c = 1.1621 ± 0.0003. These values confirm previous ones obtained with 16 European stations. The theoretical body tides model DDW99/NH provides the best agreement for M2 (1.1620) and MATH01/NH for O1 (1.1540) and K1 (1.1350). The largest discrepancy is for O1 (0.05%). The corrected phase α_c does not differ significantly from zero except for K1 and S2. The calibrations of the two SG's are consistent within 0.025% and agree with Strasbourg results within 0.05%.     

On some of the properties of the discrete model of turbulent diffusion

Zusammenfassung Den Prozess der Übertragung passiver Substanz im Felde der turbulenten Strömung untersuchen wir an einem Modell der zufälligen Bewegung. Es besteht eine enge Beziehung zwischen der geometrischen Struktur des gewählten stochastischen Modells und den Invarianten isomorpher Abbildungen, von denen die eine als ein Bewegungsgesetz der Evolution des Systems gilt und die zweite die sog. K-adische Abbildung darstellt. Diese Invarianten werden durch die Ergodizität des Systems, sein Durchmischen (die Durchmischungs-Eigenschaft) und durch die Entropie charakterisiert. Die Existenz des Durchmischungs bei der Bewegung des Systems bildet eine unerlässliche Bedingung für die Erklärung des Begriffes der Irreversibilität und des Relaxations-prozesses.

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Dedicated to 90th Birthday of Professor Frantiek Fiala     

On the stability relationships between tidal asymmetry and morphologies of tidal basins and estuaries

Simple stability relationships are practically useful to provide a rapid assessment of coastal and estuarine landforms in response to human interventions and long‐term climate change. In this contribution, we review a variety of simple stability relationships which are based on the analysis of tidal asymmetry (TA). Most of the existing TA‐based stability relationships are derived using the one‐dimensional tidal flow equations assuming a certain regular shape of the tidal channel cross‐sections. To facilitate analytical solutions, specific assumptions inevitably need to be made, for example by linearizing the friction term and dropping some negligible terms in the tidal flow equations. We find that three major types of TA‐based stability relationships have been proposed between three non‐dimensional channel geometric ratios (represented by the ratio of channel widths, ratio of wet surface areas and ratio of storage volumes) and the tide‐related parameter a/h (i.e. the ratio between tidal amplitude and mean water depth). Based on established geometric relations, we use these non‐dimensional ratios to restate the existing relationships so that they are directly comparable. Available datasets are further extended to examine the utility of these TA‐based relationships. Although a certain agreement is shown for these relationships, we also observe a large scatter of data points which are collected in different types of landscape, hydrodynamic and sedimentological settings over the world. We discuss in detail the potential reasons for this large scatter and subsequently elaborate on the limited applicability of the various TA‐based stability relationships for practical use. We highlight the need to delve further into what constitutes equilibrium and what is needed to develop more robust measures to determine the morphological state of these systems. Copyright © 2018 John Wiley & Sons, Ltd.     

地球引潮力极大值和强潮汐周期性指数的建立与定性分析

日、月对地球表层海水的引潮力导致潮汐的周期性变化是一种成熟理论.地球除具有日、月、年潮汐规律外,还具有明显的准1800年、200年、50～70年、18.6年、9.3年和2.5～7年不同尺度的周期.本文通过将地球赤道半径和月球轨道半径投影到黄道面上,标定二者矢量半径之和的模的极值状态,创建了引潮力极大值和强潮汐的周期性指数K_SEM.这对探讨和预测潮汐的时间分布和推断地球自转角速度变化规律提供了一种新途径.行星系统中木星和金星对地球的摄动影响最突出,但目前还没有一个行之有效的模型将日、地、月、木星、金星作为一个统一整体,对地球潮汐极值状态进行刻画.通过辨析这五大天体运动预设的位置关系的结构特征,进而考察K_SEM指数与月球升交点和月球近地点会合周期的对应关系,以及对月球轨道运动不同的特征周期的叠加和定性分析,这对探讨强潮汐周期、厄尔尼诺现象和地震的时间分布规律提供了重要参考.     

用小波分析提取重力固体潮

地球固体潮观测对验证各种地球模型、研究地球内部构造具有重要意义,可为地震预报提供重要的参考依据.BBVS-120甚宽带地震计具有较低的自噪声水平,在低频端输出信号的频率很低,涵盖固体潮信息频带范围.本文提出:BBVS-120地震计输出信号中存在周日波、半日波和1/3日波的固体潮信号,利用小波分析,提取垂直分量中的重力固体潮信号,并作调和分析.     

