The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Digital particle image velocimetry (DPIV) is a non-intrusive analysis technique that is very popular for mapping flows quantitatively. To get accurate results, in particular in complex flow fields, a number of challenges have to be faced and solved: The quality of the flow measurements is affected by computational details such as image pre-conditioning, sub-pixel peak estimators, data validation procedures, interpolation algorithms and smoothing methods. The accuracy of several algorithms was determined and the best performing methods were implemented in a user-friendly open-source tool for performing DPIV flow analysis in Matlab.

/pdf/pivlab-towards-user-friendly-affordable-and-accurate-digital-3pwqyjh6ub.pdf

PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB

OUTPU T 29 OUTPU T 30 OUTPU T 31 OUTPU T 32 OUTPU T 25 OUTPU T 26 OUTPU T 27 OUTPU T 28 OUTPU T 21 OUTPU T 22 OUTPU T 23 OUTPU T 24 OUTPU T 17 OUTPU T 18 OUTPU T 19 OUTPU T 20 OUTPU T 13 OUTPU T 14 OUTPU T 15 OUTPU T 16 OUTPU T 9 OUTPU T 10 OUTPU T 11 OUTPU T 12 OUTPU T 5 OUTPU T 6 OUTPU T 7 OUTPU T 8 OUTPU T 1 OUTPU T 2 OUTPU T 3 OUTPU T 4 29 30 31 32 25 26 27 28 21 22 23 24 17 18 19 20 13 14 15 16 9

A User’s Guide

Marine vegetated habitats occupy a small fraction of the ocean surface, but contribute about 50% of the carbon that is buried in marine sediments. In this Review the potential benefits of conservation, restoration and use of these habitats for coastal protection and climate change mitigation are assessed. Marine vegetated habitats (seagrasses, salt-marshes, macroalgae and mangroves) occupy 0.2% of the ocean surface, but contribute 50% of carbon burial in marine sediments. Their canopies dissipate wave energy and high burial rates raise the seafloor, buffering the impacts of rising sea level and wave action that are associated with climate change. The loss of a third of the global cover of these ecosystems involves a loss of CO2 sinks and the emission of 1 Pg CO2 annually. The conservation, restoration and use of vegetated coastal habitats in eco-engineering solutions for coastal protection provide a promising strategy, delivering significant capacity for climate change mitigation and adaption.

The role of coastal plant communities for climate change mitigation and adaptation

Aquatic plants convert mean kinetic energy into turbulent kinetic energy at the scale of the plant stems and branches. This energy transfer, linked to wake generation, affects vegetative drag and turbulence intensity. Drawing on this physical link, a model is developed to describe the drag, turbulence and diffusion for flow through emergent vegetation which for the first time captures the relevant underlying physics, and covers the natural range of vegetation density and stem Reynolds' numbers. The model is supported by laboratory and field observations. In addition, this work extends the cylinder-based model for vegetative resistance by including the dependence of the drag coefficient, CD, on the stem population density, and introduces the importance of mechanical diffusion in vegetated flows.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998WR900069

Drag, turbulence, and diffusion in flow through emergent vegetation

Aquatic vegetation controls the mean and turbulent flow structure in channels and coastal regions and thus impacts the fate and transport of sediment and contaminants. Experiments in an open-channel flume with model vegetation were used to better understand how vegetation impacts flow. In particular, this study describes the transition between submerged and emergent regimes based on three aspects of canopy flow: mean momentum, turbulence, and exchange dynamics. The observations suggest that flow within an aquatic canopy may be divided into two regions. In the upper canopy, called the “vertical exchange zone”, vertical turbulent exchange with the overlying water is dynamically significant to the momentum balance and turbulence; and turbulence produced by mean shear at the top of the canopy is important. The lower canopy is called the “longitudinal exchange zone” because it communicates with surrounding water predominantly through longitudinal advection. In this region turbulence is generated locally by the canopy elements, and the momentum budget is a simple balance of vegetative drag and pressure gradient. In emergent canopies, only a longitudinal exchange zone is present. When the canopy becomes submerged, a vertical exchange zone appears at the top of the canopy and deepens into the canopy as the depth of submergence increases.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JC900145

Flow structure in depth-limited, vegetated flow

This review describes mean and turbulent flow and mass transport in the presence of aquatic vegetation. Within emergent canopies, the turbulent length scales are set by the stem diameter and spacing, and the mean flow is determined by the distribution of the canopy frontal area. Near sparse submerged canopies, the bed roughness and near-bed turbulence are enhanced, but the velocity profile remains logarithmic. For dense submerged canopies, the drag discontinuity at the top of the canopy generates a shear layer, which contains canopy-scale vortices that control the exchange of mass and momentum between the canopy and the overflow. The canopy-scale vortices penetrate a finite distance into the canopy, δe, set by the canopy drag. This length scale segregates the canopy into two regions: The upper canopy experiences energetic turbulent transport, controlled by canopy-scale vortices, whereas the lower canopy experiences diminished transport, associated with the smaller stem-scale turbulence. The canopy-scale vortices induce a waving motion in flexible blades, called a monami.

Flow and Transport in Regions with Aquatic Vegetation

[1] To date, flow through submerged aquatic vegetation has largely been viewed as perturbed boundary layer flow, with vegetative drag treated as an extension of bed drag. However, recent studies of terrestrial canopies demonstrate that the flow structure within and just above an unconfined canopy more strongly resembles a mixing layer than a boundary layer. This paper presents laboratory measurements, obtained from a scaled seagrass model, that demonstrate the applicability of the mixing layer analogy to aquatic systems. Specifically, all vertical profiles of mean velocity contained an inflection point, which makes the flow susceptible to Kelvin-Helmholtz instability. This instability leads to the generation of large, coherent vortices within the mixing layer (observed in the model at frequencies between 0.01 and 0.11 Hz), which dominate the vertical transport of momentum through the layer. The downstream advection of these vortices is shown to cause the progressive, coherent waving of aquatic vegetation, known as the monami. When the monami is present, the turbulent vertical transport of momentum is enhanced, with turbulent stresses penetrating an additional 30% of the plant height into the canopy.

/pdf/mixing-layers-and-coherent-structures-in-vegetated-aquatic-3cttu00nc1.pdf

Heidi Nepf

Papers

Drag, turbulence, and diffusion in flow through emergent vegetation

Flow structure in depth-limited, vegetated flow

Flow and Transport in Regions with Aquatic Vegetation

Mixing layers and coherent structures in vegetated aquatic flows

Flow and Transport in Regions with Aquatic Vegetation