Research

This example of circulation in North San Francisco Bay involved the leading-order effects of tides and baroclinic circulation. In many cases, however, we seek results related to high-order or secondary processes (such as wind-driven circulation, tidal residuals, ocean-driven circulation) which can be much more difficult to model when both high- and low-frequency processes are simulated. As an example, the work by Sankaranarayanan and Fringer (2013) in San Francisco Bay shows that forcing from the Pacific Ocean accounts for less than 5% of the variance in the currents in Central San Francisco Bay. This implies that model errors in computing the other dominant processes, such as the tides in the bay, must be very small if one seeks to model low-frequency effects due to the Pacific Ocean.

Circulation in a microtidal estuary

back to top

In much of San Francisco Bay, the tides are the dominant physical mechanism controlling the circulation given that the averge tidal range is roughly 2 m. However, in microtidal systems like Galveston Bay, TX (Figure 3), where the tidal range is much less than 2 m, all forcing mechanisms are of similar magnitude. Therefore, all must be faithfully computed to obtain reasonable model skill, including tides, winds, fresh water discharges, atmospheric heating and cooling, evaporation and precipitation, and possibly, meso-scale coastal phenomena. At the same time, model validation must separately validate the low- and high-frequency results to demonstrate model skill at resolving processes over different time scales. Rayson et al. (2015) showed this to be an essential component of obtaining accurate SUNTANS results in Galveston Bay, where, unlike San Francisco Bay, the low-frequency wind- and Gulf-driven currents account for the same fraction of the variance as the relatively weak tides. We used the model of Rayson et al. (2015) to study the complex spatio-temporal variability of residence times in the Bay (Rayson et al., 2016) as well as an analysis of the seasonal varibility of the salt flux (Rayson et al., 2017). Figure 4 shows an example of particle motion in Galveston Bay used to compute Lagrangian residence times, while Figure 5 shows model prediction of a hypothetical tracer release at the mouth of the bay.

High-resolution simulations of a macrotidal estuary

back to top

In contrast to microtidal estuaries, tides dominate the circulation in macrotidal estuaries, which are defined by a tidal surface range exceeding 4 m. My group studied the salinity dynamics in the Snohomish River Estuary near Everett, WA, a macrotidal salt wedge estuary. We employed the SUNTANS model with very high grid resolution in order to understand the impact of complex bathymetric features on the circulation (Figure 6). Such high grid resolution enables simulation of flow separation around a sill that is exposed during low tide, as shown in Figure 7. Macrotidal estuaries are hard to model because of extensive wetting and drying of tidal mudflats, which imposes strict stability limitations on the free-surface solver in order to make sure that the water depth remains positive. Additionally, owing to the strong dependence on the bathymetry, results depend to great extent on accurate bathymetry surveys (Figure 8).

In addition to accurate bathymetry, accurate predictions of salinity require a turbulence model to parameterize the effect of turbulence on the vertical mixing of salt. While a turbulence model is needed to parameterize the mixing, Wang et al. (2011) analyzed several turbulence closure schemes and showed that the particular closure scheme (e.g. Mellor-Yamada 2.5, k-epsilon, k-omega, etc...) is not as important as the stability function, which parameterizes the effect of the stratification and shear on the mixing. Figure 9 shows transects of the salinity and turbulent kinetic energy during flood tide along the Snohomish River. The results show little difference among the turbulence models, but a pronounced effect of the stability function. In this case the stabiilty function can overdamp the turbulence and lead to less vertical mixing and an overprediction of the upstream salt flux.

Salt marshes

back to top

Hydrodynamics of salt marshes is unique from a modeling perspective because it requires modeling of the usual estuarine processes in addition to drag by extensive vegetation and, as is typically the case in salt marshes in urban areas, engineered structures such as culvert pipes. Vegetation drag and engineered structures play essential roles both in the hydrodynamics and sediment transport in salt marsh estuaries. Understanding and modeling of these processes is important for developing informed management strategies for salt marsh restoration and sustainability.

My group has added new modules to the SUNTANS model in order to study the hydrodynamics of salt marsh estuaries. These include:

• Hybrid grid compatibility: This allows use of arbitrary-sided polygons on the unstructured grid. As an example, our work in the Castro Cove region of San Francisco Bay (Figure 10) employs both triangles and quadrilaterals (Figure 11). Quadrilaterals enable simulation of along- and cross-channel gradients much more accurately and efficiently than triangles. Although two triangles can be used in place of a quadrilateral, these triangles are typically degenerate since the Voronoi points, which are the centers of the circumcircles in each triangle, either overlap (if the triangles are right), are outside of the triangles (if they are obtuse), or incur cell centers that are very close together, leading to numerical stability problems. Regardless of the location of the Voronoi points, elongated triangles generally lead to inaccurate results.

• Vegetation drag module: This adds momentum sink terms to the right-hand side of the Navier-Stokes equations to parameterize the effects of the vegetation through a quadratic drag law that takes into account the flow speed and vegetation geometry, including density, shape, size, etc... To test the drag parameterization, we used SUNTANS to simulate flow in a laboratory tank with idealized vegetation with different vegetation heights and densities (Figure 12). The results yield suprisingly good agreement between the lab experiments and the model (Figure 13). Although the agreement is good, better agreement in the shear layer could be obtained by including the effects of the vegetation into the turbulence model. Such effects, however, are less pronounced and even more difficult to calibrate for field-scale applications.

• Culvert module: To simulate flow through culverts, we implemented the method of Casulli and Stelling (2013; doi:10.1002/fld.3817), in which the free-surface is constrained to the top of the culverts when the flow is fully discharged. A quadratic drag law is imposed in the momentum equations that ensures the correct flow-stage relationship for the culvert.

• Subgrid bathymetry module: The concept of subgrid bathymetry was developded by Casulli (2009; doi:10.1002/fld.1896) and enables use of high-resolution bathymetry without needing to employ high grid resolution. In the method, bathymetry at a resolution that is finer than the grid ("subgrid") is used to compute the volume and cross-sectional areas of the finite-volume cells when computing conservation of volume (i.e. the free surface) and mass (i.e. salt, heat, sediments). In this manner, the cross-sectional areas of the cells match the physical cross-sectional areas based on the bathymetry regardless of the grid resolution. The effect of the subgrid bathymetry is also included in the momentum equations and can reproduce the correct flow-stage relationship in simple channel cross sections when the momentum balance is predominantly between the barotropic pressure gradient and bottom friction. In channels with strong lateral variability, lateral momentum fluxes can disrupt this balance, an effect that can be alleviated by increasing the lateral grid resolution so that the method relies less on the subgrid reconstruction of momentum. Application of the subgrid method to sediment transport is discussed here.