The representation of turbulent fluxes during oceanic convective events is important to capture the evolution of the oceanic mixed layer. To improve the accuracy of turbulent fluxes, we examine the possibility of adding a non-gradient component in their expression in addition to the usual downgradient part. To do so, we extend the $k-\varepsilon$ algebraic second-moment closure by relaxing the assumption on the equilibrium of the temperature variance $\overline{\theta’^2}$. With this additional transport equation for the temperature variance, we obtain a $k - \varepsilon - \overline{\theta’^2}$ model (the “$k \varepsilon t$” model) which includes a non-gradient term for the temperature flux. We validate this new model against Large Eddy Simulations (LES) in both wind-forced and buoyancy-driven regimes. In both cases, we find that the vertical profile of temperature is well captured by the $k \varepsilon t$ model. Particularly, for the buoyancy-driven regime, the non-gradient term increases the portion of the mixed layer that is stably stratified. This is an improvement since this portion is too small with the $k - \varepsilon$ parameterization. Finally, a comparison of the non-gradient term with the KPP non-local term gives insights for refining the KPP’s ad hoc shape polynomial.

A document by Erika Henell. Click on the document to view its contents.

For better projections of sea level rise, two things are needed: an improved understanding of the contributing processes and their accurate representation in climate models. A major process is basal melting of ice shelves and glacier tongues by the ocean, which reduces ice sheet stability and increases ice discharge into the ocean. We study marine melting of Greenland’s largest floating ice tongue, the 79° North Glacier, using a high-resolution, 2D-vertical ocean model. While our fjord model is idealized, the results agree with observations of melt rate and overturning strength. Our setup is the first application of adaptive vertical coordinates to an ice cavity. Their stratification-zooming allows a vertical resolution finer than 1 m in the entrainment layer of the meltwater plume, which is important for the plume development. We find that the plume development is dominated by entrainment only initially. In the stratified upper part of the cavity, the subglacial plume shows continuous detrainment. It reaches neutral buoyancy near 100 m depth, detaches from the ice, and transports meltwater out of the fjord. Melting almost stops there. In a sensitivity study, we show that the detachment depth depends primarily on stratification. Our results contribute to the understanding of ice–ocean interactions in glacier cavities. Furthermore, we suggest that our modeling approach with stratification-zooming coordinates will improve the representation of these interactions in global ocean models. Finally, our idealized model topography and forcing are close to a real fjord and completely defined analytically, making the setup an interesting reference case for future model developments.

River plumes play an essential role in the transport of terrestrially derived materials (like nutrients, sediments, pollutants, etc.) into the coastal ocean. Quantifying the cross-shore transport in river plumes can help to better understand the contribution of river-borne substances to marine biogeochemical cycles and to parameterize these processes in global ocean models which are usually too coarse to resolve individual rivers. It is known that besides external factors (like runoff, latitude, wind, and tides), also internal estuarine processes like salt mixing affect the exchange flow between an estuary and the coastal ocean. A theoretical framework to separate the plume and the estuary mixing in isohaline coordinates is presented. An idealized coastal ocean model setup resolving the whole plume-estuary continuum is used to validate the theoretical relation and to study the link between the estuarine pre-conditioning and the cross-shore export of river water under different forcing scenarios. It is found that the most effective cross-shore transport of river water happens under moderately upwelling favorable wind conditions and weak tidal forcing. This scenario is characterized by relatively small estuarine mixing, strong stratification, and little interaction between the surface and bottom boundary layers such that a thin layer of buoyant river water can extend far into the ocean. We conclude that reduced estuarine mixing is indicative of an enhanced accumulation of fresh water near the shore, but is not directly related to the cross-shore transport in river plumes.

Realistically approximating the basal melting of ice shelves is critical for reliable climate model projections and the process representations in ice-ocean interaction. In this regard, extensive research attributes the massive thinning of vulnerable ice shelves to basal melting enhancement driven by ocean water warming, focusing mainly on oceanic warm water intrusion into the sub-shelf basins. However, climate models mainly underestimated the impacts of probable small-scale processes at the ice-ocean interface on basal melting by using smooth ice base topographies. This paper provides new insights into how small-scale features on the ice-ocean interface contribute to basal melting enhancement and spatial distribution. We developed a time-dependent, two-dimensional ice-shelf plume model as an optimal tool that allows a high-resolution representation of basal topography and with the unique ability to provide valuable information from the mixed boundary layer between ocean and ice shelves. In an exemplary case study for the floating ice tongue of the 79◦ North Glacier, systematic sensitive analyses were performed with the developed model. Our results show that the sub-km-scale basal channels with realistic dimensions increase the mean basal melt rate and generate extreme and sizeable lateral variability of melting at the grounding line. This mechanism is not reproducible with the tuning of drag coefficient. Besides, it reveals that the subglacial discharge in the channels has contradicting effects of reducing the melt rate by refreshing the sea water and increasing the freezing point while increasing the melt rate due to high water speed. However, the latter was dominant in our experiments.

Basal melting of marine-terminating glaciers, through its impact on the forces that control the flow of the glaciers, is one of the major factors determining sea level rise in a world of global warming. Detailed quantitative understanding of dynamic and thermodynamic processes in melt-water plumes underneath the ice-ocean interface is essential for calculating the subglacial melt rate. The aim of this study is therefore to develop a numerical model of high spatial and process resolution to consistently reproduce the transports of heat and salt from the ambient water across the plume into the glacial ice. Based on boundary layer relations for momentum and tracers, stationary analytical solutions for the vertical structure of subglacial non-rotational plumes are derived, including entrainment at the plume base. These solutions are used to develop and test convergent numerical formulations for the momentum and tracer fluxes across the ice-ocean interface. After implementation of these formulations into a water-column model coupled to a second-moment turbulence closure model, simulations of a transient rotational subglacial plume are performed. The simulated entrainment rate of ambient water entering the plume at its base is compared to existing entrainment parameterizations based on bulk properties of the plume. A sensitivity study with variations of interfacial slope, interfacial roughness and ambient water temperature reveals substantial performance differences between these bulk formulations. An existing entrainment parameterization based on the Froude number and the Ekman number proves to have the highest predictive skill. Recalibration to subglacial plumes using a variable drag coefficient further improves its performance.

Glider observations show a subsurface chlorophyll maximum (SCM) at the base of the seasonal pycnocline (PCB) in the central North Sea during stable summer conditions. A co-located peak in the dissipation rate of turbulent kinetic energy suggests the presence of active turbulence that generates the nutrient fluxes necessary to fuel the SCM. A one-dimensional turbulence closure model is used to investigate the dynamics behind this local maximum in turbulent dissipation at the PCB as well as its associated nutrient fluxes. Based on a number of increasingly idealized forcing setups of the model, we are able to draw the following conclusions: (1) only turbulence generated inside the stratified PCB is able to entrain nutrients from the bottom mixed layer into the SCM region; (2) surface wind forcing only plays a secondary role during stable summer conditions; (3) interfacial shear from the tide accounts for the majority of turbulence production at the PCB; (4) in stable summer conditions the strength of the turbulent nutrient fluxes at the PCB is set by the strength of the anticyclonic component of the tidal currents.