Related papers: Earth tides in MacDonald's model
We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This…
Any model of tides is based on a specific hypothesis of how lagging depends on the tidal-flexure frequency. For example, Gerstenkorn (1955), MacDonald (1964), and Kaula (1964) assumed constancy of the geometric lag angle, while Singer…
This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction.…
Spin-orbit coupling can be described in two approaches. The method known as "the MacDonald torque" is often combined with an assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because the…
Description of tides is based on the form of dependence of the geometric lag on the tidal frequency. Some authors assume the lag angle to be constant, others set it to be linear in the frequency. The actual dependence of the lag on the…
Spin-orbit coupling is often described in the "MacDonald torque" approach which has become the textbook standard. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (1964; Rev. Geophys. 2,…
This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly…
We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and focus on the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short…
Tidal torques play a key role in rotational dynamics of celestial bodies. They govern these bodies' tidal despinning, and also participate in the subtle process of entrapment of these bodies into spin-orbit resonances. This makes tidal…
Rotational dynamics of the Earth, over geological timescales, have profoundly affected local and global climatic evolution, probably contributing to the evolution of life. To better retrieve the Earth's rotational history, and motivated by…
In geophysics and seismology, it is a common knowledge that the quality factors Q of the mantle and crust materials scale as the tidal frequency to a positive fractional power (Karato 2007, Efroimsky and Lainey 2007). In astronomy, there…
Thermal atmospheric tides have a strong impact on the rotation of terrestrial planets. They can lock these planets into an asynchronous rotation state of equilibrium. We aim at characterizing the dependence of the tidal torque resulting…
The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in…
We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean…
Atmospheric tides can have a strong impact on the rotational dynamics of planets. They are of most importance for terrestrial planets located in the habitable zone of their host star, where their competition with solid tides is likely to…
By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $\epsilon=\Omega^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
Paper on the creep tide theory and its applications to satellites and planets with emphasis on a new set of differential equations allowing easier numerical studies. The creep tide theory is a new paradigm that does not fix a priori the…
The aim of this letter is to discuss the virtual identity of two recent tidal theories: the creep tide theory of Ferraz-Mello (Cel. Mech. Dyn. Astron. 116, 109, 2013) and the Maxwell model developed by Correia et al. (Astron. Astrophys.…
In hydrodynamics, Taylor's frozen-in hypothesis connects the wavenumber spectrum to the frequency spectrum of a time series measured in real space. In this paper, we generalize Taylor's hypothesis to magnetohydrodynamic turbulence. We…