The impact of plant morphology on flow structure: comparative analysis of two types of submerged flexible macrophyte

ABSTRACT

The presence of aquatic vegetation in riverine and lacustrine environments alters the mean and turbulent flow structure and thus impacts the fate and transport of sediment and contaminants. Turbulent flows through Vallisneria natans (V. natans) and Potamogeton malaianus (P. malaianus) were investigated in a laboratory flume. The impact of plant morphology on mean velocity profile and turbulence distribution was analysed and discrepancies in flow alteration caused by different types of macrophyte were highlighted. Results show that a dense canopy of submerged macrophyte leads to a velocity profile featuring a counter velocity gradient in the lower part of the canopy. Negative Reynolds stress and its local maximum were observed there. Discrepancies in flow structure caused by different morphologies of both tested plants were further identified. With smaller frontal area in the lower part of the canopy, P. malaianus causes a much bigger gradient and local maximum in the velocity profile, and thus a larger local stress maximum than V. natans. The mean velocity gradient around the top of canopy, the Reynolds stress and the turbulence kinetic energy at the canopy interface are smaller than for the flow through the V. natans canopy. Larger reduction of the mean velocity within the V. natans canopy makes the suspended sediment of fine particles more easily deposited than in the P. malaianus canopy.     

Field study on flow structures within aquatic vegetation under combined currents and small-scale waves

Field measurements were conducted to study the influence of aquatic vegetation on flow structures in floodplains under combined currents and wind-driven waves. Wave and turbulent velocities were decomposed from the time series of instantaneous velocity and analysed separately. In the present study, the wind waves were small, leading to the ratios of wave excursion (E_w) to stem spacing (S) for all cases tested here were less than 0.5. This caused the vertical distributions of time-averaged velocity (U_horiz) and turbulent kinetic energy (TKE) impacted by vegetation similar with the vegetated flow structures under pure current conditions. For emergent vegetation, U_horiz and TKE distributed uniformly through the entire water column or increased slightly from bed to water surface. Similar distributions were present in the lower part of submerged vegetation. In the upper part of submerged vegetation, U_horiz and TKE increased rapidly toward water surface and TKE reached its maximum near the top of vegetation. The measured wave orbital velocity (U_w) fitted linear wave theory well through the entire water depth for both the emergent and submerged cases, so that with small E_w/S the wave velocity was not attenuated within vegetation and U_w within canopy can be predicted by the linear wave theory under combined currents and waves. However, wind-driven waves made the turbulence generated near the top of canopy penetrate a deeper depth into vegetation than predictions under pure current conditions.     

Velocity and turbulence variations at the edge of saltmarshes

Saltmarsh vegetation significantly influences tidal currents and sediment deposition by decelerating the water velocity in the canopy. In order to complement previous field results, detailed profiles of velocity and turbulence were measured in a laboratory flume. Natural Spartina anglica plants were installed in a 3 m length test section in a straight, recirculating flume. Different vegetation densities, water depths and surface velocities were investigated. The logarithmic velocity profile, which existed in front of the vegetation, was altered gradually to a skimming-flow profile, typical for submerged saltmarsh vegetation. The flow reduction in the denser part of the canopy also induced an upward flow (the current was partially deflected by the canopy). The skimming flow was accompanied by a zone of high turbulence co-located with the strongest velocity gradient. This gradient moved upward and the turbulence increased with distance from the edge of the vegetation. Below the skimming flow, the velocity and the turbulence were low. The structure of the flow in the canopy was relatively stable 2 m into the vegetation. The roughness length (z₀) of the vegetation depends only on the vegetation characteristics, and is not sensitive to the current velocity or the water depth. Both the reduced turbulence in the dense canopy and the high turbulence at the top of the canopy should increase sediment deposition. On the other hand, the high turbulence zone just beyond the vegetation edge and the oblique upward flow may produce reduced sedimentation; a phenomenon that was observed near the vegetation edge in the field.     

