Plume spreading test case for coastal ocean models

We present a test case of river plume spreading to evaluate numerical methods used in coastal ocean modeling. It includes an estuary–shelf system whose dynamics combine nonlinear flow regimes with sharp frontal boundaries and linear regimes with cross-shore geostrophic balance. This system is highly sensitive to physical or numerical dissipation and mixing. The main characteristics of the plume dynamics are predicted analytically but are difficult to reproduce numerically because of numerical mixing present in the models. Our test case reveals the level of numerical mixing as well as the ability of models to reproduce nonlinear processes and frontal zone dynamics. We document numerical solutions for the Thetis and FESOM-C models on an unstructured triangular mesh, as well as ones for the GETM and FESOM-C models on a quadrilateral mesh. We propose an analysis of simulated plume spreading which may be useful in more general studies of plume dynamics. The major result of our comparative study is that accuracy in reproducing the analytical solution depends less on the type of model discretization or computational grid than it does on the type of advection scheme.

Mixing time in yield stress fluids

Yield stress fluids are commonly encountered in the pharmaceutical, wastewater and bioprocess industries. On agitation of these fluids with an impeller, a zone of significant motion (cavern) is formed surrounded by stagnant regions. These inhomogeneous conditions are undesirable from a product quality standpoint. Therefore, to evolve a mixing system design that would eliminate these problems, experimental measurements of mixing time were obtained and combined with power consumption to provide a measure of mixing system efficiency. The effect of different parameters such as fluid rheology, impeller rotational speed, impeller type and impeller clearance on the mixing times was also investigated. In addition, using CFD, numerical mixing times were calculated and a comparison of the numerical and experimental mixing times were conducted to investigate the capability of the CFD tool to correctly predict the homogenization process in mixing tanks. In general, it was observed that the power characteristics of the different agitators were well reproduced by the computational package. In addition, CFD was able to correctly predict the effect of impeller rotational speed and fluid yield stress on the mixing times. However, the effect of impeller clearance on the mixing time was not correctly predicted by the CFD package when compared with experimental results obtained in this work as well as those obtained by other researchers. A comparison of the impellers used in this study (Pitched Blade Turbine (PBT), marine propeller and Lightnin A320) using the mixing time correlations available in the literature to fit the experimental data revealed that the PBT was superior to the other impellers in mixing yield stress fluids. In addition, the validated CFD model was used to measure the dimensions of the cavern formed around the impeller and it showed good agreement with the Elson's cavern model.

Mixing time in yield stress fluids

Yield stress fluids are commonly encountered in the pharmaceutical, wastewater and bioprocess industries. On agitation of these fluids with an impeller, a zone of significant motion (cavern) is formed surrounded by stagnant regions. These inhomogeneous conditions are undesirable from a product quality standpoint. Therefore, to evolve a mixing system design that would eliminate these problems, experimental measurements of mixing time were obtained and combined with power consumption to provide a measure of mixing system efficiency. The effect of different parameters such as fluid rheology, impeller rotational speed, impeller type and impeller clearance on the mixing times was also investigated. In addition, using CFD, numerical mixing times were calculated and a comparison of the numerical and experimental mixing times were conducted to investigate the capability of the CFD tool to correctly predict the homogenization process in mixing tanks. In general, it was observed that the power characteristics of the different agitators were well reproduced by the computational package. In addition, CFD was able to correctly predict the effect of impeller rotational speed and fluid yield stress on the mixing times. However, the effect of impeller clearance on the mixing time was not correctly predicted by the CFD package when compared with experimental results obtained in this work as well as those obtained by other researchers. A comparison of the impellers used in this study (Pitched Blade Turbine (PBT), marine propeller and Lightnin A320) using the mixing time correlations available in the literature to fit the experimental data revealed that the PBT was superior to the other impellers in mixing yield stress fluids. In addition, the validated CFD model was used to measure the dimensions of the cavern formed around the impeller and it showed good agreement with the Elson's cavern model.

