# 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} }

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

#### 993 Citations

Quasi-geostrophic turbulence in a rotating homogeneous fluid

- Physics
- 1980

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 2000… Expand

Laboratory model of two-dimensional polar beta-plane turbulence

- Physics
- 2007

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 is… Expand

Energy spectra and coherent structures in forced two-dimensional and beta-plane turbulence

- Physics
- 1991

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 flow… Expand

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

- Physics
- 1987

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 the… Expand

Angular distribution of energy spectrum in two-dimensional β-plane turbulence in the long-wave limit

- Physics
- 2013

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 Rossby… Expand

Anisotropic turbulence and zonal jets in rotating flows with a β-effect

- Physics
- 2006

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 the… Expand

Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere

- Physics
- 2001

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 with… Expand

The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere

- Physics
- 1996

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 spherical… Expand

A New Surface Model for β-Plane Turbulence

- Physics
- 2007

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

- Physics
- 1980

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 horizontal… Expand

#### References

SHOWING 1-10 OF 43 REFERENCES

Observations of the energy-containing oceanic Eddies, and theoretical models of waves and turbulence

- Physics
- 1973

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 cascade… Expand

Decay of two-dimensional homogeneous turbulence

- Physics
- 1974

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 by… Expand

The stability of planetary waves on an infinite beta‐plane

- Physics
- 1974

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 its… Expand

Numerical simulation of developing and decaying two-dimensional turbulence

- Physics
- 1971

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

- Physics
- 1969

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. The… Expand

Degeneration of resonantly-excited standing internal gravity waves

- Physics
- 1971

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 and… Expand

Topographic Rossby waves in a rough-bottomed ocean

- Geology
- 1973

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 choices… Expand

Computation of the Energy Spectrum in Homogeneous Two‐Dimensional Turbulence

- Physics
- 1969

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 statistical… Expand

Numerical simulation studies of two-Dimensional turbulence: I. Models of statistically steady turbulence

- Physics
- 1972

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-state… Expand

Numerical simulation studies of two-Dimensional turbulence: II. Stability and predictability studies

- Physics
- 1972

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 initial… Expand