Influence of Zostera marina canopies on unidirectional flow,hydraulic roughness and sediment movement

Seagrasses develop extensive or patchy underwater meadows in coastal areas around the world, forming complex, highly productive ecosystems. Seagrass canopies exert strong effects on water flow inside and around them, thereby affecting flow structure, sediment transport and benthic ecology. The influence of Zostera marina canopies on flow velocity, turbulence, hydraulic roughness and sediment movement was evaluated through laboratory experiments in 2 flumes and using live Z. marina and a mobile sand bed. Profiles of instantaneous velocities were measured and sediment movement was identified upstream, within and downstream of patches of different sizes and shoot density and at different free-stream velocities. Flow structure was characterised by time-averaged velocity, turbulence intensity and Turbulent Kinetic Energy (TKE). When velocity data were available above the canopy, they were fitted to the Law of the Wall and shear velocities and roughness lengths were calculated. When a seagrass canopy was present, three layers were distinguishable in the water column: (1) within canopy represented by low velocities and high turbulence; (2) transition zone around the height of the canopy, where velocities increased, turbulence decreased and TKE was high; and (3) above canopy where velocities were equal or higher than free-stream velocities and turbulence and TKE were lower than below. Shoot density and patch-width influenced this partitioning of the flow when the canopy was long enough (based on flume experiments, at least more than 1 m-long). The enhanced TKE observed at the canopy/water interface suggests that large-scale turbulence is generated at the canopy surface. These oscillations, likely to be related to the canopy undulations, are then broken down within the canopy and high-frequency turbulence takes place near the bed. This turbulence ‘cascade’ through the canopy may have an important impact on biogeochemical processes. The velocity above the canopy generally followed a logarithmic profile. Roughness lengths were higher above the canopy than over bare sand and increased with increasing distance from the leading edge of the canopy; however, they were still small (<1 cm) compared to other studies in the literature. Within and downstream of the canopy, sediment movement was observed at velocities below the threshold of motion. It was likely caused by the increased turbulence at those positions. This has large implications for sediment transport in coastal zones where seagrass beds develop.     

Flow analysis in a channel with flexible vegetation using double-averaging method

The paper addresses the problem of the resistance due to vegetation in an open channel flow, characterized by partially and fully submerged vegetation formed by colonies of bushes. The flow is characterized by significant spatial variations of velocity between vertical profiles that make the traditional approach based on time averaging of turbulent fluctuations inconvenient. A more useful procedure, based on time and spatial averaging (Double-Averaging Method) is applied for the flow field analysis and characterization. The vertical distribution of mean velocity and turbulent stresses at different spatial locations has been measured with a 3D Acoustic Doppler Velocimeter (ADV) for two different vegetation densities where fully submerged real bushes (salix pentandra) have been used. Velocity measurements were completed together with the measurements of drag exerted on the flow by bushes at different flow depths. The analysis of velocity measurements allows depicting the fundamental characteristics of both the mean flow field and turbulence. The experimental data show that the contribution of form-induced stresses to the momentum balance cannot be neglected. The mean velocity profiles and the spatially averaged turbulent intensity profiles allow inferring that the vegetation density is a driving parameter for the development of a mixing layer at the canopy top in the case of submerged vegetation. Moreover, the net upward turbulent momentum flux, evaluated with the methodology proposed by Lu and Willmarth (1973), appears to be damped for increased vegetation density; this finding can rationally explain the reduction of the suspended sediment transport capacity typically observed in free surface flows over a vegetated bed.     

Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation

Based on the detailed laboratory experiments and theoretical analysis, a new three-layer model is proposed to predict the vertical velocity distribution in an open channel flow with submerged vegetation. The time averaged velocity and turbulence behaviour of a steady uniform flow with fully submerged artificial rigid vegetation was measured using a 3D Micro ADV, and the vertical distribution of velocity and Reynolds shear stress at different vegetation height, vegetation density and measuring positions were obtained. The results show that the velocity profile consists of three hydrodynamic regimes (i.e. the upper non-vegetated layer, the outer and bottom layer within vegetation); accordingly different methods had been adopted to describe the vertical velocity distribution. For the upper non-vegetated layer, a modified mixing length theory combined with the concept of ‘the new vegetation boundary layer’ was adopted, and an analytical model was presented to predict the vertical velocity distribution in this region. For the bottom layer within vegetation, the depth average velocity was obtained by numerically solving the momentum equations. For the upper layer within vegetation, the analytical solution was presented by expressing the shear stress as a formula fitted to the experimental data. Finally, the analytical predictions of the vertical velocity over the whole flow depth were compared with the results obtained by other researchers, and the good agreement proved that the three-layer model can be used to predict the velocity distribution of the open channel flow with submerged rigid vegetation.     