Experimental analysis of tidal network growth and development

In this paper we present the results of a first series of laboratory experiments carried out in a large experimental apparatus, aimed at reproducing a typical lagoonal environment subject to tidal forcings. The experiments were designed in order to improve our understanding of the main processes governing tidal network initiation and its progressive morphodynamic evolution. During the experiments we observed the growth and development of tidal networks and analyzed their most relevant geomorphic features, taking into account the role played by the characteristics of the tidal forcing in driving the development of channeled patterns. The synthetic networks displayed geomorphic features which compare favorably with those of actual networks, showing that our experimental framework proves useful for analyzing the processes governing the formation and evolution of tidal channel networks. In particular, the synthetic networks develop via headward growth driven by the exceedance of a critical bottom shear stress, and display width-to-depth ratios and seaward exponential widening in accordance with observational evidence. Furthermore experimental networks reproduce statistical network characteristics of geomorphic relevance, such as the exponential probability distribution of unchanneled path lengths.     

A method for extracting storm surges from tidal records

Summary A method is described for extracting storm surge heights from hourly tabulations of tidal heights, which dispense with the use of a tide predicting machine. Within limits the method is adaptable according to the nature of the tidal regime encountered, and is particularly useful where shallow water effects are important. The computational work involved requires only slide rule, adding machine and graph paper. Two examples are given; one theoretical to justify the method, and one from nature.

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Eine Methode zur Bestimmung von Sturmfluthöhen aus Gezeitenregistrierungen

Zusammenfassung Eine Methode, mit der sich die Höhe von Sturmfluten aus stündlichen Gezeitentafeln errechnen läßt, wird besprochen. Diese Methode macht den Gebrauch einer Gezeitenmaschine überflüssig. Innerhalb bestimmter Grenzen läßt sich die Methode der jeweilig angetroffenen Gezeitenform anpassen; sie eignet sich besonders gut bei Vorhandensein von stärkeren Flachwassertiden. Für die Rechenarbeit sind nur Rechenschieber, Addiermaschine und Zeichenpapier erforderlich. Zwei Beispiele werden angeführt, ein theoretisches, um die Methode zu belegen, und ein Beispiel aus der Natur.

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Sur une méthode de détermination des hauteurs des ondes de tempête à partir des enregistrements des marées

Résumé On discute une méthode qui permet de calculer des hauteurs des ondes de tempête à partir des annuaires horaires des marées. Cette méthode rend inutile l'emploi d'une machine à prédire les marées. Elle se laisse adapter jusqu'à un certain degré à la nature individuelle de la marée rencontrée et est particulièrement convenable en présence de fortes ondes des petits fonds. Pour faire le calcul on a seulement besoin d'une règle à calcul, d'une machine à additionner et de papier à dessins. On offre deux exemples, dont l'un est de caractère théorique pour justifier la méthode pendant l'autre s'appuie sur des observations.

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The author wishes to acknowledge the encouragement and advice given to him during the development of the method by Dr. A. T. Doodson and Mr. G. W. Lennon.     

Spectral techniques for the analysis of tidal time series

Summary Three different methods are given for the Fourier analysis of time series leading to the determination of high reliable values of frequencies, amplitudes and phases of the inherent components. For two methods the hypothesis is made that the time series is sufficiently long to separate very close components, while for the third the frequencies are supposed to be given. Two of these methods have been applied to a time series obtained by sampling an artificial tidal function.     

Lateral dynamic analysis and classification of barotropic tidal inlets

The dynamical balances at shallow tidal inlets are highly nonlinear, and can vary substantially over sub-kilometer scales. In this study, barotropic dynamics are examined with numerical experiments on a series of idealized inlets with differing inlet widths and lengths. Circulation and elevation fields obtained from fully nonlinear depth-integrated circulation models are used to reconstruct the contribution of each term in the momentum equations. Momentum terms are rotated into a streamline coordinate system to simplify interpretation of the dynamics. Spatial patterns in momentum reveal that the lateral balances at inlets can vary from nearly geostrophic to strongly cyclostrophic. Marked dynamical differences are seen between inlets with different lengths and widths. Inlet regions of geostrophic or cyclostrophic balances can be predicted using two dimensionless parameters, the dynamic length L^* and dynamic width W^*. A classification scheme is proposed using L^* and W^* to compare the idealized inlets analyzed here with inlets from 20 previous studies. Four distinct inlet types are identified and discussed.     

On the environmental isotope method for determining the water balance components of some lakes

The paper deals with the isotope balance method applied to lakes, which can be assumed as being under steady-state conditions. It is shown that the long-term averages and non-normalized temperatures can be used in the balance equations. The applicability of the proposed approach was tested by the interpretation or reinterpretation of several known case studies (Chala, Titicaca, Waid, Burdur, Beysehir and Egridir lakes). An isotope study of a small artificial lake (1.2 · 10⁶ m³) is presented and compared with whole-body tracing by K₃⁶⁰ Co(CN)₆. This artificial tracer does not appear useful for long-term tracing of surface waters.The water balance equation for each of the lakes considered was solved with the aid of the isotope balance equation of ¹⁸O. Applying the calculated components of the water balance, the isotope balance equation of deuterium was solved for finding the values of kinetic enrichment for deuterium. These values, which give the fit of the evaporation lines to the experimental data, do not agree with the values known from direct laboratory experiments, thus they have to be treated as apparent values, which may be useful for future field work.     

