The three-dimensional vortical nature of atmospheric and oceanic turbulent flows

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale LLR, where LR is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juárez, J. Fluid. Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with LR. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids. Two-dimensional models are not valid for scales below LR. ©1999 American Institute of Physics.

Seasonality of submesoscale flows in the ocean surface boundary layer

A signature of submesoscale flows in the upper ocean is skewness in the distribution of relative vorticity. Expected to result for high Rossby-number flows, such skewness has implications for mixing, dissipation and stratification within the upper ocean. An array of moorings deployed in the Northeast Atlantic for one year as part of the OSMOSIS experiment reveals that relative vorticity is positively skewed during winter even though the scale of the Rossby number is less than 0.5. Furthermore, this skewness is reduced to zero during spring and autumn. There is also evidence of modest seasonal variations in the gradient Rossby number. The proposed mechanism by which relative vorticity is skewed is that the ratio of lateral to vertical buoyancy gradients, as summarized by the inverse gradient Richardson number, restricts its range during winter but less so at other times of the year. These results support recent observations and model simulations suggesting the upper ocean is host to a seasonal cycle in submesoscale turbulence.

Referencing of street-level flows measured during the DAPPLE 2004 campaign

Street-level mean flow and turbulence govern the dispersion of gases away from their sources in urban areas. A suitable reference measurement in the driving flow above the urban canopy is needed to both understand and model complex street-level flow for pollutant dispersion or emergency response purposes. In vegetation canopies, a reference at mean canopy height is often used, but it is unclear whether this is suitable for urban canopies. This paper presents an evaluation of the quality of reference measurements at both roof-top (height = H) and at height z = 9H = 190 m, and their ability to explain mean and turbulent variations of street-level flow. Fast response wind data were measured at street canyon and reference sites during the six-week long DAPPLE project field campaign in spring 2004, in central London, UK, and an averaging time of 10 min was used to distinguish recirculation-type mean flow patterns from turbulence. Flow distortion at each reference site was assessed by considering turbulence intensity and streamline deflection. Then each reference was used as the dependent variable in the model of Dobre et al. (2005) which decomposes street-level flow into channelling and recirculating components. The high reference explained more of the variability of the mean flow. Coupling of turbulent kinetic energy was also stronger between street-level and the high reference flow rather than the roof-top. This coupling was weaker when overnight flow was stratified, and turbulence was suppressed at the high reference site. However, such events were rare (<1% of data) over the six-week long period. The potential usefulness of a centralised, high reference site in London was thus demonstrated with application to emergency response and air quality modelling.

On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.

An interpretation of baroclinic initial value problems: results for simple basic states with nonzero interior PV gradients

In the Eady model, where the meridional potential vorticity (PV) gradient is zero, perturbation energy growth can be partitioned cleanly into three mechanisms: (i) shear instability, (ii) resonance, and (iii) the Orr mechanism. Shear instability involves two-way interaction between Rossby edge waves on the ground and lid, resonance occurs as interior PV anomalies excite the edge waves, and the Orr mechanism involves only interior PV anomalies. These mechanisms have distinct implications for the structural and temporal linear evolution of perturbations. Here, a new framework is developed in which the same mechanisms can be distinguished for growth on basic states with nonzero interior PV gradients. It is further shown that the evolution from quite general initial conditions can be accurately described (peak error in perturbation total energy typically less than 10%) by a reduced system that involves only three Rossby wave components. Two of these are counterpropagating Rossby waves—that is, generalizations of the Rossby edge waves when the interior PV gradient is nonzero—whereas the other component depends on the structure of the initial condition and its PV is advected passively with the shear flow. In the cases considered, the three-component model outperforms approximate solutions based on truncating a modal or singular vector basis.

Bryozoan populations reflect nutrient enrichment and productivity gradients in rivers

1. The hypothesis that nutrient enrichment will affect bryozoan abundance was tested using two complementary investigations; a field-based method determining bryozoan abundance in 20 rivers of different nutrient concentrations by deploying statoblast (dormant propagule) traps and an experimental laboratory microcosm study measuring bryozoan growth and mortality. These two methods confirmed independently that increased nutrient concentrations in water promote increases in the biomass of freshwater bryozoans. 2. Statoblasts of the genus Plumatella were recorded in all rivers, regardless of nutrient concentrations, demonstrating that freshwater bryozoans are widespread. Concentrations of Plumatella statoblasts were high in rivers with high nutrient concentrations relative to those with low to moderate nutrient concentrations. Regression analyses indicated that phosphorus concentrations, in particular, significantly influenced statoblast concentrations. 3. Concentrations of Lophopus crystallinus statoblasts were also higher in sites characterised by high nutrient concentrations. Logistic regression analysis revealed that the presence of L. crystallinus statoblasts was significantly associated with decreasing altitude and increasing phosphorus concentrations. This apparently rare species was found in nine rivers (out of 20), seven of which were new sites for L. crystallinus. 4. Growth rates of Fredericella sultana in laboratory microcosms increased with increasing nutrient concentration and high mortality rates were associated with low nutrient concentrations. 5. Our results indicate that bryozoans respond to increasing nutrient concentrations by increased growth, resulting in higher biomasses in enriched waters. We also found that an important component of bryozoan diets can derive from food items lacking chlorophyll a. Finally, bryozoans may be used as independent proxies for inferring trophic conditions, a feature that may be especially valuable in reconstructing historical environments by assessing the abundance of statoblasts in sediment cores.

Salt marsh morphodynamics: An investigation of tidal flows and marsh channel equilibrium

Although numerous field studies have evaluated flow and transport processes in salt marsh channels, the overall role of channels in delivering and removing material from salt marsh platforms is still poorly characterised. In this paper, we consider this issue based on a numerical hydrodynamic model for a prototype marsh system and on a field survey of the cross-sectional geometry of a marsh channel network. Results of the numerical simulations indicate that the channel transfers approximately three times the volume of water that would be estimated from mass balance considerations alone. Marsh platform roughness exerts a significant influence on the partitioning of discharge between the channel and the marsh platform edge, alters flow patterns on the marsh platform due to its effects on channel-to-platform transfer and also controls the timing of peak discharge relative to marsh-edge overtopping. Although peak channel discharges and velocities are associated with the flood tide and marsh inundation, a larger volume of water is transferred by the channel during ebb flows, a portion of which transfer takes place after the tidal height is below the marsh platform. Detailed surveys of the marsh channels crossing a series of transects at Upper Stiffkey Marsh, north Norfolk, England, show that the total channel cross-sectional area increases linearly with catchment area in the inner part of the marsh, which is consistent with the increase in shoreward tidal prism removed by the channels. Toward the marsh edge, however, a deficit in the total cross-sectional area develops, suggesting that discharge partitioning between the marsh channels and the marsh platform edge may also be expressed in the morphology of marsh channel systems.

Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.