Equation of State and Bottom Boundary¶

`equation_of_state`¶

Controls the seawater density formulation used to compute buoyancy, stratification, and the baroclinic pressure gradient.

The density calculation feeds directly into the stratification module pygotm.meanflow.stratification and all buoyancy-dependent turbulence terms.

equation_of_state:
  method: full_teos-10
  rho0: 1027.0
  linear:
    T0: 10.0
    S0: 35.0
    p0: 0.0
    alpha: 2.0e-4
    beta: 7.5e-4
    cp: 3991.87

`equation_of_state.method`¶

Type	string
Valid values	`full_teos-10`, `linear_teos-10`, `linear_custom`
Default	`"full_teos-10"`

Selects the density formulation.

full_teos-10

Full nonlinear TEOS-10 equation of state (IOC et al. 2010). Uses the GSW toolbox to compute density, thermal expansion coefficient \(\alpha\), and saline contraction coefficient \(\beta\) at every level and every time step. Most accurate option; recommended for open-ocean and lake simulations.

linear_teos-10

Linearised equation of state using TEOS-10 to compute \(\alpha\), \(\beta\), and \(c_p\) at a reference state (\(T_0\), \(S_0\), \(p_0\)); these coefficients are then held constant:

\[\rho = \rho_0 \left[1 - \alpha(T - T_0) + \beta(S - S_0)\right]\]

Faster than full_teos-10 and appropriate when T/S variations are small.

linear_custom

Same linearised formula as above, but \(\alpha\), \(\beta\), \(\rho_0\), and \(c_p\) are all specified directly by the user in the linear sub-block rather than computed from TEOS-10. Use when you want full control over the equation of state (e.g., for idealised freshwater lake studies).

`equation_of_state.rho0`¶

Units	kg m⁻³
Default	`1027.0`

Reference density. Used throughout the model to non-dimensionalise fluxes. Specifically:

Surface wind stress is divided by rho0 to give kinematic stress \(\tau/\rho_0\) [m² s⁻²].
Heat flux is converted to temperature flux via \(Q / (\rho_0 c_p)\).

`equation_of_state.linear`¶

Sub-block for the linearised EOS. Only used when method: linear_teos-10 or method: linear_custom.

T0: Reference temperature (°C). Default: 15.0; range: −2 to 40 °C.
S0: Reference salinity (g kg⁻¹). Default: 35.0; range: ≥ 0.
p0: Reference pressure (dbar). Default: 0.0; range: ≥ 0.
alpha: Thermal expansion coefficient \(\alpha = -\partial\rho/(\rho_0\partial T)\) (K⁻¹). Default: 2.0e-4. Used when method: linear_custom.
beta: Saline contraction coefficient \(\beta = \partial\rho/(\rho_0\partial S)\) (kg g⁻¹). Default: 7.5e-4. Used when method: linear_custom.
cp: Specific heat capacity at constant pressure (J kg⁻¹ K⁻¹). Default: 3991.87. Used when method: linear_custom to convert heat fluxes to temperature tendencies.

`meanflow`¶

Physical constants and switches for the mean-flow equations. These keys appear directly under a meanflow block in full GOTM YAML files.

meanflow:
  gravity: 9.81
  rho0: 1027.0
  cori: 0.0
  avmolu: 1.3e-6
  avmolT: 1.4e-7
  avmolS: 1.1e-9
  cp: 3991.87
  h0b: 0.05
  z0s_min: 0.02
  calc_bottom_stress: true
  charnock: false
  MaxItz0b: 10

`meanflow.gravity`¶

Units	m s⁻²
Default	`9.81`

Gravitational acceleration. Used in buoyancy frequency and pressure gradient calculations.

`meanflow.rho0`¶

Reference density (see equation_of_state.rho0). Default: 1027.0.

`meanflow.cori`¶

Units	s⁻¹
Default	computed from latitude

Coriolis parameter \(f = 2\Omega\sin\phi\). By default pyGOTM computes this from location.latitude. Setting an explicit value here overrides the geographic computation.

`meanflow.avmolu`¶

Units	m² s⁻¹
Default	`1.3e-6`

Molecular kinematic viscosity of seawater. Added to the turbulent eddy viscosity as a background value.

`meanflow.avmolT`¶

Units	m² s⁻¹
Default	`1.4e-7`

Molecular thermal diffusivity.

`meanflow.avmolS`¶

Units	m² s⁻¹
Default	`1.1e-9`

Molecular salinity (haline) diffusivity.

`meanflow.cp`¶

Specific heat capacity of seawater (J kg⁻¹ K⁻¹). Default: 3991.87.

`bottom`¶

Bottom boundary condition parameters for the mean-flow equations.

bottom:
  calc_bottom_stress: true
  h0b: 0.05

`bottom.calc_bottom_stress`¶

Type	boolean
Default	`true`

If true, the bottom stress is computed from the law of the wall using the bottom roughness length h0b and the velocity at the first grid level. If false, the bottom boundary condition is a no-stress (free-slip) condition.

Implemented in pygotm.meanflow.friction.friction().

`bottom.h0b`¶

Units	m
Range	≥ 0.0
Default	`0.05`

Physical bottom roughness length \(z_{0b}\). Used in the logarithmic law of the wall to compute bottom friction velocity:

\[u_{\tau b} = \frac{\kappa \, u(z_1)}{\ln(z_1 / z_{0b})}\]

where \(z_1\) is the height of the first grid level and \(u(z_1)\) is the velocity magnitude at that level.

Larger values of h0b represent rougher bottoms (gravel, boulders) while smaller values represent smoother bottoms (fine sediment, mud).

`meanflow.z0s_min`¶

Units	m
Default	`0.02`

Minimum surface roughness length \(z_{0s}\). When the Charnock parameterisation is inactive, the surface roughness is held at this constant value.

`meanflow.charnock`¶

Type	boolean
Default	`false`

If true, use the Charnock (1955) relation to derive the surface roughness length from the surface friction velocity: \(z_{0s} = \alpha_c u_{\tau s}^2 / g\). [unsupported in compiled runtime] in the current release.

`meanflow.MaxItz0b`¶

Type	integer
Default	`10`

Maximum number of iterations for the implicit roughness-velocity coupling at the bottom boundary.

References

IOC, SCOR, IAPSO (2010). The International Thermodynamic Equation of Seawater — 2010. UNESCO.

Charnock, H. (1955). Wind stress over a water surface. Q. J. R. Meteorol. Soc., 81, 639–640.

Equation of State and Bottom Boundary¶