Related papers: Earth tides in MacDonald's model

A formula for the tidal dissipation rate in a spherical body is derived from first principles, to correct some mathematical inaccuracies found in the literature. The development is combined with the Darwin-Kaula formalism for tides. Our…

Mathematical modeling of bodily tides can be carried out in various ways. Most straightforward is the method of complex amplitudes, which is often used in the planetary science. Another method, employed both in planetary science and…

Atmospheric thermal tides arise from the diurnal contrast in stellar irradiation. They exert a significant influence on the long-term rotational evolution of rocky planets because they can accelerate the planetary spin, thereby…

Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, 2D models commonly used for the Earth cannot be applied to extrasolar telluric planets…

A theory of fossil turbulence presented in the 11th Liege Colloquium on Marine turbulence is "revisited" in the 29th Liege Colloquium "Marine Turbulence Revisited". The Gibson (1980) theory applied universal similarity theories of…

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method…

Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…

The baroclinic instability problem is considered in the framework of Laplacian tidal theory. The Hilbert space of the quasigeostrophic vorticity budget is spanned by spheroidal functions. The fluid is linearly stable against…

We review the work of Bryan (1889) on the normal modes of a Maclaurin spheroid, carrying out numerical calculations of the frequencies and spatial forms of these modes that have not been previously published. We study all modes of degree $l…

This paper reviews the basic equations used in the study of the tidal variations of the rotational and orbital elements of a system formed by one star and one close-in planet as given by the creep tide theory and Darwin's constant time lag…

We discuss the linear response to low-frequency tidal forcing of fluid bodies that are slowly and uniformly rotating, are neutrally stratified and may contain a solid or fluid core. This problem may be regarded as a simplified model of…

We revisit the two body problem, where one body can be deformed under the action of tides raised by the companion. Tidal deformation and consequent dissipation result in spin and orbital evolution of the system. In general, the equations of…

The purpose of this article is to clarify the Cauchy theory of the water waves equations as well in terms of regularity indexes for the initial conditions as for the smoothness of the bottom of the domain (namely no regularity assumption is…

We address the expressions for the rates of the Keplerian orbital elements within a two-body problem perturbed by the tides in both partners. The formulae for these rates have appeared in the literature in various forms, at times with…

Due to tidal interactions in the Earth-Moon system, the spin of the Earth slows down and the Moon drifts away. This recession of the Moon is now measured with great precision, but it has been realized, more than fifty years ago, that simple…

After the initial suggestion by Zahnle and Walker (1987) that the torque accelerating the spin rate of the Earth and produced by the heating of the atmosphere by the Sun could counteract the braking lunir-solar gravitational torque in the…

Semidiurnal atmospheric thermal tides are important for terrestrial exoplanets in the habitable zone of their host stars. With solid tides, they torque these planets, thus contributing to determine their rotation states as well as their…

We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and self-gravitation of a body as a whole. For a qualitative…

A nonlinear stability analysis entirely in the Lagrangian frame is conducted, revealing the fundamental role of the wave-induced mean flow in modifying further wave growth and providing new insight into the classic problem of wave…