Abstract This paper summarizes the results of the first investigation into the effect of particle‐laden plumes on glacier melting using laboratory experiments. We find that the melt rate, when the ice is exposed to a particle‐laden plume, can be larger than when exposed to an equivalent plume without particles. The increased melt rate is linked to an increase in the plume velocity in response to the presence of suspended particles. Including this increased velocity in a plume model improves melt rate predictions from the “three‐equation model” by approximately 45% for the range of particle concentrations used in this study.

Environmental fluid mechanics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that need to be tackled, ranging from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing, to applied studies of pollution transport in the ocean, atmosphere and urban environments. A workshop was organized in the Les Houches School of Physics in France in January 2019 with the objective of gathering leading figures in the field to produce a road map for the scientific community. Five subject areas were addressed: multiphase flow, stratified flow, ocean transport, atmospheric and urban transport, and weather and climate prediction. This article summarizes the discussions and outcomes of the meeting, with the intent of providing a resource for the community going forward.

An earlier study indicates that the side melting of icebergs subject to vertically homogeneous horizontal velocities is controlled by two distinct regimes, which depend on the melt plume behavior and produce a nonlinear dependence of side melt rate on velocity. Here, we extend this study to consider ice blocks melting in a two-layer vertically sheared flow in a laboratory setting. It is found that the use of the vertically averaged flow speed in current melt parameterizations gives an underestimate of the submarine side melt rate, in part because of the nonlinearity of the dependence of the side melt rate on flow speed but also because vertical shear in the horizontal velocity profile fundamentally changes the flow splitting around the ice block and consequently the velocity felt by the ice surface. An observational record of 90 icebergs in a Greenland fjord suggests that this effect could produce an average underestimate of iceberg side melt rates of 21%.

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).

Icebergs calving into Greenlandic Fjords frequently experience strongly sheared flows over their draft, but the impact of this flow past the iceberg is not fully captured by existing parameterizations. We present a series of novel laboratory experiments to determine the dependence of submarine melting along iceberg sides on a background flow. We show, for the first time, that two distinct regimes of melting exist depending on the flow magnitude and consequent behavior of melt plumes (side‐attached or side‐detached), with correspondingly different meltwater spreading characteristics. When this velocity dependence is included in melt parameterizations, melt rates estimated for observed icebergs in the attached regime increase, consistent with observed iceberg submarine melt rates. We show that both attached and detached plume regimes are relevant to icebergs observed in a Greenland fjord. Further, depending on the regime, iceberg meltwater may either be confined to a surface layer or distributed over the iceberg draft.

Icebergs account for approximately half the freshwater flux into the ocean from the Greenland and Antarctic ice sheets and play a major role in the distribution of meltwater into the ocean. Global climate models distribute this freshwater by parameterizing iceberg motion and melt, but these parameterizations are presently informed by limited observations. Here we present a record of speed and draft for 90 icebergs from Sermilik Fjord, southeastern Greenland, collected in conjunction with wind and ocean velocity data over an 8 month period. It is shown that icebergs subject to strongly sheared flows predominantly move with the vertical average of the ocean currents. If, as typical in iceberg parameterizations, only the surface ocean velocity is taken into account, iceberg speed and basal melt may have errors in excess of 60%. These results emphasize the need for parameterizations to consider ocean properties over the entire iceberg draft.

Laboratory experiments have been conducted to investigate the mechanisms regulating mixing in a lock-release dense gravity current flowing over a bottom roughness represented by an array of cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Experimental results suggest that enhanced mixing can occur via two different mechanisms. For a sparse configuration the dense current moves between the cylinders and the mixing is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration the dense current propagates over the top of the cylinders and the mixing is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. As expected, for small values of the cylinder height to the water depth, h/H, the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of h/H.

The interaction of gravity currents with significant boundary roughness is a relatively unexplored field of research. Results from an experimental campaign aimed at exploring the impact of roughness configuration and relative roughness height on the dynamics of a dense boundary gravity current are presented. A PTV system provides detailed velocity field data for gravity currents created using a standard lock exchange configuration and flowing through a roughness field of vertical circular cylinders. Particular attention is paid to the general flow regimes observed and the dependence of the Froude number of the current front, Fr, on the roughness field characteristics. It is demonstrated that it is possible that increasing roughness density can lead, first, to a decrease in Fr and then to an increase.

