Enstrophy

About: Enstrophy is a research topic. Over the lifetime, 2266 publications have been published within this topic receiving 64266 citations.

Inertial Ranges in Two‐Dimensional Turbulence

Abstract: Two‐dimensional turbulence has both kinetic energy and mean‐square vorticity as inviscid constants of motion. Consequently it admits two formal inertial ranges, E(k)∼e2/3k−5/3 and E(k)∼η2/3k−3, where e is the rate of cascade of kinetic energy per unit mass, η is the rate of cascade of mean‐square vorticity, and the kinetic energy per unit mass is ∫0∞E(k) dk. The −53 range is found to entail backward energy cascade, from higher to lower wavenumbers k, together with zero‐vorticity flow. The −3 range gives an upward vorticity flow and zero‐energy flow. The paradox in these results is resolved by the irreducibly triangular nature of the elementary wavenumber interactions. The formal −3 range gives a nonlocal cascade and consequently must be modified by logarithmic factors. If energy is fed in at a constant rate to a band of wavenumbers ∼ki and the Reynolds number is large, it is conjectured that a quasi‐steady‐state results with a −53 range for k « ki and a −3 range for k » ki, up to the viscous cutoff. The t...

Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model

Abstract: The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

A Formulation of a Phase-Independent Wave-Activity Flux for Stationary and Migratory Quasigeostrophic Eddies on a Zonally Varying Basic Flow

Abstract: A new formulation of an approximate conservation relation of wave-activity pseudomomentum is derived, which is applicable for either stationary or migratory quasigeostrophic (QG) eddies on a zonally varying basic flow. The authors utilize a combination of a quantity A that is proportional to wave enstrophy and another quantity E that is proportional to wave energy. Both A and E are approximately related to the wave-activity pseudomomentum. It is shown for QG eddies on a slowly varying, unforced nonzonal flow that a particular linear combination of A and E, namely, M ≡ (A + E)/2, is independent of the wave phase, even if unaveraged, in the limit of a small-amplitude plane wave. In the same limit, a flux of M is also free from an oscillatory component on a scale of one-half wavelength even without any averaging. It is shown that M is conserved under steady, unforced, and nondissipative conditions and the flux of M is parallel to the local three-dimensional group velocity in the WKB limit. The autho...

Two-dimensional turbulence

Abstract: The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered. The topics covered include some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two-dimensional superflow. Finally, an attempt is made to assess the status and future of the principal research topics which have been discussed.