Flow field downstream of individual aquatic plants—Experiments in a natural river with Potamogeton crispus L. and Myriophyllum spicatum L.

Flow disturbances generated by individual patches of submerged, flexible aquatic vegetation were investigated for two naturally growing macrophyte species, Potamogeton crispus L. and Myriophyllum spicatum L., in a sandy lowland river. Through acoustic Doppler velocimetry, 24 vertical profiles of the 3D velocity field were recorded downstream of each of the patches. The morphological features and biomechanical properties of the plants were also evaluated. The experiments showed the relationship between biomechanical characteristics and turbulence statistics. M. spicatum, which was stiffer and therefore less prone to dynamic reconfiguration, showed a greater effect on velocity damping, causing an increase in Reynold stresses, turbulence intensities, and turbulent kinetic energy downstream of the patch. These effects were present in regions both above and below plant height. In contrast for P. crispus, these effects were present only below plant height. The stiffer plant produced a mixing layer in its wake similar to that of dense plant canopies. The patch of less stiff and more streamlined P. crispus with longer leaves presented a much weaker effect on the flow. In contrast to previous studies conducted with rigid plant surrogates, we concluded that reconfiguration of the living flexible plants allows the plants to minimize drag forces, and therefore, their influence on the flow field was weaker than the effects reported for rigid surrogates.     

Turbulence characteristics of flow past submerged vanes

Submerged vanes are hydrofoils utilized to manage the sediment transport through the river by generating the turbulence in the flow in the form of helical currents.The vanes are placed in the flow with respect to its direction at angle of 10°to 40°.In the current study,an attempt has been made to study the effect of the introduction of vanes in form of rows on parameters like turbulence intensities,Reynolds stresses,turbulent kinetic energy,anisotropy index,and the velocity profile of the flow.It is observed that the profile of variation of turbulence intensities,turbulent kinetic energy,vertical Reynolds stress and velocity over three different marked verticals on a transect are nearly identical whereas a large scatter is observed in the variation of transverse Reynolds stress over the vertical of the aforementioned vertical locations.This observation suggests that flow turbulence is homogeneous over the vertical while scattering in the variation of the transverse Reynolds stress component may be attributed to the presence of secondary currents in the flow.After introducing rows of submerged vanes,the bed turbulence is reduced,hence,helping reduce many scour related phenomenon.It is also observed that a vortex occurred at 0.85 times the height of the vane and the variation of turbulence quantities in the presence of vanes shows the existence of a peak in these quantities.It is observed that as flow moves away from the vane rows,due to the interaction of vortices and the action of vorticity,vortices dampens down and the flow regains homogeneity.After the introduction of submerged vane rows,bed shear stress reduces as fluid from the surface replaces the slow-moving fluid near the bed due to the secondary currents generated by the vanes leading to reduction in the magnitude of turbulence intensities,Reynolds stresses,and turbulent kinetic energy near the bed.The anisotropy index is observed to increase near the bed as induced secondary currents enhanced the turbulence production in the near bed region.All the profiles of parameters obtained in the current study show the existence of a peak or inflexions at a height of 0.85 H from bed(Where,H is the height of the submerged vane).Profiles of parameters obtained in the current study suggest that as the vorticity dampens the vane-generated secondary currents,the scattering in the profiles along the vertical reduces and profiles are observed to regain the variation which they had before the introduction of vane rows,suggesting that flow turbulence has regained its homogeneity.     

The influence of macrophyte growth,typical of eutrophic conditions,on river flow velocities and turbulence production

