(ocean-seamount)=

# seamount

The ``ocean/seamount`` test is a standard sigma coordinate test problem, which is documented in 
[Beckmann and Haidvogel (1993)](https://journals.ametsoc.org/view/journals/phoc/23/8/1520-0485_1993_023_1736_nsofaa_2_0_co_2.xml), [Haidvogel et al. (1993)](https://journals.ametsoc.org/view/journals/phoc/23/11/1520-0485_1993_023_2373_nsofaa_2_0_co_2.xml) and [Shchepetkin and McWilliams (2003)](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2001JC001047).
This case tests the error due to pressure gradients in tilted layers. 

## supported models

These tasks support only MPAS-Ocean.

(ocean-seamount-default)=

## default task

### description

The test case begins with a zero velocity field and is unforced, so the exact solution is to remain motionless. 
The seamount rises from a flat sea floor in the center of the domain. 
In a pure z-level vertical coordinate without partial bottom cells (`partial_cell_type = full`), the pressure gradient will remain zero and induce no flow to machine precision. When any layer tilting is added, including from partial bottom cells, some flow is introduced by the pressure gradient error. This is fundamentally because the pressure must be extrapolated vertically at cell centers to the mid-depth of the edge. The default setting is the sigma coordinate. These are the images produced in the `viz` folder.

```{image} images/seamount_velocity_max_t.png
:align: center
:width: 700 px
```

```{image} images/seamount_final_kineticEnergyCell_section.png
:align: center
:width: 700 px
```

```{image} images/seamount_final_normalVelocity.png
:align: center
:width: 400 px
```


### mesh

The domain is planar and periodic on the zonal and the
meridional boundaries. The 6.7 km resolution is tested by default, 
which is set by the ``resolution`` config option. The domain is
320 km by 320 km, as given by the config options ``lx`` and ``ly``.

### vertical grid

The default setting is a sigma (terrain-following) vertical coordinate. One may also test z-level coordinates (`coord_type = z-level`) with full cells (`partial_cell_type = full`) or partial bottom cells (`partial_cell_type = None`). Here `None` means no alteration, so it uses original bottom depth. 

```cfg
# Options related to the vertical grid
[vertical_grid]

# Depth of the bottom of the ocean (m)
bottom_depth = 5000.0

# Number of vertical levels
vert_levels = 10

# The type of vertical grid
grid_type = uniform

# The type of vertical coordinate (e.g. z-level, z-star)
coord_type = sigma

# Whether to use "partial" or "full", or "None" to not alter the topography
partial_cell_type = None
```

### initial conditions

Salinity is constant throughout the domain at the value given by the config
option ``constant_salinity`` (35 PSU by default).  The initial density 
is based on the formulas given in [Beckmann and Haidvogel (1993)](https://journals.ametsoc.org/view/journals/phoc/23/8/1520-0485_1993_023_1736_nsofaa_2_0_co_2.xml) equations 15-16.
The initial temperature is back-computed from this density with an assumed linear equation of state using 
`seamount_density_Tref` and `seamount_density_alpha`.

### forcing

N/A

### time step and run duration

The time step for forward integration is automatically computed based on the gridcell size. The run duration is as follows.

```cfg
[seamount_default]

# Run duration (days)
run_duration = 6.

# Output interval (hours)
output_interval = 1.
```

### config options

The following config section is specific to this test case:

```cfg
# Options related to the seamount case
[seamount]

# Timestep per km horizontal resolution (s)
dt_per_km = 10.

# Barotropic timestep per km horizontal resolution (s)
btr_dt_per_km = 2.5

# The width of the domain in the across-slope dimension (km)
ly = 320

# The length of the domain in the along-slope dimension (km)
lx = 320

# Distance from two cell centers (km)
resolution = 6.7

# Bottom depth at bottom of seamount
max_bottom_depth = ${vertical_grid:bottom_depth}

# Logical flag that controls how the vertical profile of tracers.  See Beckmann and Haidvogel 1993 eqn 15-16 (unitless)
# possible_values="linear, exponential"
seamount_stratification_type = exponential

# Density coefficient for linear vertical stratification (kg m^{-3})
seamount_density_coef_linear = 1024.0

# Density coefficient for exponential vertical stratification (kg m^{-3})
seamount_density_coef_exp = 1028.0

# Density gradient for linear vertical stratification, Delta_z rho in Beckmann and Haidvogel eqn 15 (kg m^{-3})
seamount_density_gradient_linear = 0.1

# Density gradient for exponential vertical stratification, Delta_z rho in Beckmann and Haidvogel eqn 16 (kg m^{-3})
seamount_density_gradient_exp = 3.0

# Density reference depth for linear vertical stratification (m)
seamount_density_depth_linear = 4500.0

# Density reference depth for exponential vertical stratification (m)
seamount_density_depth_exp = 500.0

# Density reference for eos to initialize temperature (kg m^{-3})
seamount_density_ref = 1028.0

# Reference temperature for eos to initialize temperature (C)
seamount_density_Tref = 5.0

# Linear thermal expansion coefficient to initialize temperature (kg m^{-3} C^{-1})
seamount_density_alpha = 0.2

# Height of sea mount, H_0 (m)
seamount_height = 4500.0

# Width parameter of sea mount, e-folding length (m)
seamount_width = 40.0e3

# Salinity of the water in the entire domain (PSU)
constant_salinity = 35.0

# Coriolis parameter for entire domain (s^{-1})
coriolis_parameter = -1.0e-4
```

### cores

The number of cores is determined by `goal_cells_per_core` and
`max_cells_per_core` in the `ocean` section of the config file.