The submarine melting of a vertical glacier front, induced by an intermediary circulation forced by periodic density variations at the mouth of a fjord, is investigated using a nonhydrostatic ocean general circulation model and idealized laboratory experiments. The idealized configurations broadly match that of Sermilik Fjord, southeast Greenland, a largely two layers system characterized by strong seasonal variability of subglacial discharge. Consistent with observations, the numerical results suggest that the intermediary circulation is an effective mechanism for the advection of shelf anomalies inside the fjord. In the numerical simulations, the advection mechanism is a density intrusion with a velocity which is an order of magnitude larger than the velocities associated with a glacier-driven circulation. In summer, submarine melting is mostly influenced by the discharge of surface runoff at the base of the glacier and the intermediary circulation induces small changes in submarine melting. In winter, on the other hand, submarine melting depends only on the water properties and velocity distribution at the glacier front. Hence, the properties of the waters advected by the intermediary circulation to the glacier front are found to be the primary control of the submarine melting. When the density of the intrusion is intermediate between those found in the fjord's two layers, there is a significant reduction in submarine melting. On the other hand, when the density is close to that of the bottom layer, only a slight reduction in submarine melting is observed. The numerical results compare favorably to idealized laboratory experiments with a similar setup.

A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an 'effective' entrainment constant, alpha(eff), as the value of alpha needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of alpha(eff) allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.

Abstract We extend previous work of Boyer, Davies & Guo (Fluid Dyn. Res., vol. 21, 1997, pp. 381–401) to consider the evolution of an initially two-layer stratified fluid in a cylindrical tank which is driven by a horizontal rotating disk. The turbulent motions induced by the disk drive entrainment at the interface, and similarly to the results of Boyer et al. (1997), the layer nearer to the disk deepens. Through high-frequency conductivity probe measurements, we establish that the deepening layer is very well-mixed, and the thickness of the interface between the two evolving layers appears to be approximately constant. Under certain circumstances, we find that the rate of increase in depth of the deepening layer decreases with time, at variance with the results of Boyer et al. (1997), and implying that the characteristic velocity in the deepening layer decreases as the upper layer deepens. We propose that such time-dependent deepening, and the associated weakening of the upper-layer velocities, occurs naturally because of the combined power requirements of entrainment and layer homogenization which inhibit, when the stratification is very strong, the characteristic velocities of the deepening layer approaching the (constant) velocities of the driving disk, as assumed by Boyer et al. (1997).

The circulation in a glacial fjord driven by a large tidewater glacier is investigated using a nonhydrostatic ocean general circulation model with a melt rate parameterization at the vertical glacier front. The model configuration and water properties are based on data collected in Sermilik Fjord near Helheim Glacier, a major Greenland outlet glacier. The approximately two‐layer stratification of the fjord's ambient waters causes the meltwater plume at the glacier front to drive a “double cell” circulation with two distinct outflows, one at the free surface and one at the layers' interface. In summer, the discharge of surface runoff at the base of the glacier (subglacial discharge) causes the circulation to be much more vigorous and associated with a larger melt rate than in winter. The simulated “double cell” circulation is consistent, in both seasons, with observations from Sermilik Fjord. Seasonal differences are also present in the vertical structure of the melt rate, which is maximum at the base of the glacier in summer and at the layers' interface in winter. Simulated submarine melt rates are strongly sensitive to the amount of subglacial discharge, to changes in water temperature, and to the height of the layers. They are also consistent with those inferred from simplified one‐dimensional models based on the theory of buoyant plumes. Our results also indicate that to correctly represent the dynamics of the meltwater plume, care must be taken in the choice of viscosity and diffusivity values in the model.

We investigate the early-time coalescence of two co-flowing axisymmetric turbulent plumes and the later-time flow of the induced vortices in a rotating, homogeneous fluid using laboratory experiments. The experiments demonstrate the critical importance of the rotation period Tf=2π/f, where f is the Coriolis parameter of the background rotation. We find that if the plumes’ sources are sufficiently “close” for the plumes to merge initially at an “early time” tm≲tr=3Tf/4, the experimentally observed merging height zme agrees well with the non-rotating theoretical relationship of zmt≈(0.44/α)x0tr, however, the flow dynamics are substantially more complicated, as the flow becomes significantly affected by rotation. The propagation and entrainment of the plumes becomes strongly affected by the vortices induced by the entrainment flow in a rotating environment. Also, the plume fluid itself starts to interact with these vortices. If the plumes have already initially merged by the time t=tr, a single vortex (initially located at the midpoint of the line connecting the two plume sources) develops, which both advects and modifies the geometry of the merging plumes. Coupled with the various suppressing effects of rotation on the radial plume entrainment, the “apparent” observed height of merger can vary substantially from its initial value. Conversely, for more widely separated “distant” plumes, where x0>xc=(25α/2)F01/4f-3/4, the plumes do not merge before the critical time tr when rotation becomes significant in the flow dynamics and two vortices are observed, each located over a plume source. The combined effect of these vortices with the associated suppression of entrainment by rotation thus significantly further delays the merger of the two plumes, which apparently becomes possible only through the merger of the induced vortices.

