Mixing and entrainment in hydraulically driven stratified sill flows

Author Posting. © Cambridge University Press, 2004. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 515 (2004): 415-443, doi:10.1017/S0022112004000576.The investigation involves the hydraulic behaviour of a dense layer of fluid flowing over an obstacle and subject to entrainment of mass and momentum from a dynamically inactive (but possibly moving) overlying fluid. An approach based on the use of reduced gravity, shallow-water theory with a cross-interface entrainment velocity is compared with numerical simulations based on a model with continuously varying stratification and velocity. The locations of critical flow (hydraulic control) in the continuous model are estimated by observing the direction of propagation of small-amplitude long-wave disturbances introduced into the flow field. Although some of the trends predicted by the shallow-water model are observed in the continuous model, the agreement between the interface profiles and the position of critical flow is quantitatively poor. A reformulation of the equations governing the continuous flow suggests that the reduced gravity model systematically underestimates inertia and overestimates buoyancy. These differences are quantified by shape coefficients that measure the vertical non-uniformities of the density and horizontal velocity that arise, in part, by incomplete mixing of entrained mass and momentum over the lower-layer depth. Under conditions of self-similarity (as in Wood's similarity solution) the shape coefficients are constant and the formulation determines a new criterion for and location of critical flow. This location generally lies upstream of the critical section predicted by the reduced-gravity model. Self-similarity is not observed in the numerically generated flow, but the observed critical section continues to lie upstream of the location predicted by the reduced gravity model. The factors influencing this result are explored.M. H. N. would like to thank the Danish Natural Science Research Council for financial support. L. P. and K. H. were supported by the Office of Naval Research under grant N00014-1-01-0167 and by the National Science Foundation under grant OCE-0132903

Summer meltwater and spring sea ice primary production, light climate and nutrients in an Arctic estuary, Kangedussuaq, west Greenland

The estuary is dominated by sea ice and snow cover from winter to spring, and a highly turbid meltwater plume during summer. The aims were to quantify the variability in optical conditions, inorganic nutrients, and primary production between these two extremes, and identify the drivers of variability. Data were obtained during a summer cruise along a transect in the estuary in August 2007, and a spring campaign on the ice in March 2011. The study comprises conductivity, temperature, and depth (CTD), K(PAR), K(λ), PAR transmittance, photic depth, chl-a, nutrients (NO₃, NO₂, NH₃, PO₄, and SiO₂), primary production, and sediment concentrations. PAR transmittance varied between 5% below snow and ice and 85% in clear water with 44% in turbid meltwater. Primary production rates were similar below the ice in March (76.8 mg C m⁻² d⁻¹) and in the highly turbid meltwater in August (94.8 mg C m⁻² d⁻¹), but higher (246.6 mg C m⁻² d⁻¹) at the mouth of the fjord. Meltwater inflow was the main driver of variability during summer and the snow and sea ice during spring. Under-ice primary production will increase three-fold with less snow on the sea ice, and the higher meltwater turbidity with increased melting of glacial ice and runoff will only reduce primary production slightly

Hypsometric amplification and routing moderation of Greenland ice sheet meltwater release

Concurrent ice sheet surface runoff and proglacial discharge monitoring are essential for understanding Greenland ice sheet meltwater release. We use an updated, well-constrained river discharge time series from the Watson River in southwest Greenland, with an accurate, observation-based ice sheet surface mass balance model of the  ∼  12 000 km² ice sheet area feeding the river. For the 2006–2015 decade, we find a large range of a factor of 3 in interannual variability in discharge. The amount of discharge is amplified  ∼  56 % by the ice sheet's hypsometry, i.e., area increase with elevation. A good match between river discharge and ice sheet surface meltwater production is found after introducing elevation-dependent transit delays that moderate diurnal variability in meltwater release by a factor of 10–20. The routing lag time increases with ice sheet elevation and attains values in excess of 1 week for the upper reaches of the runoff area at  ∼  1800 m above sea level. These multi-day routing delays ensure that the highest proglacial discharge levels and thus overbank flooding events are more likely to occur after multi-day melt episodes. Finally, for the Watson River ice sheet catchment, we find no evidence of meltwater storage in or release from the en- and subglacial environments in quantities exceeding our methodological uncertainty, based on the good match between ice sheet runoff and proglacial discharge