Related papers: The complementary Betz Theory
The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this…
We develop a new theory of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a new fluid variable, the kinetic mass density, which is needed…
A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law…
Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
This article describes the third law of thermodynamics. This law is often poorly known and is often decried, or even considered optional and irrelevant to describe weather and climate phenomena. This, however, is inaccurate and contrary to…
This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of…
Aiming to explore physical limits of wind turbines, we develop a model for determining the work extractable from a compressible fluid flow. The model employs conservation of mass, energy and entropy and leads to a universal bound for the…
Using fully-resolved simulations, we investigate the torque experienced by a finite-length circular cylinder rotating steadily perpendicularly to its symmetry axis. The aspect ratio $\chi$, i.e. the ratio of the length of the cylinder to…
The Lorenz system was derived on the basis of a model of convective atmospheric motions and may serve as a paradigmatic model for considering a complex climate system. In this study, we formulated the thermodynamic efficiency of convective…
An inverse cascade - energy transfer to progressively larger scales - is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and…
Arnold showed that the Euler equations of an ideal fluid describe geodesics on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
There is intense effort into understanding the universal properties of finite-time models of thermal machines---at optimal performance---such as efficiency at maximum power, coefficient of performance at maximum cooling power, and other…
Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow,…
It is known that an object translating parallel to a soft wall in a viscous fluid produces hydro- dynamic stresses that deform the wall, which, in turn, results in a lift force on the object. Recent experiments with cylinders sliding under…
The production of renewable and sustainable energy is one of the most important challenges currently facing mankind. Wind has made an increasing contribution to the world's energy supply mix, but still remains a long way from reaching its…
The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by…
Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the {\em inverse problem}.…
Airborne Wind Energy is a lightweight technology that allows power extraction from the wind using airborne devices such as kites and gliders, where the airfoil orientation can be dynamically controlled in order to maximize performance. The…