Double Averaging method - Revision history

Bendikhansen at 14:07, 8 October 2020

2020-10-08T14:07:33Z

Bendikhansen at 14:06, 8 October 2020

2020-10-08T14:06:21Z

Bendikhansen at 14:05, 8 October 2020

2020-10-08T14:05:22Z

Bendikhansen at 14:05, 8 October 2020

2020-10-08T14:05:10Z

Bendikhansen at 14:01, 8 October 2020

2020-10-08T14:01:59Z

Bendikhansen at 13:59, 8 October 2020

2020-10-08T13:59:51Z

Bendikhansen: /* Quick summary */

2020-10-08T13:52:06Z

Quick summary

Bendikhansen at 13:51, 8 October 2020

2020-10-08T13:51:54Z

Bendikhansen at 13:50, 8 October 2020

2020-10-08T13:50:09Z

Bendikhansen: /* How can the DAM be applied? */

2020-10-08T13:47:52Z

How can the DAM be applied?

@@ Line 1: / Line 1: @@
 {{Note|This technology has been enhanced in the FIThydro project! See [[Innovative technologies from FIThydro]] for a complete list.|reminder}}
 =Quick summary=
 [[file:dam_velocity.png|thumb|500px|Figure 1: Reynolds decomposition for the velocity component ''u'']]

@@ Line 5: / Line 5: @@
 [[file:dam_flow_layers.png|thumb|500px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]
-Date: 2007
+Date: 2007 (enhanced in 2020)
-Developed by: Nikora et al., 2007 a and b (see references)
+Developed by: Nikora et al., 2007 a and b (see references) (enhanced in the FIThydro project in 2020)
 Type: [[:Category:Methods|Method]]

@@ Line 2: / Line 2: @@
 '''Note: This article will be finished with the submission of deliverable 3.3 and 3.4 in October, 2020'''
 =Quick summary=
-[[file:dam_velocity.png|thumb|5000px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
+[[file:dam_velocity.png|thumb|500px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
 [[file:dam_flow_layers.png|thumb|500px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]

@@ Line 2: / Line 2: @@
 '''Note: This article will be finished with the submission of deliverable 3.3 and 3.4 in October, 2020'''
 =Quick summary=
-[[file:dam_velocity.png|thumb|250px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
+[[file:dam_velocity.png|thumb|5000px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
-[[file:dam_flow_layers.png|thumb|250px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]
+[[file:dam_flow_layers.png|thumb|500px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]
 Date: 2007

@@ Line 2: / Line 2: @@
 '''Note: This article will be finished with the submission of deliverable 3.3 and 3.4 in October, 2020'''
 =Quick summary=
-[[file:3d_fish_trackingtion1.jpg|thumb|250px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
+[[file:dam_velocity.png|thumb|250px|Figure 1: Reynolds decomposition for the velocity component ''u'']]
-[[file:3d_fish_trackingtion1.jpg|thumb|250px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]
+[[file:dam_flow_layers.png|thumb|250px|Figure 2: Subdivison of turbulent open channel flow into flow layers]]
 Date: 2007

← Older revision		Revision as of 13:52, 8 October 2020
Line 5:		Line 5:


−	Date:	+	Date: 2007

	Developed by: Nikora et al., 2007 a and b (see references)		Developed by: Nikora et al., 2007 a and b (see references)

@@ Line 7: / Line 7: @@
 Date:
-Developed by:
+Developed by: Nikora et al., 2007 a and b (see references)
 Type: [[:Category:Methods|Method]]
@@ Line 63: / Line 63: @@
 *Mignot, Emmanuel, E. Barthelemy, and D. Hurther. 2009. ‘Double-Averaging Analysis and Local Flow Characterization of near-Bed Turbulence in Gravel-Bed Channel Flows’. Journal of Fluid Mechanics 618 (January): 279–303. https://doi.org/10.1017/S0022112008004643.
 *Nikora, Vladimir, Derek Goring, Ian McEwan, and George Griffiths. 2001. ‘Spatially Averaged Open-Channel Flow over Rough Bed’. Journal of Hydraulic Engineering 127 (2): 123–33. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(123).
-*Nikora, Vladimir, Ian McEwan, Stephen McLean, Stephen Coleman, Dubravka Pokrajac, and Roy Walters. 2007. ‘Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background’. Journal of Hydraulic Engineering 133 (8): 873–83. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(873).
+*Nikora, Vladimir, Ian McEwan, Stephen McLean, Stephen Coleman, Dubravka Pokrajac, and Roy Walters. 2007 (a). ‘Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: Theoretical Background’. Journal of Hydraulic Engineering 133 (8): 873–83. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(873).
-*Nikora, Vladimir, Stephen McLean, Stephen Coleman, Dubravka Pokrajac, Ian McEwan, Lorna Campbell, Jochen Aberle, Dougal Clunie, and Katinka Koll. 2007. ‘Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: *Applications’. Journal of Hydraulic Engineering 133 (8): 884–95. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(884).
+*Nikora, Vladimir, Stephen McLean, Stephen Coleman, Dubravka Pokrajac, Ian McEwan, Lorna Campbell, Jochen Aberle, Dougal Clunie, and Katinka Koll. 2007 (b). ‘Double-Averaging Concept for Rough-Bed Open-Channel and Overland Flows: *Applications’. Journal of Hydraulic Engineering 133 (8): 884–95. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(884).
 *Papadopoulos, Konstantinos, Vladimir Nikora, Stuart Cameron, Mark Stewart, Hamish Biggs, and Christopher Gibbins. 2016. ‘Time-Averaged Hydrodynamic Equations for Mobile-Bed Conditions’. In Hydrodynamic and Mass Transport at Freshwater Aquatic Interfaces: 34th International School of Hydraulics, edited by Pawe\l Rowiński and Andrea Marion, 1–9. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-27750-9_1.
 [[Category:Methods]] [[Category:developed in FIThydro]]

