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Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
We propose a mathematical derivation of stochastic compressible Navier-Stokes equation. We consider many-particle systems with a Hamiltonian dynamics supplemented by a friction term and environmental noise. Both the interaction potential…
This article analyses the assumptions regarding the influence of pressure forces during the calculation of the motion of a Newtonian fluid. The purpose of the analysis is to determine the reasonableness of the assumptions and their impact…
This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for…
Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…
Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
A widely used approach to mathematically describe the atmosphere is to consider it as a geophysical fluid in a shallow domain -- and thus to model it using classical fluid dynamical equations combined with the explicit inclusion of an…
The climate is a forced and dissipative nonlinear system featuring non-trivial dynamics of a vast range of spatial and temporal scales. The understanding of the climate's structural and multiscale properties is crucial for the provision of…
An objective revision of the Laplace barometric formula for isothermal planetary atmospheres is proposed. From Clausius virial theorem equating the root mean square kinetic energy to half the gravitational potential energy, planetary…
We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas,…
Starting from basic physical principles, we present a novel derivation linking the global wind power to measurable atmospheric parameters. The resulting expression distinguishes three components of the atmospheric power (the kinetic power…
The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A…
The appeal of thermodynamics to problems outside physics is undeniable, as is the growing recognition of its apparent universality, yet in the absence of a rigorous formalism divorced from the peculiarities of molecular systems all attempts…
The basic concepts and hypotheses of Newtonian Cosmology necessary for a consistent treatment of the averaged cosmological dynamics are formulated and discussed in details. The space-time, space, time and ensemble averages for the…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
This article proposes an in-depth investigation into the emergence of thermoacoustic waves from a variational formalism rooted in non-equilibrium thermodynamics. Differing from traditional approaches based on linear simplifications, this…
We use the formalism of Geometrothermodynamics to derive a series of fundamental equations for thermodynamic systems. It is shown that all these fundamental equations can be used in the context of relativistic cosmology to derive diverse…
The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as…