beom

The Back of Envelope Ocean Model (beom) is a numerical solver for the multi-layer shallow-water equations. The code differs from traditional isopycnal models (e.g., [1]) by its treatment of vanishing layers [2] and its regular-unstructured grid on the horizontal [3]. The motivation behind beom is to simulate tides and flooding in estuaries of complex geometry. The model is written in strict Fortran 95 and targets computers ranging from laptops to workstations with multiple processors.

beom is an unfunded rainy Sunday afternoon project. The code is being evaluated against a series of test-cases and the results are promising. I am sharing the test-cases and the code under a copyleft license: Documentation and source for beom.

Snapshot from numerical simulation of subtropical gyre
Figure 1: Spin-up of the subtropical gyre in the North Atlantic Ocean. The colorscale represents the surface geostrophic velocity. The domain has closed boundaries and is forced with the climatological wind stress from Forget 2010 [4]. Right-click on this link and select "Save File As" to download a movie.

Snapshot from numerical simulation of North Atlantic
Figure 2: Potential vorticity in the ocean interior (permanent pycnocline) for the same period. Right-click on this link and select "Save File As" to download a movie.


Figure 3: Bottom layer vorticity for varying sill height (image from a poster at OS2018 by Zhao et al.).
Ken Zhao (UCLA) recently published a study titled Sill-Influenced Exchange Flows in Ice Shelf Cavities in J.Phys.Oceanogr. His study brings much needed insight into the dynamics of ice shelf cavities such as Pine Island Glacier. He implemented a rigid lid in beom and used a 2-layer setup to highlight the 3 regimes characterizing the circulation.

Snapshot from numerical simulation of flooding in Chesapeake Bay
Figure 4: Sea surface elevation during an extreme nor'easter. Right-click on this link and select "Save File As" to download a movie. The horizontal resolution is 100 meters everywhere and the bathymetry is from NOAA.

Snapshot from numerical simulation of surface M2 tide in Chesapeake Bay
Figure 5: First attempt at simulating the sea surface elevation associated with the principal lunar tide (M2, period of 12 hours and 25 minutes). Right-click on this link and select "Save File As" to download a movie.

Snapshot from numerical simulation of internal M2 tide in Chesapeake Bay
Figure 6: First attempt at simulating the pycnocline elevation associated with the principal lunar tide (M2, period of 12 hours and 25 minutes). Right-click on this link and select "Save File As" to download a movie.

Snapshot from numerical simulation of finite wave on sloping beach
Figure 7: Water wave of finite amplitude collapsing on a sloping beach. Right-click on this link and select "Save File As" to download a movie. The theoretical motion of the shoreline is from Carrier and Greenspan 1958 [5].

Snapshot from numerical simulation of semidiurnal tide over a Gaussian ridge
Figure 8: Semi-diurnal flow over a Gaussian ridge. The oscillating flow and the stratification generate internal waves radiating away from the ridge. Right-click on this link and select "Save File As" to download a movie.

Snapshot from numerical simulation of two-dimensional turbulence
Figure 9: Growth of vortices in a zonal jet (potential vorticity after 70 days). A narrow barotropic jet flows in a double-periodic basin with two ridges running north-south (red anomalies on day 0). Barotropic instability generates vortices drifting along the ridges. Note the symmetry in the north-south and east-west directions. The calculation uses the modified-Leith viscosity of Fox-Kemper and Menemenlis (2008). Right-click on this link and select "Save File As" to download a movie.


References

  1. Bleck, R., and L.T. Smith, 1990, A wind-driven isopycnic coordinate model of the North and Equatorial Atlantic Ocean. 1. Model development and supporting experiments, J. Geophys. Res., vol.95, no C3, p.3273-3285.
  2. Salmon, R., 2002. Numerical solution of the two-layer shallow water equations with bottom topography. J. Mar. Res., vol.60, p.605-638.
  3. Backhaus., J. O., 2008. Improved representation of topographic effects by a vertical adaptive grid in vector-ocean-model (VOM)---Part I: Generation of adaptive grids. Ocean Modelling, vol.22, p.114-127.
  4. Forget, G., 2010. Mapping Ocean Observations in a Dynamical Framework: A 2004-06 Ocean Atlas. J. Phys. Oceanogr., vol.40, p.1201-1221.
  5. Carrier, G.F., and H. P. Greenspan, 1958. Water waves of finite-amplitude on a sloping beach. J. Fluid. Mech. v.4, p.97-109.
  6. Fox-Kemper, B., and D. Menemenlis, 2008. Can Large Eddy Simulation techniques improve mesoscale rich ocean models? In: Hecht, M., Hasumi, H. (Eds.), Ocean Modeling in an Eddying Regime. vol.177. AGU Geophysical Monograph Series, pp. 319-338.