The influence of emergent and submerged macrophytes on flow velocity and turbulence production is demonstrated in a 140 m reach of the River Blackwater in Farnborough, Hampshire, UK. Macrophyte growth occurs in patches and is dominated by Sparganium erectum and Sparganium emersum. In May 2001, patches of S. erectum were already established and occupied 18% of the channel area. The flow adjusted to these (predominantly lateral) patches by being channelled through a narrower cross‐section. The measured velocity profiles showed a logarithmic form, with deviations attributable to topographic control. The channel bed was the main source of turbulence. In September 2001, in‐stream macrophytes occupied 27% of the channel, and overhanging bank vegetation affected 32% of the area. Overall flow resistance, described by Manning's n, showed a threefold increase that could be attributed to the growth of S. emersum in the middle of the channel. Velocity profiles showed different characteristic forms depending on their position relative to plant stems and leaves. The overall velocity field had a three‐dimensional structure. Turbulence intensities were generally higher and turbulence profiles tended to mirror the velocity profiles. Evidence for the generation of coherent eddies was provided by ratios of the root mean square velocities. Spectral analysis identified deviations from the Kolmogorov ?5/3 power law and provided statistical evidence for a spectral short‐cut, indicative of additional turbulence production. This was most marked for the submerged vegetation and, in some instances, the overhanging bank vegetation. The long strap‐like leaves of S. emersum being aligned approximately parallel to the flow and the highly variable velocity field created by the patch arrangement of macrophytes suggest that the dominant mechanism for turbulence production is vortex shedding along shear zones. Wake production around individual stems of S. emersum close to the bed may also be important locally. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of submerged aquatic vegetation on turbulence induced by an oscillating grid

In wetlands wind-induced turbulence significantly affects the bottom boundary, and the interaction between turbulence and plant canopies is therefore particularly important. The aim of this study is to advance understanding of the impact of this interaction in submerged aquatic vegetation (SAV)¹ on vertical mixing in a fluid dominated by turbulence. Wind-generated turbulence was simulated in the laboratory using an oscillating grid. We quantify the vertical distribution of turbulent kinetic energy (TKE)² above and within different types of vegetation, measured by an acoustic Doppler velocimeter. Experimental conditions are analysed in two canopy models (rigid and semi-rigid) with seven solid plant fractions (SPFs)³, three stem diameters (d)⁴ and three oscillation grid frequencies (f)⁵ and four natural SAVs (Cladium mariscus, Potamogeton nodosus, Myriophyllum verticillatum and Ruppia maritima).     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.     

2DV modelling of sediment transport processes over full-scale ripples in regular asymmetric oscillatory flow

Wave-induced, steep vortex ripples are ubiquitous features in shallow coastal seas and it is therefore important to fully understand and model the sediment transport processes that occur over them. To this end, two two-dimensional vertical (2DV) models have been critically tested against detailed velocity and sediment concentration measurements above mobile ripples in regular asymmetric oscillatory flow. The two models are a k–ω turbulence-closure model and a discrete-vortex, particle-tracking (DVPT) model, while the data are obtained in the Aberdeen oscillatory flow tunnel (AOFT). The models and the data demonstrate that the time-dependent velocity and suspended sediment concentration above the ripple are dominated by the generation of lee-side vortices and their subsequent ejection at flow reversal. The DVPT model predicts the positions and strengths of the vortices reasonably well, but tends to overpredict the velocity close to the ripple surface. The k–ω model, on the other hand, underpredicts the height to which the vortices are lifted, but is better able to predict the velocity close to the bed. In terms of the cycle- and ripple-averaged horizontal velocity, both models are able to reproduce the observed offshore flow close to and below the ripple crest and the DVPT model is able to produce the onshore flow higher up. In the vicinity of the vortices, the DVPT model better represents the concentration (because of its better prediction of vorticity). The k–ω model, on the other hand, better represents the concentration close to the ripple surface and higher up in the flow (because of the better representation of the near-bed flow and background turbulence). The measured and predicted cycle- and ripple-averaged suspended sediment concentrations are in reasonable agreement and demonstrate the expected region of exponential decay. The models are able to reproduce the observed offshore cycle- and ripple-averaged suspended sediment flux from the ripple troughs upwards, and as a result, produce net offshore suspended sediment transport rates that are in reasonable agreement. The net measured offshore suspended transport rate, based on the integration of fluxes, was found to be consistent with the total net offshore transport measured in the tunnel as a whole once the onshore transport resulting from ripple migration was taken into account, as would be expected. This demonstrates the importance of models being able to predict ripple-migration rates. However, at present neither of the models is able to do so.     

