Quasi-two-dimensional turbulence in shallow fluid layers: The role of bottom friction and fluid layer depth

An experimental investigation of plane turbulent jets in bounded fluid layers is presented. The development of the jet is regular up to a distance from the orifice of approximately twice the depth of the fluid layer. From there on to a distance of about ten times the depth, the flow is dominated by secondary currents. The velocity distribution over a cross-section of the jet becomes three-dimensional and the jet undergoes a constriction in the midplane and a widening near the bounding surfaces. Beyond a distance of approximately ten times the depth of the bounded fluid layer the secondary currents disappear and the jet starts to meander around its centreplane. Large vortical structures develop with axes perpendicular to the bounding surfaces of the fluid layer. With increasing distance the size of these structures increases by pairing. These features of the jet are associated with the development of quasi two-dimensional turbulence. It is shown that the secondary currents and the meandering do not significantly affect the spreading of the jet. The quasi-two-dimensional turbulence, however, developing in the meandering jet, significantly influences the mixing of entrained fluid.

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The discharge plume parameter and its implications for an emptying–filling box

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.130 ◽

2017 ◽

Vol 817 ◽

pp. 171-182 ◽

Cited By ~ 3

Author(s):

O. Vauquelin ◽

E. M. Koutaiba ◽

E. Blanchard ◽

P. Fromy

Keyword(s):

Steady State ◽

Natural Ventilation ◽

Discharge Coefficient ◽

Fluid Layer ◽

Buoyant Plume ◽

Layer Depth ◽

Dimensional Parameter ◽

Fluid Layers ◽

Momentum Fluxes ◽

Lower Opening

The natural ventilation flow driven by an internal buoyant plume in a box involving an upper opening (vent) located at the ceiling (for the outflow) and a large lower opening at the floor (for the inflow) is examined theoretically in a general non-Boussinesq case. Analytical solutions of this emptying–filling box problem allow the characteristics of the flow at the vent to be determined. From these characteristics, a non-dimensional parameter $\unicode[STIX]{x1D6E4}_{d}$ (called the discharge plume parameter) is expressed. This parameter characterizes the initial balance of volume, buoyancy and momentum fluxes in the plume-like flow that forms above the vent. We then note that the value of $\unicode[STIX]{x1D6E4}_{d}$ allows the buoyant fluid layer depth in the box to be estimated, which is a new and interesting result for natural ventilation problems. Following previous experimental results, the decrease of the vent discharge coefficient $C_{d}$ when $\unicode[STIX]{x1D6E4}_{d}$ increases is discussed and a theoretical model based on plume necking is proposed. The emptying–filling box model is then extended for a variable $C_{d}$ (depending on $\unicode[STIX]{x1D6E4}_{d}$). Even though the discharge coefficient may be markedly reduced at high values of $\unicode[STIX]{x1D6E4}_{d}$, our results show that this only affects transients and the steady state of an emptying–filling box for relatively thin buoyant fluid layers.

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Synchronization of flexible sheets

Journal of Fluid Mechanics ◽

10.1017/s0022112011000814 ◽

2011 ◽

Vol 674 ◽

pp. 163-173 ◽

Cited By ~ 25

Author(s):

GWYNN J. ELFRING ◽

ERIC LAUGA

Keyword(s):

Energy Dissipation ◽

Symmetry Breaking ◽

Crucial Role ◽

Physical Mechanism ◽

Fluid Layer ◽

Two Dimensional ◽

Dimensional Model ◽

Close Proximity ◽

Two Dimensional Model

When swimming in close proximity, some microorganisms such as spermatozoa synchronize their flagella. Previous work on swimming sheets showed that such synchronization requires a geometrical asymmetry in the flagellar waveforms. Here we inquire about a physical mechanism responsible for such symmetry breaking in nature. Using a two-dimensional model, we demonstrate that flexible sheets with symmetric internal forcing deform when interacting with each other via a thin fluid layer in such a way as to systematically break the overall waveform symmetry, thereby always evolving to an in-phase conformation where energy dissipation is minimized. This dynamics is shown to be mathematically equivalent to that obtained for prescribed waveforms in viscoelastic fluids, emphasizing the crucial role of elasticity in symmetry breaking and synchronization.

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Two-Dimensional Navier–Stokes Turbulence in Bounded Domains

Applied Mechanics Reviews ◽

10.1115/1.3077489 ◽

2009 ◽

Vol 62 (2) ◽

Cited By ~ 56

Author(s):

H. J. H. Clercx ◽

G. J. F. van Heijst

Keyword(s):

Laboratory Experiments ◽

Self Organization ◽

Navier Stokes ◽

Bounded Domains ◽

Final States ◽

Two Dimensional ◽

The Past ◽

Fluid Layers ◽

Circular Domains

In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the past 10 years. The scope of this review concerns the self-organization of two-dimensional Navier–Stokes turbulence, the quasi-stationary final states in domains with no-slip boundaries, the role of the lateral no-slip walls on two-dimensional turbulence, and their role on the possible destabilization of domain-sized vortices. The overview of the laboratory experiments on quasi-two-dimensional turbulence is restricted to include only those carried out in thin electromagnetically forced shallow fluid layers and in stratified fluids. The effects of the quasi-two-dimensional character of the turbulence in the laboratory experiments will be discussed briefly. As a supplement, the main results from numerical simulations of forced and decaying two-dimensional turbulence in rectangular and circular domains, thus explicitly taking into account the lateral sidewalls, will be summarized and compared with the experimental observations.

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