The continental slopes in the oceans are often covered by small-scale topographic features such as submarine canyons and ridges. When dense plumes, flowing geostrophically along the slope, encounter such features they may be steered downslope inside and alongside the topography. A set of laboratory experiments was conducted at the rotating Coriolis platform to investigate the effect of small-scale topography on plume mixing. A dense water source was placed on top of a slope, and experiments were repeated with three topographies: a smooth slope, a slope with a ridge, and a slope with a canyon. Three flow regimes were studied: laminar, waves, and eddies. When a ridge or a canyon were present on the slope, the dense plume was steered downslope and instabilities developed along the ridge and canyon wall. This happened regardless of the flow characteristics on the smooth slope. Froude and Reynolds numbers were estimated, and were found to be higher for the topographically steered flow than for flow on smooth topography. The stratification in the collecting basin was monitored and the mixing inferred. The total mixing and the entrainment rate increased when a ridge or a canyon were present. The difference in mixing levels between the regimes was smaller when topography was present, indicating that it was the small-scale topography and not the large-scale characteristics of the flow that determined the properties of the product water.

The sensitivity of ocean stratification to the vertical distribution of plume entrainment is analyzed. A large ocean basin supplied by dense water from an adjoining marginal sea is considered. The dense water flows into the ocean basin as an entraining density current and interleaves at the bottom, or at the level of neutral density, where it deposits a mixture of marginal sea- and basin water. As the basin water, i.e. 'old' plume water, is entrained and re-circulated in the plume, a stratification develops in the basin. The mixture deposited at the bottom hence contains an increasing fraction of marginal sea water, and the basin density increases with depth as well as with time. A stationary solution in which diffusion of buoyancy from above is important is approached asymptotically in time.Non-diffusive solutions to the initial transient adjustment, as well as the diffusive asymptotic state, have been studied in four different parameterizations of plume entrainment. It is shown that in the transient regime the basin stratification and plume density are highly sensitive to how mixing is parameterized. The stationary diffusive solution that is approached asymptotically in time is less sensitive to parameterization, but depends strongly on basin topography, source water density, and buoyancy flux at the surface. (c) 2006 Elsevier Ltd. All rights reserved.

Irminger rings are warm-core eddies formed off the west coast of Greenland. Recent studies suggest that these eddies, which are implicated in the rapid springtime rest ratification of the Labrador Sea, are formed by an internal instability of the West Greenland Current (WGC), triggered by bathymetric variations. This study seeks to explore the effect of the magnitude and downstream length scale of bathymetric variations on the stability of a simple model of the WGC in a series of laboratory experiments in which a buoyant coastal current was allowed to flow over bathymetry consisting of piecewise constant slopes of varying magnitude. The currents did not form eddies over gently sloping bathymetry and only formed eddies over steep bathymetry if the current width exceeded the width of the sloping bathymetry. Eddying currents were immediately stabilized if they flowed onto gently sloping topography. Bathymetric variations that persisted only a short distance downstream perturbed the flow locally but did not lead to eddy formation. Eddies formed only once the downstream length of the bathymetric variations exceeded a critical scale of about 8 Rossby radii. These results are consistent with the observed behavior of the WGC, which begins to form Irminger rings after entering a region where the continental slope abruptly steepens and becomes narrower than the WGC itself in a region spanning about 20-80 Rossby radii of downstream distance.

Laboratory experiments have been performed to investigate the physical processes that govern the interaction of a self‐propagating barotropic cyclonic vortex with aligned circular cylinders. The motivation was to understand the dynamics which controls the interaction of North Brazil Current (NBC) rings with the Lesser Antilles (LA) in the Eastern Caribbean Sea. The geometrical parameter regulating the flow in the experiments was the ratio of the gap size to the diameter of the incident vortex, G / d . The range 0.03 ≤ G / d ≤ 0.4 was studied. Since the passages of the LA have values of 0.07 ≤ G / d ≤ 0.3 [2], the experimental results might explain recent oceanic observations [3]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)