Equations

The model equations are the layer-integrated vector-invariant form of the hydrostatic primitive equations (either Boussinesq or non-Boussinesq).

We present the equations starting from the hydrostatic Boussinesq equation in height coordinates and progress through vector-invariant and general-coordinate equations to the final equations used in the vertical Lagrangian algorithm, taken from [1] and [22].

• Notation for equations
  • Symbols for variables
  • Vector notation
• Governing Equations
  • Vector invariant velocity equation
• Generalized vertical coordinate equations
• Specifics
  • Specifics of the Ocean Model Equations
  • Horizontal Momentum Equation
  • Hydrostatic balance
  • Thickness and tracer equations
  • Equation of state
• Vertical Lagrangian method: conceptual
  • Lagrangian and ALE
  • Vertical Lagrangian regrid/remap method
  • Outlining the numerical algorithm