Tidal theory

Kobrick M. and Kaula W. M. (1979) A tidal theory for the origin of the solar nebula. Moon Planet. 20, 61 -101. 

The second part of the chapter deals with tides in the Baltic Sea, a much neglected subject in the author s opinion. The topic is introduced by a brief historic summary of Baltic Sea tidal theory, followed by an outline of present tidal theory for the Baltic Sea. The conclusion at the end of this chapter is that inclusion of the tides in numerical models of the Baltic Sea will lead to more realistic sea level forecasts. 

In the following, the history of Baltic Sea tidal research will be outlined (7.2.1). In order to achieve a noticeable improvement of these approaches, a concept rooted in tidal theory is discussed that allows Baltic tides to be taken into account adequately in a numerical model (7.2.2). Finally, a new tidal model for the Baltic Sea derived from a... 

Tidal theory applied to observations of tectonic and thermal features suggests that the ice is significantly thinner, so that the ocean can connect with the surface through cracks and melt sites. Tidal stress can probably open cracks no deeper than a few km, so we infer that the ice is probably less than 10 km thick. 

All of the activity on Europa is driven by tides, so it is worth considering what we know about the amplitude of these tides. According to Tidal theory, Europa s figure is distorted by the tide-raising potential of Jupiter according to... 

These early writings detailed the observed connections between the daily, monthly, and annual tidal variations however, it was sixteen centuries, and many tidal observations and tidal theories later, that Newton expressed the gravitational forces between astronomic bodies with the equation, F = Gmxm lr )- The detailed examination and expansion of tidal harmonics continues to this day. 

Because the time scale of the anticipated atmospheric motion associated with the temperature fluctuations is only one day, the thermal wind approximation caimot be used. However, diurnal variations in the pressure and wind fields can be estimated from the observed temperature field using classical tidal theory. The basic concept of the formulation is sketched here a detailed treatment can be found in Chapman Lindzen (1970). The theory is based on a linearization of the primative equations. A motionless atmospheric reference state is assumed with temperature profile To z) and a corresponding geopotential surface 4>o(z). It is further assumed that the diabatic heating and all other quantities vary as exp[i(j < — cot)] where s is a longitudinal wavenumber and co is 2 7r/(solar day) or integer multiples thereof. The amplitudes of the time-varying, dependent variables are taken to be sufficiently small so that only terms of first order need be retained. With these assumptions. 

Book II investigates the dynamical conditions of fluid motion. Book III displays the law of gi avitatioii at work in the solar system. It is demonstrated from the revolutions of the six known planets, including Earth, and their satellites, though Newton could never quite perfect the difficult theory of the Moon s motion. It is also demonstrated from the motions of comets. The gravitational forces of the heavenly bodies are used to calculate their relative masses. The tidal ebb and flow and the precession of the equinoxes is explained m terms of the forces exerted by the Sun and Moon. These demonstrations are carried out with precise calculations. 

Nitrous oxide decreases tidal volume and increases the rate of breathing and minute ventilation. Although arterial carbon dioxide partial pressures tend not to be affected the normal ventilatory responses to carbon dioxide and to hypoxia are depressed. Alveolar collapse in structured lung segments may be more rapid in the presence of nitrous oxide than with oxygen due to its greater solubility. Similarly, it depresses mucous flow and chemotaxis. In theory these factors predispose to postoperative respiratoiy complications. 

Early in the development of the theory of nucleosynthesis, an alternative to the high-T r-process canonical model (Sects. 7.1 and 7.2) has been proposed [63], It relies on the fact that very high densities (say p > 1010 gem-3) can lead material deep inside the neutron-rich side of the valley of nuclear stability as a result of the operation of endothermic free-electron captures, this so-called neutronisation of the material being possible even at the T = 0 limit. The astrophysical plausibility of this scenario in accounting for the production of the r-nuclides has long been questioned, and has remained largely unexplored until the study of the composition of the outer and inner crusts of neutron stars and of the decompression of cold neutronised matter resulting from tidal effects of a black hole on a neutron-star companion ([24] for references). The decompression of cold neutron star matter has recently been studied further (Sect. 9). 

The contents of this paper include, with variable emphasis, the topics of a series of lectures whose main title was Routes to Order Capture into resonance . This was indeed the subject of the last section above. The study of this subject has, however, shown that - unlike the restricted three-body problem - capture into resonance drives the system immediately to stationary solutions known as Apsidal corotations . The whole theory of these solutions was also included in the paper from the beginning - that is, from the formulation of the Hamiltonian equations of the planetary motions and the expansion of the disturbing function in the high-eccentricity planetary three-body problem. The secular theory of non-resonant systems was also given. Motions with aligned or anti-aligned periapses, resonant or not, resulting from non-conservative processes (tidal interactions with the disc) in the early phases of the life of the system, seem to be frequent in extra-solar planetary systems. 

The lag in the tidal response to Non-synchronous rotation causes a torque that tends to make the rotation synchronous, but that effect is counteracted in the case of an eccentric orbit. In the latter case, the lag in the diurnal tide yields a torque that varies over each orbit. The torque, averaged over each orbit, tends to drive the rotation to a rate slightly different from synchronous. That rate depends on details of the tidal response, but according to theory is expected to be only slightly faster than synchronous (Greenberg and Weidenschilling 1984). 

Anonymous (1955). C.F. Wicker. 6 lAHR Congress La Haye, Frontispiece. P Anonymous (1994). Wicker, Clarence F. Who s who in engineering 9 2012. Lewis New York. Wicker, C.F., Rosenzweig, O. (1950). Theories on tidal hydraulics. Report 1 101-125. ASCE Commission on Tidal Hydraulics New York. 

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