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

Boundary layer models of ocean floor spreading

Summary The equations of conservations of momentum and energy scaled with the characteristic values of the mantle indicate the presence of the upper boundary layer to produce the estimated rate of the ocean floor spreading by convection and the importance of the frictional heating. The depth of the upper boundary layer can be estimated from the balance of the viscous force with the horizontal pressure gradient at the sea floor. It is of the orders of 100 km and becomes deeper for the Pacific than for the Atlantic Ocean and also with frictional heating than without it. The frictional heating increases the surface heat flow of the heat conduction by ten to twenty percent for the Pacific Ocean but only by a few percent for the Atlantic Ocean. The similarity solutions are determined for the temperature and horizontal velocity in the upper boundary layer. These solutions are expressed in power series of the variabley x ^–n , wherex, y, andn are horizontal and vertical coordinates and numerical constant, respectively. Both temperature and horizontal velocity within the boundary layer are higher for the Pacific than for the Atlantic Ocean. When a larger viscosity is applied, it causes the increase of horizontal velocity below the surface because of the surface boundary conditions of the finite velocity and of vanishment of the velocity shear. The higher horizontal velocity generates higher temperature because it advects hotter material from the mid-ocean ridge site. The direct effect of frictional heating on the temperature distribution of the similarity solution is almost negligible, since the shear zone is deep and near the lower boundary of the upper boundary layer. In the similarity solution, the surface heat flow which is increased by the frictional heating is given as the boundary value. The effect of the frictional heating is important below the mid-ocean ridge.     

Turbulent mixing in a rotating,stratified fluid

Abstract

An experimental study was carried out to investigate the effect of rotation on turbulent mixing in a stratified fluid when the turbulence in the mixed layer is generated by an oscillating grid. Two types of experiments were carried out: one of them is concerned with the deepening of the upper mixed layer in a stable, two-fluid system, and the other deals with the interaction between a stabilizing buoyancy flux and turbulence.

In the first type of experiments, it was found that rotation suppresses entrainment at larger Rossby numbers. As the Rossby number becomes smaller (Ro 0.1), the entrainment rate increases with rotation—the onset of this phenomenon, however, was found to coincide with the appearance of coherent vortices within the mixed layer. The radiation of energy from the mixed layer to the lower non-turbulent layer was found to occur and the magnitude of the energy flux was found to be increased with the rotational frequency. It was also observed that vortices are generated, rather abruptly, in the lower layer as the mixed layer deepens.

In the second set of experiments a quasi-steady mixed layer was found to develop of which the thickness varies with rotation in a fashion that is consistent with the result of the first experiment. Also the rotation was found to delay the formation of a pycnocline.     

Assessing the dye‐tracer correction factor for documenting the mean velocity of sheet flow over smooth and grassed surfaces

In the investigation of overland flow hydraulics, mean flow velocity (V) is frequently estimated using the measured surface flow velocity (Vs) multiplied by a correction factor, α. In total, 291 tests were performed in a flume with three beds [smooth glass (GL), sandpaper (SD), and plastic grass (GR)] to investigate α under submerged and non‐submerged flows, and Vs was observed using dye‐tracer method whilst V was calculated by the measured water depth and flow rate. For GL with 5.2% slope and 100 < Re < 5000 [Reynolds number (Re)], α ranged from 0.35 to 0.79, with an average of 0.54. For SD with slopes ranging from 2.6% to 25.9% and 300 < Re < 1200, α varied from 0.18 to 0.48 with an average of 0.32. Raindrop impacts decreased α for GL at 5.2% slope, but the effect diminished for SD as the slope increased. The α‐values less than the theoretical value of 0.67 in laminar flows may be attributed to the greater spatial variability in overland flow compared with channel flow. For GR with non‐submerged flows and Re < 4200, α varied inversely with sediment concentration (SC) at 5.2% slope but was only slightly related to SC at steep slopes of 15.6% and 25.9%. The α‐values were approximately 0.8 for turbulent flows and even greater than 1.0 under high flow discharges. This finding may relate to sheet flow disturbance and retarded surface velocity due to the protruding scattered grass stems. For each surface, α varied positively with Re; α was inversely related to slope for SD but positively related to slope for GR. There was a positive relation between h and α for GL and SD but a negative relation for GR, which highlights the importance of flow inundation status to α. The inundation ratio (h/Δ) is a promising indicator for predicting α; thus, further investigations using different submerged and non‐submerged surfaces are required to predict α effectively based on (h/Δ). Copyright © 2015 John Wiley & Sons, Ltd.     