Sensitivity of tidal characteristics in double inlet systems to momentum dissipation on tidal flats: a perturbation analysis

In a tidal channel with adjacent tidal flats, along–channel momentum is dissipated on the flats during rising tides. This leads to a sink of along–channel momentum. Using a perturbative method, it is shown that the momentum sink slightly reduces the M₂ amplitude of both the sea surface elevation and current velocity and favours flood dominant tides. These changes in tidal characteristics (phase and amplitude of sea surface elevations and currents) are noticeable if widths of tidal flats are at least of the same order as the channel width, and amplitudes and gradients of along–channel velocity are large. The M₂ amplitudes are reduced because stagnant water flows from the flats into the channel, thereby slowing down the current. The M₄ amplitudes and phases change because the momentum sink acts as an advective term during the fall of the tide, such a term generates flood dominant currents. For a prototype embayment that resembles the Marsdiep–Vlie double–inlet system of the Western Wadden Sea, it is found that for both the sea surface elevation and current velocity, including the momentum sink, lead to a decrease of approximately 2% in M₂ amplitudes and an increase of approximately 25% in M₄ amplitudes. As a result, the net import of coarse sediment is increased by approximately 35%, while the transport of fine sediment is hardly influenced by the momentum sink. For the Marsdiep–Vlie system, the M₂ sea surface amplitude obtained from the idealised model is similar to that computed with a realistic three–dimensional numerical model whilst the comparison with regard to M₄ improves if momentum sink is accounted for.     

On some properties in the emergence and evolution of the oscillations of the Earth after earthquakes

The records from wideband seismic stations are analyzed for studying the oscillations of the Earth that emerged after the earthquakes in Sumatra on December 26, 2004 (M = 9.2), Chile on February 27, 2010 (M = 8.8), and after the Tohoku megaearthquake on March 11, 2011 (M = 9.0). Attention is focused on the band with a period of 20.46 min, which includes the free radial mode ₀S₀. It is established that the emergence of oscillations in the frequency interval corresponding to the free oscillations of the Earth is delayed by a lag, which increases with increasing period. Pulsations of the 20.46-min band, which appear in the interval from 5 to 7 days after the earthquake and have a period of 127–129 min, are revealed. The patterns of the amplitude attenuation of the 20.46-min band are different at stations located in zones with different tectonic activity. These features manifest themselves in the search through different stations and through different earthquakes.     

Magnetic and microstructural properties of some lodestones

An iron ore which behaves as a permanent magnet is lodestone. The intrinsic magnetic properties and the microstructual characteristics which are responsible for the permanent-magnet properties of the lodestone have never been described or explained. Iron ores capable of being charged sufficiently strongly to behave as permanent magnets are defined here as proto-lodestones and fall into two categories — Class I which contains Fe as the only significant cation, and Class II which contains considerable Ti, Mg and Al as well. Proto-Lodestones are magnetically hardened by oxidation and precipitation processes which produce the microstructure responsible for the permanent-magnet properties. Lodestones are charged proto-lodestone iron ores. Lodestones have R_H values (ratio of remanent coercive force, H_R, to coercive force, H_C) between 2.0 and 2.5; R_I values (ratio of saturation remanence, I_SR, to saturation magnetization, I_S) >0.1–0.25 and the ratio of NRM/SIRM (natural remanence to saturation remanence) is 0.15–0.7. The intrinsic magnetic properties and microstructural characteristics of proto-lodestones and other iron ores are described and explained. The mechanism of charging the proto-lodestone appears to be either transient magnetic fields associated with lightning-discharge currents or presently obscure aspects of magnetization intensity enhancement associated with maghemitization of massive iron ores.     

Estimation of deformational properties of a stratum-borehole system based on analysis of barometric and tidal responses of the water level in a borehole

Statically isolated conditions in the stratum-borehole hydrogeological system under consideration at periods of ≥ 3 h are established on the basis of the investigation of barometric and tidal responses of the water level in a borehole located in the territory of the Mikhnevo Geophysical Observatory, Institute of Geosphere Dynamics, Russian Academy of Sciences. The barometric effectiveness, tidal sensitivity of the water level, elastic parameters, and porosity of water-bearing rocks are estimated. A model of the inertial character of the water exchange in the stratum-borehole system is constructed depending on the period of variations with allowance for the borehole design, as well as the water transmissibility and elastic capacity of the aquifer. The results of modeling are in compliance with the dependence of the amplitude transfer function from variations in the atmospheric pressure to variations in the water level. The results of processing the data of high-precision measurements made it possible to refine the transmissibility of the aquifer obtained from the data of experimental filtration works.     

论地脉动场地动力特性分析中的Nakamura方法

地脉动工程应用中的Ｎａｋａｍｕｒａ方法即用测点地脉动的水平分量与竖向分量谱比确定场地动力特性的方法,近年来成为工程场地动力特性分析中的研究热点。本文详细阐述了导出这一方法的试验依据和过程,并指出了其中存在的问题。