scholarly journals Three dimensional flows beneath a thin layer of 2D turbulence induced by Faraday waves

2020 ◽  
Vol 62 (1) ◽  
Author(s):  
Raffaele Colombi ◽  
Michael Schlüter ◽  
Alexandra von Kameke
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Velocity Fields ◽  
Surface Flow ◽  
Two Dimensional ◽  
Faraday Waves ◽  
2D Turbulence

Abstract Faraday waves occur on a fluid being subject to vertical shaking. Although it is well known that form and shape of the wave pattern depend on driving amplitude and frequency, only recent studies discovered the existence of a horizontal velocity field at the surface, called Faraday flow. This flow exhibits attributes of two-dimensional turbulence and is replicated in this study. Despite the increasing attention towards the inverse energy flux in the Faraday flow and other not strictly two-dimensional (2D) systems, little is known about the velocity fields developing beneath the fluid surface. In this study, planar velocity fields are measured by means of particle image velocimetry with high spatio-temporal resolution on the water surface and at different depths below it. A sudden drop in velocity and turbulent kinetic energy is observed at half a Faraday wavelength below the surface revealing that the surface flow is the main source of turbulent fluid motion. The flow structures below the surface comprise much larger spatial scales than those on the surface leading to very long-tailed temporal and spatial velocity (auto-) correlation functions. The three-dimensionality of the flow is estimated by the compressibility, which increases strongly with depth while the divergence changes its appearance from intermittent and single events to a large scale pattern resembling 2D cut-planes of convection rolls. Our findings demonstrate that the overall fluid flow beneath the surface is highly three-dimensional and that an inverse cascade and aspects of a confined 2D turbulence can coexist with a three-dimensional flow. Graphic abstract

scholarly journals Energy spectra of Sub-Surface Velocity Fields Beneath Faraday Waves

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Raffaele Colombi ◽  
Niclas Rohde ◽  
Michael Schlüter ◽  
Alexandra Von Kameke
Keyword(s):  
Three Dimensional ◽  
Vertical Direction ◽  
Velocity Fields ◽  
Surface Flow ◽  
Energy Cascade ◽  
Surface Velocity ◽  
Faraday Waves ◽  
Piv Measurements ◽  
Fluid Surface ◽  
Inverse Energy Cascade

Faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. Some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (Couder et al. (2005); Saylor and Kinard (2005)). Moreover, recent studies discovered the existence of a horizontal velocity field at  the fluid surface, called Faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von Kameke et al., 2011, 2013; Francois et al., 2013). Additionally, three-dimensionality effects have been part of recent investigations in quasi-2D flows (both electromagnetically-driven (Kelley and Ouellette, 2011; Martell et al., 2019) or produced by parametrically-excited waves (Francois et al., 2014; Xia and Francois, 2017)). Furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2D and 3D turbulence (Biferale et al., 2012; Kokot et al., 2017; Biferale et al., 2017). By performing 2D PIV measurements at horizontal planes beneath the Faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (Colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the Faraday wavelength λF). This in turn reveals that an inverse energy cascade and aspects of a confined 2D turbulence can coexist with a three dimensional bulk flow. In this work, 2D PIV measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in Faraday waves. The results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. Furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one Faraday wavelength) below the fluid surface.

Turbulence structure in a boundary layer with two-dimensional roughness

2009 ◽  
Vol 635 ◽  
pp. 75-101 ◽  
Author(s):  
R. J. VOLINO ◽  
M. P. SCHULTZ ◽  
K. A. FLACK
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Outer Flow ◽  
Dominant Feature

Turbulence measurements for a zero pressure gradient boundary layer over a two-dimensional roughness are presented and compared to previous results for a smooth wall and a three-dimensional roughness (Volino, Schultz & Flack, J. Fluid Mech., vol. 592, 2007, p. 263). The present experiments were made on transverse square bars in the fully rough flow regime. The turbulence structure was documented through the fluctuating velocity components, two-point correlations of the fluctuating velocity and swirl strength and linear stochastic estimation conditioned on the swirl and Reynolds shear stress. The two-dimensional bars lead to significant changes in the turbulence in the outer flow. Reynolds stresses, particularly $\overline {{v'}^2} ^ +$ and $ - \overline {{u}'{v}'} ^ + $, increase, although the mean flow is not as significantly affected. Large-scale turbulent motions originating at the wall lead to increased spatial scales in the outer flow. The dominant feature of the outer flow, however, remains hairpin vortex packets which have similar inclination angles for all wall conditions. The differences between boundary layers over two-dimensional and three-dimensional roughness are attributable to the scales of the motion induced by each type of roughness. This study has shown three-dimensional roughness produces turbulence scales of the order of the roughness height k while the motions generated by two-dimensional roughness may be much larger due to the width of the roughness elements. It is also noted that there are fundamental differences in the response of internal and external flows to strong wall perturbations, with internal flows being less sensitive to roughness effects.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

Turbulence Evaluation Within the Secondary Flow Region of a Turbine Cascade

1992 ◽  
Author(s):  
D. G. Gregory-Smith ◽  
Th. Biesinger
Keyword(s):  
Large Scale ◽  
Energy Equation ◽  
Three Dimensional ◽  
Flow Region ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Mean Velocity ◽  
Turbulent Kinetic Energy Equation ◽  
Transition Modelling

Three-dimensional turbulent and mean velocity fields have been measured within a large-scale axial turbine cascade. The results indicate a complex turbulent flow field especially within the secondary vortex. The turbulence is shown to he significantly non-isotropic, and the production and dissipation terms in the turbulent kinetic energy equation have been evaluated in order to illustrate the unusual turbulence behaviour. Comparisons with a Navier-Stokes computation indicate areas for improvement in turbulence and transition modelling.