The geography of numerical mixing in a suite of global ocean models

<p>Numerical mixing, the physically spurious diffusion of tracers due to the numerical discretization of advection, is known to contribute to biases in ocean circulation models. However, quantifying numerical mixing is non-trivial, with most studies utilizing specifically targeted experiments in idealized settings. Here, we present a precise method based on water-mass transformation for quantifying numerical mixing, including its spatial structure, that can be applied to any conserved variable in global general circulation ocean models. The method is applied to a suite of global MOM5 ocean-sea ice model simulations with differing grid spacings and sub-grid scale parameterizations. In all configurations numerical mixing drives across-isotherm heat transport of comparable magnitude to that associated with explicitly-parameterized mixing. Numerical mixing is prominent at warm temperatures in the tropical thermocline, where it is sensitive to the vertical diffusivity and resolution. At colder temperatures, numerical mixing is sensitive to the presence of explicit neutral diffusion, suggesting that much of the numerical mixing in these regions acts as a proxy for neutral diffusion when it is explicitly absent. Comparison of equivalent (with respect to vertical resolution and explicit mixing parameters) 1/4-degree and 1/10-degree horizontal resolution configurations shows only a modest enhancement in numerical mixing at the eddy-permitting 1/4-degree resolution. Our results provide a detailed view of numerical mixing in ocean models and pave the way for future improvements in numerical methods.</p>

Effective Diahaline Diffusivities in Estuaries

<p>The present study aims to estimate effective diahaline turbulent salinity fluxes and diffusivities in numerical model simulations of estuarine scenarios. The underlying method is based on a quantification of salinity mixing per salinity class, which is shown to be twice the turbulent salinity transport across the respective isohaline. Using this relation, the recently derived universal law of estuarine mixing, predicting that average mixing per salinity class is twice the respective salinity times the river run‐off, can be directly derived. The turbulent salinity transport is accurately decomposed into physical (due to the turbulence closure) and numerical (due to truncation errors of the salinity advection scheme) contributions. The effective diahaline diffusivity representative for a salinity class and an estuarine region results as the ratio of the diahaline turbulent salinity transport and the respective (negative) salinity gradient, both integrated over the isohaline area in that region and averaged over a specified period. With this approach, the physical (or numerical) diffusivities are calculated as half of the product of physical (or numerical) mixing and the isohaline volume, divided by the square of the isohaline area. The method for accurately calculating physical and numerical diahaline diffusivities is tested and demonstrated for a three‐dimensional idealized exponential estuary. As a major product of this study, maps of the spatial distribution of the effective diahaline diffusivities are shown for the model estuary.</p>

Evaluation of the z-tilde vertical coordinate in a 1/4° global NEMO

<p>The eddy-permitting 1/4° resolution in NEMO has been known to suffer from significant numerical diapycnal mixing. This arises from truncations in the advection scheme, which causes spurious mixing of tracers where there are transient vertical motions from internal tides and near-inertial waves, as well as from computational modes associated with partly-resolved mesoscale features. Suppressing the near-gridscale noise by increasing the viscosity has been shown to offer a useful reduction in that contribution to numerical mixing, but does not have a significant effect on tides and inertial waves.</p><p>The z~ scheme replaces eulerian vertical tracer advection across the vertical coordinate surfaces, on time scales less than a few days, with displacements of the coordinate surfaces themselves, in a manner more consistent with the nearly adiabatic nature of near-inertial gravity waves and tides. This has been shown to give substantial reduction in numerical mixing in an idealised configuration, but has yet to be fully evaluated in a global ocean domain. It is shown, using a new prototype eORCA025 global NEMO configuration, that <strong>z~</strong> with the default filter timescales reduces the effective diapycnal diffusivity and temperature drifts by only about 10%. Preliminary results will be presented for the sensitivity of the numerical mixing to the z~ timescale and other parameters. The application of z~ to a tidally-forced simulation will also be discussed.</p>

Plume spreading test case for coastal ocean models

We present a test case of river plume spreading to evaluate numerical methods used in coastal ocean modeling. The main characteristics of the plume dynamics are predicted analytically, but are difficult to reproduce numerically because of numerical mixing present in the models. Our test case reveals the level of numerical mixing as well as the ability of models to reproduce nonlinear processes and frontal zone dynamics. We propose an analysis of simulated plume spreading which may be useful in more general studies of plume dynamics. The major result of our comparative study is that accuracy in reproducing the analytical solution depends less on the type of applied model architecture or numerical grid than it does on the type of advection scheme.