A phenomenological closure model of the normal dispersive stresses

Moltchanov, Sharon; Shavit, Uri

doi:10.1002/2013wr014488

Cited by 14 publications

(16 citation statements)

References 66 publications

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“…These dispersive stresses can be calculated as

⟨ U_{i}^{''} U_{j}^{''} ⟩ = ⟨ U_{i} U_{j} ⟩ - ⟨ U_{i} ⟩ ⟨ U_{j} ⟩

. Several studies recently suggested that dispersive stresses should be included in the highly three‐dimensional canopy‐flow and wind‐farm models where the assumption of spanwise invariance is not fulfilled. However, modelling the flow together with the effect of dispersive stresses is complex without adequate closure models.…”

Section: Resultsmentioning

confidence: 99%

A linearized numerical model of wind-farm flows

et al. 2016

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A fast and reasonably accurate numerical three‐dimensional wake model able to predict the flow behaviour of a wind farm over a flat terrain has been developed. The model is based on the boundary‐layer approximation of the Navier–Stokes equations, linearized around the incoming atmospheric boundary layer, with the assumption that the wind turbines provide a small perturbation to the velocity field. The linearization of the actuator‐disc theory brought additional insights that could be used to understand the behaviour, as well as the limitations, of a flow model based on linear methods: for instance, it is shown that an adjustment of the turbine's thrust coefficient is necessary in order to obtain the same wake velocity field provided by the actuator disc theory within the used linear framework. The model is here validated against two independent wind‐tunnel campaigns with a small and a large wind farm aimed at the characterization of the flow above and upstream of the farms, respectively. The developed model is, in contrary to current engineering wake models, able to account for effects occurring in the upstream flow region, thereby including more physical mechanisms than other simplified approaches. The conducted simulations (in agreement with the measurement results) show that the presence of a wind farm affects the approaching flow far more upstream than generally expected and definitely beyond the current industrial standards. Despite the model assumptions, several velocity statistics above wind farms have been properly estimated providing an insight into the transfer of momentum inside the turbine rows. Copyright © 2016 John Wiley & Sons, Ltd.

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“…These dispersive stresses can be calculated as

⟨ U_{i}^{''} U_{j}^{''} ⟩ = ⟨ U_{i} U_{j} ⟩ - ⟨ U_{i} ⟩ ⟨ U_{j} ⟩

Section: Resultsmentioning

confidence: 99%

A linearized numerical model of wind-farm flows

et al. 2016

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“…As a result, canopy flow models often ignore the potential modification of drag inside the canopy and do not include the role of dispersive stresses [ Breugem and Boersma , ; Lien et al ., ; Luhar et al ., ; Tanino and Nepf , , to name a few]. In the past several years, there has been a growing attention toward understanding the role of these terms with a special interest on dispersive stresses [ Bohm et al ., ; Poggi et al ., ; Poggi and Katul , ; Moltchanov et al ., ; Moltchanov and Shavit , ]. In this study, we evaluate the spatially averaged momentum equation and discuss the relative role of each of the terms focusing our attention on the canopy entry region.…”

Section: Introductionmentioning

confidence: 99%

Canopy edge flow: A momentum balance analysis

Moltchanov

Bohbot-Raviv

Duman

et al. 2015

Water Resources Research

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Canopy flow models are often dedicated to ideal, infinite, homogenous systems. However, real canopy systems have physical boundaries, where the flow enters and leaves patches of vegetation, generating a complex pressure field and velocity variations. Here we focus our study on the canopy entry region by examining the terms involved in the double (space and time) averaged momentum equations and their relative contribution to the total momentum balance. The estimation of each term is made possible by particle image velocimetry (PIV) measurements in a model canopy constructed of randomly distributed thin glass plates. The instantaneous velocity fields were used to calculate the mean velocities, pressure, drag, Reynolds stresses, and dispersive stresses. It was found that within the entry region, the pressure gradient, the drag forces, and dispersive stresses are the three most significant terms that affect the balance in the streamwise momentum equation. In the vertical direction, the dispersive stresses are also significant and their contribution to the total momentum cannot be ignored. The study shows that dispersive stresses are initially formed around canopy edges; at both the entry region and the canopy top boundary. They start as a sink term, extracting momentum from the flow, and then become a source term that contributes momentum to the flow until they eventually decay at some short penetration distance into the canopy. These results reveal a new understanding on the evolution of momentum within the entry region, necessary in any closure modeling of flow in real canopies.

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“…Under low tide conditions, this feature of turbulent mixing is likely to improve the well‐being of the coral reefs. Substantial dispersive stress at magnitudes comparable to (in H / h c > 1) and even greater than (in H / h c = 1) Reynolds stress was measured within the exchange zone. As dispersive stresses scale with the velocity square (Moltchanov & Shavit, ), a confusion is expected in other studies, where increased calibrated drag force replaces the actual increase in dispersive stress. Quadrant analysis reveals that the vertical distribution of the ejections to sweeps ratio (S 2 / S 4 ) is similar to that of an urban canopy in and above the exchange zone. The flipping in the number of occurrences of inward/outward interactions versus sweeps/ejections occurs in the wake zone because of the sign change in the mean flow gradient. Integral length scales show a local peak value in the wake zone.…”

Section: Discussionmentioning

confidence: 88%

“…Substantial dispersive stress at magnitudes comparable to (in H/h c > 1) and even greater than (in H/ h c = 1) Reynolds stress was measured within the exchange zone. As dispersive stresses scale with the velocity square (Moltchanov & Shavit, 2013), a confusion is expected in other studies, where increased calibrated drag force replaces the actual increase in dispersive stress. 3.…”

Section: Discussionmentioning

confidence: 93%

The Effect of Water Depth and Internal Geometry on the Turbulent Flow Inside a Coral Reef

Asher

Shavit

2019

JGR Oceans

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The flow of water through coral reefs controls the transport of mass, momentum, and energy and, as a result, affects key processes such as feeding, photosynthesis, and reproduction. While it is often analyzed as a typical canopy flow, the flow through coral reefs is different from both terrestrial and aquatic canopies. A combination of a nonuniform vertical distribution of porosity and resistance and variations in relative submergence generates regions of high‐velocity gradients, increased integral length scales and instabilities which have not previously been quantified in detail. Here we report on velocity measurements inside and above a laboratory reef made of 81 Pocillopora Meandrina skeletons, for a range of relative submergence and flow rates. Under the action of a pressure gradient, the mean velocity shows an increase in the wake zone, generating a potential source for mixing due to a second inflection point. Unlike classical boundary layers and other canopy flows, a quadrant analysis shows that the number of inward/outward interactions events is larger than sweeps/ejections inside the canopy wake zone, due to the sign change in the mean velocity gradient. The vertical distribution of the integral length scales shows a local maximum in the lower part of the wake zone. Finally, under fully submerged conditions, the stream‐wise turbulent energy spectra inside the reef follow an approximate kx−7/3, as opposed to the expected kx−5/3 behavior above the reef. Under near‐emergent conditions, no fit to such a power law could be obtained.

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A phenomenological closure model of the normal dispersive stresses

Cited by 14 publications

References 66 publications

A linearized numerical model of wind-farm flows

A linearized numerical model of wind-farm flows

Canopy edge flow: A momentum balance analysis

The Effect of Water Depth and Internal Geometry on the Turbulent Flow Inside a Coral Reef

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