A three‐dimensional numerical investigation of the idealized planetary boundary layer

Abstract

The nonlinear equations of motion are integrated numerically in time for a region of x‐y‐z space of volume 3h × h × h, where h turns out to be a height slightly above the level where the wind first attains the geostrophic flow direction. Only the ideal case is treated of a horizontal lower boundary, neutral stability, horizontal homogeneity of all dependent mean variables except the mean pressure, and statistically steady state. The resulting flow patterns are turbulent and the eddies transport required amounts of momentum vertically.

Topics which are investigated include the relative directions of stress, wind shear and wind; differences in Ekman wind spirals for the neutral numerical case and a stable atmospheric case; profiles of dimensionless turbulence statistics; effect of allowing the mean density to be either constant or to decrease with height; effect of the wind direction or latitude upon the turbulence intensities; and characteristic structure of the eddies in the planetary boundary layer.     

Micro- and macro-dispersive fluxes in canopy flows

Resolving every detail of the three-dimensional canopy morphology and its underlying topography remains untenable when modeling high Reynolds number geophysical flows. How to represent the effects of such a complex morphological variability and any concomittant topographic variability into one-dimensional bulk flow representation remains a fundamental challenge to be confronted in canopy turbulence research. Theoretically, planar averaging to the scale of interest should be applied to the time-averaged mean momentum balance; however, such averaging gives rise to covariance or dispersive terms produced by spatial correlations of time-averaged quantities that remain ‘unclosed’ or require parameterization. When the averaging scale is commensurate with few canopy heights, these covariances can be labeled as ‘micro-dispersive’ stresses. When averaging is intended to eliminate low-wavenumber topographic variations, we refer to these covariances as ‘macro-dispersive’ terms. Two flume experiments were used to explore the magnitude and sign of both micro- and macro-dispersive fluxes relative to their conventional Reynolds stresses counterparts: a rod-canopy with variable roughness density and a dense rod canopy situated on gentle hilly terrain. When compared to the conventional momentum flux, the micro-dispersive fluxes in the lowest layers of sparse canopies can be significant (∼50%). For dense canopies, the dispersive terms remain negligible when compared to the conventional momentum fluxes throughout. For the macro-dispersive fluxes, model calculations suggest that these terms can be neglected relative to the Reynolds stresses for a deep canopy situated on a narrow hill. For the region in which topographic variations can interact with the pressure, both model calculations and flume experiments suggest that the macro-dispersive fluxes cannot be neglected, and their value can be 20% of the typical Reynolds stresses.     

Point vortex dynamics for coupled surface/interior QG and propagating heton clusters in models for ocean convection

Abstract

The dynamic behavior of baroclinic point vortices in two-layer quasi-geostrophic flow provides a compact model for studying the transport of heat in a variety of geophysical flows including recent heton models for open ocean convection as a response to spatially localized intense surface cooling. In such heton models, the exchange of heat with the region external to the compact cooling region reaches a statistical equilibrium through the propagation of tilted heton clusters. Such tilted heton clusters are aggregates of cyclonic vortices in the upper layer and anti-cyclonic vortices in the lower layer which collectively propagate almost as an elementary tilted heton pair even though the individual vortices undergo shifts in their relative locations. One main result in this paper is a mathematical theorem demonstrating the existence of large families of long-lived propagating heton clusters for the two-layer model in a fashion compatible to a remarkable degree with the earlier numerical simulations. Two-layer quasi-geostrophic flow is an idealization of coupled surface/interior quasi-geostrophic flow. The second family of results in this paper involves the systematic development of Hamiltonian point vortex dynamics for coupled surface/interior QG with an emphasis on propagating solutions that transport heat. These are novel vortex systems of mixed species where surface heat particles interact with quasi-geostrophic point vortices. The variety of elementary two-vortex exact solutions that transport heat include two surface heat particles of opposite strength, tilted pairs of a surface heat particle coupled to an interior vortex of opposite strength and two interior tilted vortices of opposite strength at different depths. The propagation speeds of the tilted elementary hetons in the coupled surface/interior QG model are compared and contrasted with those in the simpler two-layer heton models. Finally, mathematical theorems are presented for the existence of large families of propagating long-lived tilted heton clusters for point vortex solutions in coupled surface/interior QG flow.