Angular momentum of forced 2D turbulence in a square no-slip domain

Molenaar, D.; Clercx, Hjh Herman; Heijst, van Gjf Gert-Jan

doi:10.1016/j.physd.2004.06.001

Cited by 54 publications

(53 citation statements)

References 22 publications

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“…This is of importance, as boundary-generated vortices can destabilize even domain-sized vortices. 36,37 The question arises if the stronger wall-generated vortices can even prevent the formation of a domain-sized structure. If the Reynolds number is increased even further, e.g., ReϾ 10000, the eruption of vorticity spikes at the boundary leads to the formation of multiple vortices.…”

Section: Discussionmentioning

confidence: 99%

Vorticity dynamics of a dipole colliding with a no-slip wall

2007

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The active role of vorticity in the collision of a Lamb-like dipole with a no-slip wall is studied for Re values ranging between 625 and 20000. The initial approach of the dipole does not differ from the stress-free case or from a point-vortex model that incorporates the diffusive growth of the dipole core. When closer to the wall, the detachment and subsequent roll-up of the boundary layer leads to a viscous rebound, as was observed by Orlandi ͓Phys. Fluids A 2, 1429 ͑1990͔͒ in numerical simulations with Re up to 3200. The net translation of the vortex core along the wall is strongly reduced due to the cycloid-like trajectory. For Reഛ 2500 wall-generated vorticity is wrapped around the separate dipole halves, which hence become ͑partially͒ shielded monopoles. For Reտ O͑10 4 ͒, however, a shear instability causes the roll-up of the boundary layer before it is detached from the wall. This leads to the formation of a number of small-scale vortices, between which intensive, narrow eruptions of boundary-generated vorticity occur. Quantitative measures are given for the influx of vorticity at the wall and the consequent increase of boundary layer vorticity and enstrophy.

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Section: Discussionmentioning

confidence: 99%

Vorticity dynamics of a dipole colliding with a no-slip wall

2007

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“…Increasing its value in discrete steps, our results can be summarized as follows: two steady branches are observed for 0 < 37:5, a period-1 limit cycle for 37:5 As the forcing is defined in terms of Fourier modes, it is subsequently converted to Chebyshev polynomials [6]. The number of computational modes and the time step equal either 161 2 and t 3:4 10 ÿ4 or 181 2 and t 2:7 10 ÿ4 , whereas the simulations run up to T 1000 to generate time series of sufficient length.…”

Section: Transition To Chaos In a Confined Two-dimensional Fluid Flowmentioning

confidence: 94%

“…DOI Experiments on quasi-two-dimensional (2D) flows in shallow fluid layers [1,2] and stratified fluids [3], and numerical studies of confined purely 2D flows, revealed the importance of no-slip boundaries as vorticity sources. These confined flows have a remarkably different phenomenology from flows on a double-periodic domain [4 -6], with spontaneous spin-up phenomena, observed in computations of decaying and forced 2D flows [5,6] and in quasi-2D turbulence experiments in confined stratified fluids [3], as a striking example. A key issue for such flows is the possible generation of mean-square vorticity, or enstrophy Z t R !…”

Section: Transition To Chaos In a Confined Two-dimensional Fluid Flowmentioning

confidence: 99%

Transition to Chaos in a Confined Two-Dimensional Fluid Flow

2005

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“…In addition, a recent resurgence in theoretical interest in the condensate state was sparked by experimental [11] and numerical [18] observations of large scale coherent vortices associated with energy condensation in forced, bounded flows. In this letter, we report results of a set of numerical experiments designed to give a clean, detailed study of this energy condensation phenomenon in its own right.…”

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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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Angular momentum of forced 2D turbulence in a square no-slip domain

Cited by 54 publications

References 22 publications

Vorticity dynamics of a dipole colliding with a no-slip wall

Vorticity dynamics of a dipole colliding with a no-slip wall

Transition to Chaos in a Confined Two-Dimensional Fluid Flow

Dynamics of Energy Condensation in Two-Dimensional Turbulence

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