@@ Line 37: / Line 37: @@
 The flow is subdivided into three main layers according to the influence of occurring stresses: The top layer is called the outer layer, where bed roughness does not influence the velocity distribution. The next layer closer to the river bed is the logarithmic layer, where the distribution of the time-averaged velocity follows a logarithmic law. The logarithmic region does not reach until the roughness tops. The roughness layer is the first defined flow region to contain free flowing parts as well as the upper part of the roughness elements. In contrast to the other flow regions the roughness layer is influenced by the individual roughness elements of the river bed and therefore faces additional forces. It is subdivided into the form-induced sublayer just above the roughness crests and the interfacial sublayer which occupies the flow region between the troughs and the tops of the roughness elements. The form-induced sublayer was introduced because the flow is strongly affected by turbulences produced by the roughness crests which may appear as small eddies and causes an extensive spatial heterogeneity.
-This is considered as the form-induced stresses in the DA momentum equation. In the case of a rough permeable bed, the layer below the roughness troughs is the last one and is
+This is considered as the form-induced stresses in the Double Averaging momentum equation. In the case of a rough permeable bed, the layer below the roughness troughs is the last one and is
 named the subsurface layer.
 ==Where can the DAM be applied?==
 =Relevant mitigation measures and test cases=
 {{Suitable measures for Double Averaging method}}
@@ Line 47: / Line 54: @@
 =Relevant literature=
-[[Category:Methods]] [[Category:developed in FIThydro]][[category:Needs improvement]]
+[[Category:Methods]] [[Category:developed in FIThydro]]

← Older revision		Revision as of 13:47, 8 October 2020
Line 32:		Line 32:

	θ(𝑥, 𝑦, 𝑧, 𝑡) = 〈θ̅ 〉(𝑧𝑖) +θ̃ (𝑥, 𝑦, 𝑧) + θ′(𝑥, 𝑦, 𝑧, 𝑡)		θ(𝑥, 𝑦, 𝑧, 𝑡) = 〈θ̅ 〉(𝑧𝑖) +θ̃ (𝑥, 𝑦, 𝑧) + θ′(𝑥, 𝑦, 𝑧, 𝑡)
		+
		+	The overbar is the time-averaging operator. The angular brackets 〈〉 are used as the space-averaging operator. The symbol ′ indicates temporal fluctuation, whereas the tilde (~) denotes spatial fluctuation. In order to investigate and classify the flow conditions in a rough river bed, Nikora et al. (2001) defined layer specifications (figure 2).
		+
		+	The flow is subdivided into three main layers according to the influence of occurring stresses: The top layer is called the outer layer, where bed roughness does not influence the velocity distribution. The next layer closer to the river bed is the logarithmic layer, where the distribution of the time-averaged velocity follows a logarithmic law. The logarithmic region does not reach until the roughness tops. The roughness layer is the first defined flow region to contain free flowing parts as well as the upper part of the roughness elements. In contrast to the other flow regions the roughness layer is influenced by the individual roughness elements of the river bed and therefore faces additional forces. It is subdivided into the form-induced sublayer just above the roughness crests and the interfacial sublayer which occupies the flow region between the troughs and the tops of the roughness elements. The form-induced sublayer was introduced because the flow is strongly affected by turbulences produced by the roughness crests which may appear as small eddies and causes an extensive spatial heterogeneity.
		+
		+	This is considered as the form-induced stresses in the DA momentum equation. In the case of a rough permeable bed, the layer below the roughness troughs is the last one and is
		+	named the subsurface layer.

	==Where can the DAM be applied?==		==Where can the DAM be applied?==