Waves and turbulence on a beta-plane

@article{Rhines1975WavesAT,
  title={Waves and turbulence on a beta-plane},
  author={Peter B. Rhines},
  journal={Journal of Fluid Mechanics},
  year={1975},
  volume={69},
  pages={417-443}
}
  • P. Rhines
  • Published 10 June 1975
  • Physics
  • Journal of Fluid Mechanics
Two-dimensional eddies in a homogeneous fluid at large Reynolds number, if closely packed, are known to evolve towards larger scales. In the presence of a restoring force, the geophysical beta-effect, this cascade produces a field of waves without loss of energy, and the turbulent migration of the dominant scale nearly ceases at a wavenumber k β = (β/2 U ) ½ independent of the initial conditions other than U , the r.m.s. particle speed, and β, the northward gradient of the Coriolis frequency… Expand

Figures from this paper

Quasi-geostrophic turbulence in a rotating homogeneous fluid
Abstract Quasi-two-dimensional turbulence is generated in a rotating cylinder by an homogeneous distribution of bottom sources and sinks which oscillate in time. Typical Reynolds numbers reach 2000Expand
Laboratory model of two-dimensional polar beta-plane turbulence
The evolution of a two-dimensional turbulent decaying flow is experimentally analyzed in a rotating system considering the effect of the change of the Coriolis force with latitude. The flow isExpand
Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence
Results from a wide range of direct numerical simulations of forced-dissipative, differentially rotating two-dimensional turbulence are presented, in order to delineate the broad dependence of flowExpand
Rossby waves and two-dimensional turbulence in a large-scale zonal jet
The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to theExpand
Angular distribution of energy spectrum in two-dimensional β-plane turbulence in the long-wave limit
The time-evolution of two-dimensional decaying turbulence governed by the long-wave limit, in which LD/L → 0, of the quasi-geostrophic equation is investigated numerically. Here, LD is the RossbyExpand
Anisotropic turbulence and zonal jets in rotating flows with a β-effect
Abstract. Numerical studies of small-scale forced, two-dimensional turbulent flows on the surface of a rotating sphere have revealed strong large-scale anisotropization that culminates in theExpand
Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere
The anisotropic characteristics of small-scale forced 2D turbulence on the surface of a rotating sphere are investigated. In the absence of rotation, the Kolmogorov k−5/3 spectrum is recovered withExpand
The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere
Results from a series of simulations of unforced turbulence evolving within a shallow layer of fluid on a rotating sphere are presented. Simulations show that the turbulent evolution in the sphericalExpand
A New Surface Model for β-Plane Turbulence
Abstract This paper introduces a new numerical model for studying wave–turbulence interactions in a continuously stratified rotating flow, having a uniform potential vorticity and a rigid boundary.Expand
Mesoscale Inhomogeneities and Turbulence in Ocean Acoustics
Consideration of the nonlinear potential vorticity equation for quasi-geostrophic motion of a continuously stratified ocean on a β-plane shows the dynamics to be controlled by two specific horizontalExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 43 REFERENCES
Observations of the energy-containing oceanic Eddies, and theoretical models of waves and turbulence
Two of the best available observed frequency spectra of energy-containing oceanic motions are summarized. Without provoking any simple explanation, they affirm that an efficient, homogeneous cascadeExpand
Decay of two-dimensional homogeneous turbulence
The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically byExpand
The stability of planetary waves on an infinite beta‐plane
The stability of a planetary wave on an infinite s‐plane is examined. There are two parameters in the problem, (a) ? = Uκ2/β where U is the velocity amplitude of the planetary wave and κ itsExpand
Numerical simulation of developing and decaying two-dimensional turbulence
Two-dimensional isotropic turbulence is investigated in its development from an arbitrarily specified initial flow through its transformation into a statistically self-preserving decaying flow.Expand
Numerical Simulation of Two‐Dimensional Turbulence
The two‐dimensional incompressible Navier‐Stokes equations are numerically integrated in order to test the validity of Kraichnan's predictions on the structure of two‐dimensional turbulence. TheExpand
Degeneration of resonantly-excited standing internal gravity waves
The factors bringing about the irreversible distortion or degeneration of a continuously forced standing internal gravity wave in a linearly stratified fluid are studied experimentally andExpand
Topographic Rossby waves in a rough-bottomed ocean
The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level. Analytically, we are limited to special choicesExpand
Computation of the Energy Spectrum in Homogeneous Two‐Dimensional Turbulence
Two‐dimensional and three‐dimensional turbulence have different properties, but both contain the two basic ingredients of randomness and convective nonlinearity, and some of the statisticalExpand
Numerical simulation studies of two-Dimensional turbulence: I. Models of statistically steady turbulence
Abstract It is demonstrated by numerical simulation that the addition of a linear drag term on the forced viscous vorticity equation allows the development of statistically steady-stateExpand
Numerical simulation studies of two-Dimensional turbulence: II. Stability and predictability studies
Abstract The theoretical predictability of statistically steady two-dimensional turbulence is examined by means of numerical simulations of the time evolution of pairs of almost identical initialExpand
...
1
2
3
4
5
...