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

The structure

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

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

Wind speeds over the world’s oceans have increased over the past two decades, as have wave heights. Studies of climate change typically consider measurements or predictions of temperature over extended periods of time. Climate, however, is much more than temperature. Over the oceans, changes in wind speed and the surface gravity waves generated by such winds play an important role. We used a 23-year database of calibrated and validated satellite altimeter measurements to investigate global changes in oceanic wind speed and wave height over this period. We find a general global trend of increasing values of wind speed and, to a lesser degree, wave height, over this period. The rate of increase is greater for extreme events as compared to the mean condition.

https://researchbank.swinburne.edu.au/file/bca43746-6f16-4ad2-a4b7-27f8d8d60fed/1/PDF (Published version).pdf

Global trends in wind speed and wave height over the past 25 years

[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

Mixing layers and coherent structures in vegetated aquatic flows

Flume experiments were conducted with rigid and flexible model vegetation to study the structure of coherent vortices (a manifestation of the Kelvin–Helmholtz instability) and vertical transport in shallow vegetated shear flows. The vortex street in a vegetated shear layer creates a pronounced oscillation in the velocity profile, with the velocity near the top of a model canopy varying by a factor of three during vortex passage. In turn, this velocity oscillation drives the coherent waving of flexible canopies. Relative to flows over rigid vegetation, the oscillation in canopy geometry has the effect of decreasing the amount of turbulent vertical momentum transport in the shear layer. Using a waving plant to determine phase in the vortex cycle, each vortex is shown to consist of a strong sweep at its front (during which the canopy is most deflected), followed by a weak ejection at its rear (when the canopy height is at a maximum). Whereas in unobstructed mixing layers the vortices span the entire layer, they encompass only 70% of the flexibly obstructed shear layer studied here.

The structure of the shear layer in flows over rigid and flexible canopies

[1] In contrast to free shear layers, which grow continuously downstream, shear layers generated by submerged vegetation grow only to a finite thickness. Because these shear layers are characterized by coherent vortex structures and rapid vertical mixing, their thickness controls exchange between the vegetation and the overlying water. Experiments conducted in a laboratory flume show that the growth of these obstructed shear layers is arrested once the production of shear-layer-scale turbulent kinetic energy (SKE) is balanced by dissipation of SKE within the canopy. This equilibrium condition, along with a mixing length closure scheme, was used in a one-dimensional numerical model to predict the mean velocity profiles of the experimental shear layers. The agreement between model and experiment is very good, but field application of the model is limited by a lack of description of the drag coefficient in a submerged canopy.

/pdf/the-limited-growth-of-vegetated-shear-layers-1brwxx4g5u.pdf

The limited growth of vegetated shear layers

[1] The shear layer at the top of a submerged canopy generates coherent vortices that control exchange between the canopy and the overflowing water. Unlike free shear layers, the vortices in a canopy shear layer do not grow continuously downstream but reach and maintain a finite scale determined by a balance between shear production and canopy dissipation. This balance defines the length scale of vortex penetration into the canopy, δe, and the region of rapid exchange between the canopy and overflow. Deeper within the canopy, transport is constrained by smaller turbulence scales. A two-box canopy model is proposed on the basis of the length scale δe. Using diffusivity and exchange rates defined in previous studies, the model predicts the timescale required to flush the canopy through vertical exchange over a range of canopy density and height. The predicted canopy retention times, which range from minutes to an hour, are consistent with canopy retention inferred from tracer observations in the field and comparable to retention times for some hyporheic regions. The timescale for vertical exchange, along with the in-canopy velocity, determines the minimum canopy length for which vertical exchange dominates water renewal. Shorter canopies renew interior water through longitudinal advection. Finally, canopy water retention influences longitudinal dispersion through a transient storage process. When vertical exchange controls canopy retention, the transient storage dispersion increases with canopy height. When longitudinal advection controls water renewal, dispersion increases with canopy patch length.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006WR005362

Retention time and dispersion associated with submerged aquatic canopies

This paper reviews recent work on flow and transport in channels with submerged vegetation, including discussions of turbulence structure, mean velocity profiles, and dispersion. For submerged canopies of sufficient density, the dominant characteristic of the flow is the generation of a shear-layer at the top of the canopy. The shear-layer generates coherent vortices by Kelvin-Helmholtz (KH) instability. These vortices control the vertical exchange of mass and momentum, influencing both the mean velocity profile, as well as the turbulent diffusivity. For flexible canopies, the passage of the KH vortices generates a progressive wave along the canopy interface, termed monami. The KH vortices formed at the top of the canopy penetrate a distance δe into the canopy. This penetration scale segregates the canopy into an upper layer of rapid transport and a lower layer of slow transport. Flushing of the upper canopy is enhanced by the energetic shear-scale vortices. In the lower layer turbulence is limited to length-scales set by the stem geometry, and the resulting transport is significantly slower than that of the upper layer.

Marco Ghisalberti

Papers

Mixing layers and coherent structures in vegetated aquatic flows

The structure of the shear layer in flows over rigid and flexible canopies

The limited growth of vegetated shear layers

Retention time and dispersion associated with submerged aquatic canopies

Flow and transport in channels with submerged vegetation