Terminal velocities of pure and hydrate coated CO2 droplets and CH4 bubbles rising in a simulated oceanic environment

Understanding the upward motion of CO₂ droplets or CH₄ bubbles in oceanic waters is prerequisite to predict the vertical distribution of the two most important greenhouse gases in the water column after these have been released from the seabed. One of the key parameters governing the fate of droplets or bubbles dissolving into the surrounding seawater as they rise, is the terminal velocity, u_T. The latter is strongly influenced by the ability of both compounds to form skins of gas hydrate, if pressure and temperature satisfy thermodynamic framework conditions. Experimental efforts aiming to elucidate the rise properties of CO₂ droplets and CH₄ bubbles and specifically the influence of hydrate skins open the possibility to obtain a parameterization of u_T applicable to both hydrate-coated and pure fluid particles of CH₄ and CO₂. With the present study, we report on experimentally determined terminal velocities of single CH₄ bubbles released to pressurized and temperature-regulated seawater. Hydrate skins were identified by high bubble sphericities and changed motion characteristics. Based on these experiments as well as published data on the rise of hydrate-coated and pure liquid CO₂ droplets and physical principles previously successfully used for clean bubbles near atmospheric pressures, a new parameterization of u_T is proposed. Model predictions show a good agreement with the data base established from the laboratory-based measurements.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

The role of eddies on pathways,transports, and entrainment in dense water flows along a slope

Ocean Dynamics - The flow of dense water along slopes has been investigated in several numerical investigations based on the Dynamics of Overflow Mixing and Entrainment (DOME) setup. In the present...     

Flow over a rounded backward-facing step,using a <Emphasis Type="Italic">z</Emphasis>-coordinate model and a <Emphasis Type="Italic">σ</Emphasis>-coordinate model

Homogeneous, nonrotating flow over a backward-facing rounded step is simulated using the 2D vertical version of two general circulation models, a z-coordinate model—the Massachusetts Institute of Technology general circulation model (MITgcm)—and a σ-coordinate model—the Bergen Ocean Model (BOM). The backward-facing step is a well-known testcase since it is geometrically simple but still embodies important flow characteristics such as separation point, reattachment length, and recirculation of the flow. The study compares the core of the two models and uses constant eddy viscosities and diffusivities. The Reynolds numbers ranges from 2·10² to 2·10⁶. The results correspond with previously published results having a relatively stationary separation point and a fluctuating reattachment length due to downslope propagating eddies released from the reattachment zone for Reynolds numbers higher than or equal to 2 · 10⁴. For Reynolds number within the laminar regime, the flow is stationary. The discrepancies between the models increase by enhancing Reynolds numbers. The σ-coordinate model experiences a reduction in eddy sizes with increasing resolution and Reynolds numbers in correspondence with published experiments, while the size of the eddies are independent of the Reynolds number using the MITgcm. Due to mixing generated by the staircase topography, the z-coordinate model gives a better convergence of the separation point and reattachment length compared with the BOM; however, this conclusion might change with the inclusion of a relevant turbulence scheme.     

Simulating CO<Subscript>2</Subscript> transport into the ocean from a CO<Subscript>2</Subscript> lake at the seafloor using a <Emphasis Type="Italic">z</Emphasis>- and a <Emphasis Type="Italic">σ</Emphasis>-coordinate model

The ocean takes up approximately 2 GT carbon per year due to the enhanced CO₂ concentrations in the atmosphere. Several options have been suggested in order to reduce the emissions of CO₂ into the atmosphere, and among these are CO₂ storage in the deep ocean. Topographic effects of dissolution and transport from a CO₂ lake located at 3,000-m depth have been studied using the z-coordinate model Massachusetts Institute of Technology general circulation model (MITgcm) and the σ-coordinate model Bergen ocean model (BOM). Both models have been coupled with the general ocean turbulence model (GOTM) in order to account for vertical subgrid processes. The chosen vertical turbulence mixing scheme includes the damping effect from stable stratification on the turbulence intensity. Three different topographic scenarios are presented: a flat bottom and the CO₂ lake placed within a trench with depths of 10 and 20 m. The flat case scenario gives good correlation with previous numerical studies of dissolution from a CO₂ lake. When topography is introduced, it is shown that the z-coordinate model and the σ-coordinate model give different circulation patterns in the trench. This leads to different dissolution rates, 0.1 μmol cm^− 2 s^− 1 for the scenario of a 20-m-deep trench using BOM and 0.005–0.02 μmol cm^− 2 s^− 1 for the same scenario using the MITgcm. The study is also relevant for leakages of CO₂ stored in geological formations and to the ocean.