A new algorithm with square conservative exponential integral for transport equation

The SCEIM method is proposed for transport problems on the sphere. The method is a combination of Square Conservation algorithm and Exponential Integral Method. The main emphasis in the development of SCEIM is on conservation, positive-definite and reversibility as well as achieving comparable accuracy to other published schemes. The most significant advantage of SCEIM is to change the forward model to the backward model by setting negative time-step, and the backward model can be used to solve the inverse problem. Moreover, the polar problem is significantly improved by using a simple effective central skip-point deference scheme without major penalty on the overall effectiveness of SCEIM. To demonstrate the effectiveness and generality of the SCEIM, this method is evaluated by standard cosine bell tests and deformational flow tests. The numerical results show that SCEIM is a time-convergence method as well as a grid-convergence method, and has a strong shape-preserving ability. In the tests of inverse problem, the sharp fronts are successfully regressed back into their initial weak fronts and the cosine bells move against the wind direction and return to the initial position with high accuracy. The numerical results of forward simulations are compared with those of published schemes, the total mass conservation and error norms are competitive in term of accuracy.

Comparison of Physical to Numerical Mixing with Different Tracer Advection Schemes in Estuarine Environments

The numerical simulation of estuarine dynamics requires accurate prediction for the transport of tracers, such as temperature and salinity. During the simulation of these processes, all the numerical models introduce two kinds of tracer mixing: 1) by parameterizing the tracer eddy diffusivity through turbulence models leading to a source of physical mixing and 2) discretization of the tracer advection term that leads to numerical mixing. Physical and numerical mixing both vary with the choice of horizontal advection schemes, grid resolution, and time step. By simulating four idealized cases, this study compares the physical and numerical mixing for three different tracer advection schemes. Idealized domains only involving physical and numerical mixing are used to verify the implementation of mixing terms by equating them to total tracer variance. Among the three horizontal advection schemes, the scheme that causes the least numerical mixing while maintaining a sharp front also results in larger physical mixing. Instantaneous spatial comparison of mixing components shows that physical mixing is dominant in regions of large vertical gradients, while numerical mixing dominates at sharp fronts that contain large horizontal tracer gradients. In the case of estuaries, numerical mixing might locally dominate over physical mixing; however, the amount of volume integrated numerical mixing through the domain compared to integrated physical mixing remains relatively small for this particular modeling system.

Buoyant Gravity Currents Released from Tropical Instability Waves

Two extremely sharp fronts with changes in sea surface temperature >0.4°C over lateral distances of ~1 m were observed in the equatorial Pacific at 0°, 140°W and at 0.75°N, 110°W. In both cases, layers of relatively warm and fresh water extending to ~30-m depth propagated to the southwest as gravity currents. Turbulent kinetic energy dissipation rates averaging 4.5 × 10−6 W kg−1 were measured with a microstructure profiler within the warm layer behind the leading edge of the fronts—1000 times greater than dissipation in the ambient water ahead of the fronts. From satellite images, these fronts were observed to propagate ahead of the trailing edge of a tropical instability wave (TIW) cold cusp. Results from an ocean model with 6-km grid resolution suggest that TIW fronts may release gravity currents through frontogenesis and loss of balance as the fronts approach the equator and the Coriolis parameter weakens. Sharp frontal features appear to be ubiquitous in the eastern tropical Pacific, have an influence on the distribution of biogeochemical tracers and organisms, and play a role in transferring energy out of the TIW field toward smaller scales and dissipation.

Submesoscale Dynamics of a Gulf Stream Frontal Eddy in the South Atlantic Bight

Frontal eddies are commonly observed and understood as the product of an instability of the Gulf Stream along the southeastern U.S. seaboard. Here, the authors study the dynamics of a simulated Gulf Stream frontal eddy in the South Atlantic Bight, including its structure, propagation, and emergent submesoscale interior and neighboring substructure, at very high resolution (dx = 150 m). A rich submesoscale structure is revealed inside the frontal eddy. Meander-induced frontogenesis sharpens the gradients and forms very sharp fronts between the eddy and the adjacent Gulf Stream. The strong straining increases the velocity shear and suppresses the development of barotropic instability on the upstream face of the meander trough. Barotropic instability of the sheared flow develops from small-amplitude perturbations when the straining weakens at the trough. Small-scale meandering perturbations evolve into rolled-up submesoscale vortices that are advected back into the interior of the frontal eddy. The deep fronts mix the tracer properties and enhance vertical exchanges of tracers between the mixed layer and the interior, as diagnosed by virtual Lagrangian particles. The frontal eddy also locally creates a strong southward flow against the shelf leading to topographic generation of submesoscale centrifugal instability and mixing. In eddy-resolving models that do not resolve these submesoscale processes, there is a significant weakening of the intensity of the upwelling in the core of the frontal eddies, and their decay is generally too fast.

Numerical Schemes for Modelling Two Phase Flow with Interfaces

We discuss the numerical modelling of two phase flow in porous media (see [1]). We consider a one-dimensional problem describing flow of two incompressible and immiscible fluids through a porous medium where the non-wetting phase (oil) is displaced by the wetting fluid (water). The used model is based on Darcy’s law and we consider either horizontal (neglecting the influence of gravity) or vertical flow. In case of horizontal flow, we compare our solution with analytical solution published in [2]. In case of gravity driven vertical flow, there is no known analytical solution and we propose our solution as a benchmark solution.Our numerical model is based on the modelling of interface separating zones where the water is present and where it is not. We semidiscretize the problem in space and obtain a mass preserving system of ODEs. We have moving grid points only on region where the water is present, and these move accordingly to the evolution of the interface. We can choose to have non-equidistant grid with more grid points in the neighbourhood of the interface. This guarantees very good approximation of sharp fronts during infiltration. Results obtained by our methods are compared with well-known result in [2] which was obtained by semi-analytical method and they are in perfect agreement.