Decaying quasi-two-dimensional viscous flow on a square domain

Konijnenberg, van de Ja Johan; Flór, J-B Jan-Bert; Heijst, van Gjf Gert-Jan

doi:10.1063/1.869586

Cited by 22 publications

(33 citation statements)

References 20 publications

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“…[11][12][13] At early times, and at heights above the near-base region, the experimental data were found to exhibit excellent agreement with the streamfunction (19) and the corresponding velocity components defined by (21). Figure 6(a) shows a sample of streamlines from (19) compared with the streak line image already shown in Figure 2(a), from experiment C (at t = t * = 8.7 and z 0 /H = 0.329).…”

Section: The Inviscid Two-dimensional Starting Flowsupporting

confidence: 60%

“…Figure 6(a) shows a sample of streamlines from (19) compared with the streak line image already shown in Figure 2(a), from experiment C (at t = t * = 8.7 and z 0 /H = 0.329). Figure 6(b) shows measurements, also from experiment C, of the horizontal velocity component, v, extracted along the symmetry axis y = 1/2, plotted against x, and compared with the corresponding theoretical velocity profile defined using (19) and (21).…”

Section: The Inviscid Two-dimensional Starting Flowmentioning

confidence: 99%

“…and since p is a streamfunction for the horizontal motion according to (21), boundary condition (22) becomes…”

Section: Formulation Of the Motion On The α −1 And E −1/2 Time Scalesmentioning

confidence: 99%

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Stratified spin-up in a sliced, square cylinder

Munro

Foster

2014

Physics of Fluids

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We previously reported experimental and theoretical results on the linear spin-up of a linearly stratified, rotating fluid in a uniform-depth square cylinder [M. R. Foster and R. J. Munro, "The linear spin-up of a stratified, rotating fluid in a square cylinder," J. Fluid Mech. 712, 7-40 (2012)]. Here we extend that analysis to a "sliced" square cylinder, which has a base-plane inclined at a shallow angle α. Asymptotic results are derived that show the spin-up phase is achieved by a combination of the Ekman-layer eruptions (from the perimeter region of the cylinder's lid and base) and cross-slopepropagating stratified Rossby waves. The final, steady state limit for this spin-up phase is identical to that found previously for the uniform depth cylinder, but is reached somewhat more rapidly on a time scale of order E −1/2 −1 /log (α/E 1/2 ) (compared to E −1/2 −1 for the uniform-depth cylinder), where is the rotation rate and E the Ekman number. Experiments were performed for Burger numbers, S, between 0.4 and 16, and showed that for S O (1), the Rossby modes are severely damped, and it is only at small S, and during the early stages, that the presence of these wave modes was evident. These observations are supported by the theory, which shows the damping factors increase with S and are numerically large for S O (1

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Section: The Inviscid Two-dimensional Starting Flowsupporting

confidence: 60%

Section: The Inviscid Two-dimensional Starting Flowmentioning

confidence: 99%

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Stratified spin-up in a sliced, square cylinder

Munro

Foster

2014

Physics of Fluids

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“…The self-organization process strongly depends on the domain geometry and on the boundary conditions at the lateral walls, which play a fundamental role in the flow organization as they act as sources of vorticity and net angular momentum. 6 For instance, van de Konijnenberg et al 7 and Clercx et al 8 found that the final state of the self-organization process in a square container tends to be a single vortex with a size comparable to the domain. Maassen et al 9 studied the self-organization in rectangular containers and found a cell pattern of alternatesign vortices along the main axis.…”

Section: Introductionmentioning

confidence: 99%

Preferential states of rotating turbulent flows in a square container with a step topography

et al. 2013

Self Cite

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The self-organization of confined, quasi-two-dimensional turbulent flows in a rotating square container with a step-like topography is investigated by means of laboratory experiments and numerical simulations based on a rigid lid, shallow-water formulation. The domain is divided by a bottom discontinuity into two rectangular regions, one being shallow and the other deep. The existence of a preferential vorticity distribution in the long-term evolution of the decaying flow is discussed. Initially, the turbulent flow organizes into larger structures. After a few rotation periods, a continuous jet-like flow is consistently observed along the step, with the shallow region at its right. This flow is associated with the adjustment of the fluid to equilibrium over a bottom discontinuity in an anti-clockwise rotating system. At the end of the step, two persistent structures are formed due to the collision of this jet with the vertical wall: a cyclonic circulation cell in the deep region, while an anticyclonic cell occurs in the shallow part of the domain. The laboratory experiments are well-reproduced by the simulations. Due to bottom friction effects, the fluid motion is halted before a complete organization of the flow is accomplished. In order to study the full process, additional numerical simulations were performed with zero Ekman friction. Same principal features are observed as in the experiments, but now a complete organization of the flow into four vortices is obtained: in the deep part of the flow domain, a cyclone-anticyclone pair is observed that fills up the entire region, and the mirrored double cell structure occurs on the shallow side. Such a disposition of the vortices is directly associated with the interaction of the flow along the step and the downstream wall at which it collides, as observed in the experiments. It is shown that this arrangement is systematically obtained in simulations with very different initial conditions. The existence of a preferential vorticity distribution induced by a topographic step is further discussed in terms of the aspect ratio of the domain. C 2013 American Institute of Physics. [http://dx

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“…If they are indeed constrained to verify no-slip velocity conditions on a closed boundary they can only be determined by numerical approach. The present paper regards the Stokes fundamental eigenmodes in the square whose physical implications are commented in [ 12] and illustrated in [5,6,22], for instance. Only one of them is known to the authors' knowledge, the most fundamental of all, whose symmetry properties are the most straightforwardly expected [5,22].…”

Section: Introductionmentioning

confidence: 99%

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

Leriche

Labrosse

2005

Numer Algor

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The well-known Reid-Harris expansions, applied to the stream function formulation, and the projection-diffusion Chebyshev Stokes solver, in primitive variables, are used to compute the fundamental Stokes eigenmodes of each of the symmetry families characterizing the Stokes solutions in the square. The numerical accuracy of both methods, applied with several discretizations, are compared, for both the eigenvalues and the main features of the corresponding eigenmodes. The Chebyshev approach is by far the most efficient, even though the associated solver does not provide a divergence free velocity but asymptotically.

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Decaying quasi-two-dimensional viscous flow on a square domain

Cited by 22 publications

References 20 publications

Stratified spin-up in a sliced, square cylinder

Stratified spin-up in a sliced, square cylinder

Preferential states of rotating turbulent flows in a square container with a step topography

Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris?

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