scholarly journals Three-Dimensional Response of the Supported-Deep Excavation System: Case Study of a Large Scale Underground Metro Station

Geosciences ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 76
Author(s):  
Ashraf Hefny ◽  
Mohamed Ezzat Al-Atroush ◽  
Mai Abualkhair ◽  
Mariam Juma Alnuaimi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Two Dimensional ◽  
Deep Excavation ◽  
Metro Station ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The complexities and the economic computational infeasibility associated in some cases, with three-dimensional finite element models, has imposed a motive for many investigators to accept numerical modeling simplification solutions such as assuming two-dimensional (2D) plane strain conditions in simulation of several supported-deep excavation problems, especially for cases with a relatively high aspect ratio in plan dimensions. In this research, a two-dimensional finite element model was established to simulate the behavior of the supporting system of a large-scale deep excavation utilized in the construction of an underground metro station Rod El Farrag project (Egypt). The essential geotechnical engineering properties of soil layers were calculated using results of in-situ and laboratory tests and empirical correlations with SPT-N values. On the other hand, a three-dimensional finite element model was established with the same parameters adopted in the two-dimensional model. Sufficient sensitivity numerical analyses were performed to make the three-dimensional finite element model economically feasible. Results of the two-dimensional model were compared with those obtained from the field measurements and the three-dimensional numerical model. The comparison results showed that 3D high stiffening at the primary walls’ corners and also at the locations of cross walls has a significant effect on both the lateral wall deformations and the neighboring soil vertical settlement.

scholarly journals Bilge-Keel Influence on Free Decay of Roll Motion of a Realistic Hull1

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yichen Jiang ◽  
Ronald W. Yeung
Keyword(s):  
Free Surface ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Vortex Method ◽  
Roll Motion ◽  
Two Dimensional ◽  
Desktop Computer ◽  
Roll Damping ◽  
Discrete Vortex ◽  
Bilge Keel

The prediction of roll motion of a ship with bilge keels is particularly difficult because of the nonlinear characteristics of the viscous roll damping. Flow separation and vortex shedding caused by bilge keels significantly affect the roll damping and hence the magnitude of the roll response. To predict the ship motion, the Slender-Ship Free-Surface Random-Vortex Method (SSFSRVM) was employed. It is a fast discrete-vortex free-surface viscous-flow solver developed to run on a standard desktop computer. It features a quasi-three-dimensional formulation that allows the decomposition of the three-dimensional ship-hull problem into a series of two-dimensional computational planes, in which the two-dimensional free-surface Navier–Stokes solver Free-Surface Random-Vortex Method (FSRVM) can be applied. In this paper, the effectiveness of SSFSRVM modeling is examined by comparing the time histories of free roll-decay motion resulting from simulations and from experimental measurements. Furthermore, the detailed two-dimensional vorticity distribution near a bilge keel obtained from the numerical model will also be compared with the existing experimental Digital Particle Image Velocimetry (DPIV) images. Next, we will report, based on the time-domain simulation of the coupled hull and fluid motion, how the roll-decay coefficients and the flow field are altered by the span of the bilge keels. Plots of vorticity contour and vorticity isosurface along the three-dimensional hull will be presented to reveal the motion of fluid particles and vortex filaments near the keels.

Aerodynamic Aspects of Endwall Film-Cooling

1996 ◽  
Author(s):  
S. Friedrichs ◽  
H. P. Hodson ◽  
W. N. Dawes
Keyword(s):  
Secondary Flow ◽  
Film Cooling ◽  
Large Scale ◽  
Static Pressure ◽  
Three Dimensional ◽  
Surface Flow ◽  
Flow Visualisation ◽  
Film Cooling Effectiveness ◽  
Blade Passage ◽  
Endwall Film Cooling

This paper describes an investigation of the aerodynamic aspects of endwall film-cooling, in which the flow field downstream of a large-scale low-speed linear turbine cascade has been measured. The integrated losses and locations of secondary flow features with and without end wait film-cooling have been determined for variations of both the coolant supply pressure and injection location. Together with previous measurements of adiabatic film-cooling effectiveness and surface-flow visualisation, these results reveal the nature of the interactions between the ejected coolant and the flow in the blade passage. Measured hole massflows and a constant static pressure mixing analysis, together with the measured losses, allow the decomposition of the losses into three distinct entropy generation mechanisms: loss generation within the hole, loss generation due to the mixing of the coolant with the mainstream, and change in secondary loss generation in the blade passage. Results show that the loss generation within the coolant holes is substantial and that ejection into regions of low static pressure increases the loss per unit coolant massflow. Ejection upstream of the three-dimensional separation lines on the endwall changes secondary flow and reduces its associated losses. The results show that it is necessary to take the three-dimensional nature of the endwall flow into account in the design of endwall film-cooling configurations.

scholarly journals Two-dimensional fluid motion referred to a network of orthogonal curves

1949 ◽  
Vol 196 (1045) ◽  
pp. 301-310 ◽  
Keyword(s):  
Coordinate System ◽  
Gaussian Curvature ◽  
Large Scale ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Parameter Family ◽  
Two Dimensional ◽  
Gradient Wind

A theory already developed is applied to the case of two-dimensional motion parallel at each point of space to some member, Ʃ, of a one-parameter family of surfaces, the coordinate-system being a network of orthogonal curves drawn on Ʃ. The geodesic curvatures of the orthogonal curves and their relationship to the Gaussian curvature of Ʃ are worked out.The equations of motion and of continuity are expressed in terms of the geodesic curvatures. Meyer’s aerodynamical equations are derived as particular cases when the network is fixed in space and the surfaces are all planes. A formula for a large-scale gradient wind is also obtained as an example of the use of a moving network drawn on a sphere.

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