Mixing in a density-driven current flowing down a slope in a rotating fluid

Author Posting. © Cambridge University Press, 2008. 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 604 (2008): 369-388, doi:10.1017/S0022112008001237.We discuss laboratory experiments investigating mixing in a density-driven current flowing down a sloping bottom, in a rotating homogenous fluid. A systematic study spanning a wide range of Froude, 0.8 < Fr < 10, and Reynolds, 10 < Re < 1400, numbers was conducted by varying three parameters: the bottom slope; the flow rate; and the density of the dense fluid. Different flow regimes were observed, i.e. waves (non-breaking and breaking) and turbulent regimes, while changing the above parameters. Mixing in the density-driven current has been quantified within the observed regimes, and at different locations on the slope. The dependence of mixing on the relevant non-dimensional numbers, i.e. slope, Fr and Re, is discussed. The entrainment parameter, E, was found to be dependent not only on Fr, as assumed in previous studies, but also on Re. In particular, mixing increased with increasing Fr and Re. For low Fr and Re, the magnitude of the mixing was comparable to mixing in the ocean. For large Fr and Re, mixing was comparable to that observed in previous laboratory experiments that exhibited the classic turbulent entrainment behaviour.Support was given by the National Science Foundation project number OCE-0350891

An experimental study of a mesoscale vortex colliding with topography of varying geometry in a rotating fluid

Author Posting. © Sears Foundation for Marine Research, 2004. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 62 (2004): 611-638, doi:10.1357/0022240042387583.The interaction of a self-propagating barotropic cyclonic vortex with an obstacle has been investigated and the conditions for a vortex to bifurcate into two vortices determined. As in a previous study, after a self-propagating cyclonic vortex came into contact with the obstacle, fluid peeled off the outer edge of the vortex and a so-called "streamer" went around the obstacle in a counterclockwise direction. Under certain conditions, this fluid formed a new cyclonic vortex in the wake of the obstacle, causing bifurcation of the original vortex into two vortices. In the present study we performed three sets of idealized laboratory experiments with the aim of investigating the importance on the bifurcation mechanism of the obstacle's horizontal cross sectional geometry, the influence of the height of the obstacle, and the importance of the slope of the obstacle sidewalls. The present results suggest that bifurcation occurs only when the obstacle height is equal or larger than 85% of the vortex height and that steep sloping sidewalls do not influence the bifurcation mechanism. In addition, experiments performed using an obstacle with an elliptical horizontal cross section revealed that the relevant parameter governing the occurrence of bifurcation is the length which the "streamer" has to travel around the obstacle, and not the dimension of the obstacle in the direction orthogonal to the motion of the vortex. Collisions of oceanic mesoscale vortices with seamounts often result in major modifications of their structure, having significant impacts on the redistribution of water properties. Observations of a "Meddy" bifurcating after colliding with the Irving Seamount in the Canary Basin show behavior similar to these idealized laboratory experiments. This suggests that these results could be used to explain and predict the outcome of a vortex colliding with seamounts of varying geometry in the ocean.Support was given by the National Science Foundation project number OCE-0081756

Laboratory experiments and observations of cyclonic and anticyclonic eddies impinging on an island

Author Posting. © American Geophysical Union, 2013. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 118 (2013): 762–773, doi:10.1002/jgrc.20081.Laboratory experiments are conducted to investigate the interactions of self-propagating barotropic cyclones and baroclinic anticyclones with an island. Results are interpreted in the context of observations around Okinawa Island, Japan, where ubiquitous arrivals of cyclones and anticyclones on the southeastern side of the island influence the flow around it, thereby impacting both the Ryukyu Current's and the Kuroshio's transport. In the laboratory, baroclinic anticyclones generate a buoyant current that flows clockwise around an island whereas barotropic cyclones generate a counterclockwise current. In both cases, the interaction is governed by conservation of circulation Γ around the island, which establishes a balance between the dissipation along the island in contact with the eddy and the dissipation along the island in contact with the generated current. Laboratory results and scaling analysis suggest that the interaction between an anticyclone (cyclone) and Okinawa Island should result in an instantaneous increase (decrease) of the Ryukyu Current transport and a delayed increase (decrease) of the Kuroshio transport. The estimated delays are in good agreement with those obtained with field measurements suggesting that the dynamics at play in the laboratory may be relevant for the flow around Okinawa Island.M.A.was supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Ocean and Climate Change Institute and by the Penzance Endowed Fund in Support of Assistant Scientists.2013-08-1

Impact of a localized source of subglacial discharge on the heat flux and submarine melting of a tidewater glacier : a laboratory study

Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 3155-3163, doi:10.1175/JPO-D-16-0123.1.Idealized laboratory experiments have been conducted in a two-layer stratified fluid to investigate the leading-order dynamics that control submarine melting and meltwater export near a vertical ice–ocean interface as a function of subglacial discharge. In summer, the discharge of surface runoff at the base of a glacier (subglacial discharge) generates strong buoyant plumes that rise along the glacier front entraining ambient water along the way. The entrainment enhances the heat transport toward the glacier front and hence the submarine melt rate increases with the subglacial discharge rate. In the laboratory, the effect of subglacial discharge is simulated by introducing freshwater at freezing temperature from a point source at the base of an ice block representing the glacier. The circulation pattern observed both with and without subglacial discharge resembles those observed in previous observational and numerical studies. Buoyant plumes rise vertically until they find either their neutrally buoyant level or the free surface. Hence, the meltwater can deposit within the interior of the water column and not entirely at the free surface, as confirmed by field observations. The heat budget in the tank, calculated following a new framework, gives estimates of submarine melt rate that increase with the subglacial discharge and are in agreement with the directly measured submarine melting. This laboratory study provides the first direct measurements of submarine melt rates for different subglacial discharges, and the results are consistent with the predictions of previous theoretical and numerical studies.Support to C. C. was given by the NSF project OCE- 1130008 and OCE-1434041. M. G. received support from the ‘‘Gori’’ Fellowship.2017-04-0

The dispersal of dense water formed in an idealized coastal polynya on a shallow sloping shelf

Author Posting. © American Meteorological Society, 2014. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 44 (2014): 1563–1581, doi:10.1175/JPO-D-13-0188.1.This study examines the dispersal of dense water formed in an idealized coastal polynya on a sloping shelf in the absence of ambient circulation and stratification. Both numerical and laboratory experiments reveal two separate bottom pathways for the dense water: an offshore plume moving downslope into deeper ambient water and a coastal current flowing in the direction of Kelvin wave propagation. Scaling analysis shows that the velocity of the offshore plume is proportional not only to the reduced gravity, bottom slope, and inverse of the Coriolis parameter, but also to the ratio of the dense water depth to total water depth. The dense water coastal current is generated by the along-shelf baroclinic pressure gradient. Its dynamics can be separated into two stages: (i) near the source region, where viscous terms are negligible, its speed is proportional to the reduced gravity wave speed and (ii) in the far field, where bottom drag becomes important and balances the pressure gradient, the velocity is proportional to Hc[g′/(LCd)]1/2 in which Hc is the water depth at the coast, g′ the reduced gravity, Cd the quadratic bottom drag coefficient, and L the along-shelf span of the baroclinic pressure gradient. The velocity scalings are verified using numerical and laboratory sensitivity experiments. The numerical simulations suggest that only 3%–23% of the dense water enters the coastal pathway, and the percentage depends highly on the ratio of the velocities of the offshore and coastal plumes. This makes the velocity ratio potentially useful for observational studies to assess the amount of dense water formed in coastal polynyas.WGZ was sponsored by the WHOI Arctic Research Initiative program. CC received support from the National Science Foundation Project OCE-1130008.2014-12-0

Impact of a localized source of subglacial discharge on the heat flux and submarine melting of a tidewater glacier : a laboratory study

Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 3155-3163, doi:10.1175/JPO-D-16-0123.1.Idealized laboratory experiments have been conducted in a two-layer stratified fluid to investigate the leading-order dynamics that control submarine melting and meltwater export near a vertical ice–ocean interface as a function of subglacial discharge. In summer, the discharge of surface runoff at the base of a glacier (subglacial discharge) generates strong buoyant plumes that rise along the glacier front entraining ambient water along the way. The entrainment enhances the heat transport toward the glacier front and hence the submarine melt rate increases with the subglacial discharge rate. In the laboratory, the effect of subglacial discharge is simulated by introducing freshwater at freezing temperature from a point source at the base of an ice block representing the glacier. The circulation pattern observed both with and without subglacial discharge resembles those observed in previous observational and numerical studies. Buoyant plumes rise vertically until they find either their neutrally buoyant level or the free surface. Hence, the meltwater can deposit within the interior of the water column and not entirely at the free surface, as confirmed by field observations. The heat budget in the tank, calculated following a new framework, gives estimates of submarine melt rate that increase with the subglacial discharge and are in agreement with the directly measured submarine melting. This laboratory study provides the first direct measurements of submarine melt rates for different subglacial discharges, and the results are consistent with the predictions of previous theoretical and numerical studies.Support to C. C. was given by the NSF project OCE- 1130008 and OCE-1434041. M. G. received support from the ‘‘Gori’’ Fellowship.2017-04-0

Impact of two plumes’ interaction on submarine melting of tidewater glaciers : a laboratory study

Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 361–367, doi:10.1175/JPO-D-15-0171.1.Idealized laboratory experiments investigate the glacier–ocean boundary dynamics near a vertical glacier in a two-layer stratified fluid. Discharge of meltwater runoff at the base of the glacier (subglacial discharge) enhances submarine melting. In the laboratory, the effect of multiple sources of subglacial discharge is simulated by introducing freshwater at freezing temperature from two point sources at the base of an ice block representing the glacier. The buoyant plumes of cold meltwater and subglacial discharge water entrain warm ambient water, rise vertically, and interact within a layer of depth H2 if the distance between the sources x0 is smaller than H2α/0.35, where α is the entrainment constant. The plume water detaches from the glacier face at the interface between the two layers and/or at the free surface, as confirmed by previous numerical studies and field observations. A plume model is used to explain the observed nonmonotonic dependence of submarine melting on the sources’ separation. The distance between the two sources influences the entrainment of warm water in the plumes and consequently the amount of submarine melting and the final location of the meltwater within the water column. Two interacting plumes located very close together are observed to melt approximately half as much as two independent plumes. The inclusion, or parameterization, of the dynamics regulating multiple plumes’ interaction is therefore necessary for a correct estimate of submarine melting. Hence, the distribution and number of sources of subglacial discharge may play an important role in glacial melt rates and fjord stratification and circulation.Support to C.C. was given by the NSF Project OCE-1130008 and OCE-1434041. V.M.G. received support from the “Gori” Fellowship.2016-07-0

Stability of a buoyancy-driven coastal current at the shelf break

Author Posting. © Cambridge University Press, 2002. 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 452 (2002): 97-121, doi:10.1017/S0022112001006668.Buoyancy-driven surface currents were generated in the laboratory by releasing buoyant fluid from a source adjacent to a vertical boundary in a rotating container. Different bottom topographies that simulate both a continental slope and a continental ridge were introduced in the container. The topography modified the flow in comparison with the at bottom case where the current grew in width and depth until it became unstable once to non-axisymmetric disturbances. However, when topography was introduced a second instability of the buoyancy-driven current was observed. The most important parameter describing the flow is the ratio of continental shelf width W to the width L* of the current at the onset of the instability. The values of L* for the first instability, and L*[minus sign]W for the second instability were not influenced by the topography and were 2–6 times the Rossby radius. Thus, the parameter describing the flow can be expressed as the ratio of the width of the continental shelf to the Rossby radius. When this ratio is larger than 2–6 the second instability was observed on the current front. A continental ridge allowed the disturbance to grow to larger amplitude with formation of eddies and fronts, while a gentle continental slope reduced the growth rate and amplitude of the most unstable mode, when compared to the continental ridge topography. When present, eddies did not separate from the main current, and remained near the shelf break. On the other hand, for the largest values of the Rossby radius the first instability was suppressed and the flow was observed to remain stable. A small but significant variation was found in the wavelength of the first instability, which was smaller for a current over topography than over a flat bottom.Partial support for C.C. was provided by a TMR fellowship, MAS3-CT96-5017

How entraining density currents influence the ocean stratification

Author Posting. © The Authors, 2005. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 53 (2006): 172-193, doi:10.1016/j.dsr2.2005.10.019.The sensitivity of the basin-scale ocean stratification to the vertical distribution of plume entrainment is being 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 seaand 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.Part of this work was funded by Göteborg University and the Swedish Research Council under the contract G600-335/2001 through Prof. A. Omstedt. Support was given to CC by the National Science Foundation project number OCE-0050891

Dynamics of three-dimensional turbulent wall plumes and implications for estimates of submarine glacier melting

Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018):1941-1950, doi:10.1175/JPO-D-17-0194.1.Subglacial discharges have been observed to generate buoyant plumes along the ice face of Greenland tidewater glaciers. These plumes have been traditionally modeled using classical plume theory, and their characteristic parameters (e.g., velocity) are employed in the widely used three-equation melt parameterization. However, the applicability of plume theory for three-dimensional turbulent wall plumes is questionable because of the complex near-wall plume dynamics. In this study, corrections to the classical plume theory are introduced to account for the presence of a wall. In particular, the drag and entrainment coefficients are quantified for a three-dimensional turbulent wall plume using data from direct numerical simulations. The drag coefficient is found to be an order of magnitude larger than that for a boundary layer flow over a flat plate at a similar Reynolds number. This result suggests a significant increase in the melting estimates by the current parameterization. However, the volume flux in a wall plume is found to be one-half that of a conical plume that has 2 times the buoyancy flux. This finding suggests that the total entrainment (per unit area) of ambient water is the same and that the plume scalar characteristics (i.e., temperature and salinity) can be predicted reasonably well using classical plume theory.This work was supported by the Linné FLOW Centre at KTH and the Academy of Finland Center of Excellence Programme Grant 307331 (author Ezhova) and by VR Swedish Research Council GrantVR2014-5001 (author Brandt). Support to author Cenedese was given by NSF Project OCE-1434041.2019-02-2