The Lorenz energy cycle describes the generation, conversion and dissipation of energy in the general atmospheric circulation. [1] It is named after the meteorologist Edward N. Lorenz who worked on its mathematical formulation in the 1950s. [2]
Any atmospheric circulation system, whether it is a small-scale weather system or a large-scale zonal wind system, is maintained by the supply of kinetic energy. The development of such a system requires either a transformation of some other form of energy into kinetic energy, or the conversion of the kinetic energy of another system into that of the developing system. [3] On a global scale, the atmospheric circulation must carry energy polewards, because there is a net gain of energy in the tropics through incoming solar radiation and net loss of energy in high latitudes through thermal emission. At low latitudes, where the Hadley cell takes shape, the poleward transport of energy is done by the mean meridional circulation. At mid-latitudes in contrast, the influence of longitudinally asymmetric features, referred to as eddies, is dominant over the mean flow. For a closer examination, it is useful to split all parameters (e.g. P) into their zonal-mean (denoted by an overline, e.g. P) and their departures from the zonal mean due to orography, land-sea contrasts, weather systems and any other eddy-like features (denoted by a prime, e.g. P').
The available potential energy is the amount of potential energy in the atmosphere that can be converted into kinetic energy. In a statically stable atmosphere, the zonal-mean available potential energy P is approximated as:
where is the integral over the Earth's entire atmosphere, ρ0 is the mean density of air, N is the buoyancy frequency, a measure of static stability, Φ is the geopotential and z* denotes a log-pressure coordinate.
Eddy available potential energy P' is approximated as:
Zonal-mean kinetic energy K is approximated as:
where u and v are the zonal and meridional components of air velocity.
Eddy kinetic energy K' is approximated as:
The description of the Lorenz Energy Cycle is completed by a mathematical formalism for the generation of potential energy through diabatic heating, its conversion to kinetic energy through vertical motion of air and the dissipation of kinetic energy through friction. A conversion of zonal-mean energy to eddy energy and vice versa is possible where eddies interact with the mean flow and displace warm/cold air. [1]
Brownian motion, or pedesis, is the random motion of particles suspended in a medium.
In physics, the Navier–Stokes equations are certain partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes).
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In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.
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In plasma physics, the Hasegawa–Mima equation, named after Akira Hasegawa and Kunioki Mima, is an equation that describes a certain regime of plasma, where the time scales are very fast, and the distance scale in the direction of the magnetic field is long. In particular the equation is useful for describing turbulence in some tokamaks. The equation was introduced in Hasegawa and Mima's paper submitted in 1977 to Physics of Fluids, where they compared it to the results of the ATC tokamak.
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In fluid dynamics, Luke's variational principle is a Lagrangian variational description of the motion of surface waves on a fluid with a free surface, under the action of gravity. This principle is named after J.C. Luke, who published it in 1967. This variational principle is for incompressible and inviscid potential flows, and is used to derive approximate wave models like the mild-slope equation, or using the averaged Lagrangian approach for wave propagation in inhomogeneous media.
In fluid dynamics, Airy wave theory gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mean depth, and that the fluid flow is inviscid, incompressible and irrotational. This theory was first published, in correct form, by George Biddell Airy in the 19th century.
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Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.
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A baroclinic instability is a fluid dynamical instability of fundamental importance in the atmosphere and ocean. It can lead to the formation of transient mesoscale eddies, with a horizontal scale of 10-100 km. In contrast, flows on the largest scale in the ocean are described as ocean currents, the largest scale eddies are mostly created by shearing of two ocean currents and static mesoscale eddies are formed by the flow around an obstacle (as seen in the animation on eddy. Mesoscale eddies are circular currents with swirling motion and account for approximately 90% of the ocean's total kinetic energy. Therefore, they are key in mixing and transport of for example heat, salt and nutrients.
