Diffusion Approximation for Two-Dimensional Turbulence

Leith, C. E.

doi:10.1063/1.1691968

Cited by 534 publications

(316 citation statements)

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“…We use the 6-hourly wind velocity data from the two most extreme negative and positive NAO years in the instrumental record of 1969 and1989, respectively (Fig. 1a).…”

Section: B Model Calculationsmentioning

confidence: 99%

“…Tracer transport equations are solved using a high-order monotonicitypreserving scheme (Daru and Tenaud 2004). Nonlinear momentum terms are solved using a vector invariant formulation (Adcroft et al 2004) with viscous dissipation following Leith (1969), but modified to dissipate divergence as well as vorticity. In our model configuration, the parameterization of geostrophic eddies using the method of Gent-McWilliams (GM)/Redi (Redi 1982;Gent and McWilliams 1990) was disabled.…”

Section: A Model Descriptionmentioning

confidence: 99%

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Simulated Response of the Arctic Freshwater Budget to Extreme NAO Wind Forcing

et al. 2009

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The authors investigate the response of the Arctic Ocean freshwater budget to changes in the North Atlantic Oscillation (NAO) using a regional-ocean configuration of the Massachusetts Institute of Technology GCM (MITgcm) and carry out several different 10-yr and 30-yr integrations. At 1 / 6 8 (;18 km) resolution the model resolves the major Arctic transport pathways, including Bering Strait and the Canadian Archipelago. Two main calculations are performed by repeating the wind fields of two contrasting NAO years in each run for the extreme negative and positive NAO phases of 1969 and 1989, respectively. These calculations are compared both with a control run and the compiled observationally based freshwater budget estimate of Serreze et al.The results show a clear response in the Arctic freshwater budget to NAO forcing, that is, repeat NAO negative wind forcing results in virtually all freshwater being retained in the Arctic, with the bulk of the freshwater content being pooled in the Beaufort gyre. In contrast, repeat NAO positive forcing accelerates the export of freshwater out of the Arctic to the North Atlantic, primarily via Fram Strait (;900 km 3 yr 21 ) and the Canadian Archipelago (;500 km 3 yr 21 ), with a total loss in freshwater storage of ;13 000 km 3 (15%) after 10 yr. The large increase in freshwater export through the Canadian Archipelago highlights the important role that this gateway plays in redistributing the freshwater of the Arctic to subpolar seas, by providing a direct pathway from the Arctic basin to the Labrador Sea, Gulf Stream system, and Atlantic Ocean.The authors discuss the sensitivity of the Arctic Ocean to long-term fixed extreme NAO states and show that the freshwater content of the Arctic is able to be restored to initial values from a depleted freshwater state after ;20 yr.

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“…We use the 6-hourly wind velocity data from the two most extreme negative and positive NAO years in the instrumental record of 1969 and1989, respectively (Fig. 1a).…”

Section: B Model Calculationsmentioning

confidence: 99%

Section: A Model Descriptionmentioning

confidence: 99%

Simulated Response of the Arctic Freshwater Budget to Extreme NAO Wind Forcing

et al. 2009

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“…In this letter, we study the "condensate" emerging in the form of two coherent vortices in a biperiodic box in 2D. Let us begin by briefly reviewing the classical 2D turbulence theory of Kraichnan, Leith and Batchelor (KLB) [3,4,5]. The essential difference with 3D turbulence is the presence of a second inviscid invariant, in addition to energy, the enstrophy.…”

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confidence: 99%

Dynamics of Energy Condensation in Two-Dimensional Turbulence

et al. 2007

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We report a numerical study, supplemented by phenomenological explanations, of "energy condensation" in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard k −5/3 one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to k −1 . The fluctuations decay slowly as the coherent part grows.PACS numbers: 47.27.E-,92.60.hk A big difference between 2D and 3D turbulence is the generation of large scale structures from small scale motions [1,2]. This occurs because, if pumped at intermediate scales, the 2D Navier-Stokes equations favor energy transfer to larger scales [3,4,5,6], a phenomenon known as an inverse cascade. Simulations [7,8] and experiments [9,10,11] show that large scale accumulation of energy is observed if conditions permit the energy to reach the system size. In this letter, we study the "condensate" emerging in the form of two coherent vortices in a biperiodic box in 2D. Let us begin by briefly reviewing the classical 2D turbulence theory of Kraichnan, Leith and Batchelor (KLB) [3,4,5]. The essential difference with 3D turbulence is the presence of a second inviscid invariant, in addition to energy, the enstrophy. Stirring the 2D flow leads to emergence of two cascades. Enstrophy cascades from the forcing scale, l, to smaller scales (direct cascade) while energy cascades from the forcing scale to larger scales (inverse cascade). Viscosity dissipates enstrophy at the Kolmogorov scale, η, which is much smaller than l when the Reynolds number is large. The energy cascade is blocked at a scale ζ, ζ ≫ l, by a frictional dissipation (usually due to friction between the fluid and substrate although other mechanisms can be imagined) after a transient in time quasi-stationary regime. Then a stationary KLB turbulence is established [3,4,5]. Applying Kolmogorov phenomenology (see e.g.[1]) KLB predicts an energy spectrum scaling as k −3 in the direct cascade, and as k −5/3 in the inverse cascade. Here k is the modulus of the wave-vector. The KLB spectra imply that velocity fluctuations at a scale r, δv r scale as ǫ 1/3 l −2/3 r and (ǫr) 1/3 in the direct and inverse cascade ranges respectively. KLB theory is confirmed by simulations [12,13] and experiments [2,14], where a sufficient range of scales was available to form the cascades. If the frictional dissipation is weak so that ζ exceeds the system size L then ultimately the "condensate" regime emerges [3,7] where the standard KLB does not apply.One of the primary motivations for studying 2D turbulence is that it is structurally and phenomenologically similar to quasi-geostrophic turbulence [15,16] which describes planetary atmospheres [17]. In addition, a recent resurgence i...

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“…The emergence of large-scale coherent structures was already predicted on theoretical grounds by Onsager [3] and Fjørtoft [4]. With these predictions by Onsager and Fjørtoft at hand, attempts to formulate a phenomenological theory of 2D turbulence were put forward more than 40 years ago by Kraichnan [5,6], Batchelor [7], and Leith [8]. It is nowadays known as KBL theory.…”

Section: Introductionmentioning

confidence: 99%