oocgcm.core.grids.generic_2d_grid.q_vector_due_to_kinematic_deformation

generic_2d_grid.q_vector_due_to_kinematic_deformation(velocity, buoyancy)

Return the component of the generalized Q-vector associated with kinematic deformation of a two-dimensional velocity field.

Parameters:

velocity : VectorField2d

namedtuple of horisontal velocity at u,v grid locations

buoyancy : xarray.DataArray

xarray of buoyancy at grid_location=’t’

Returns:

vectorfield : VectorField2d

Two-dimensional vector field of \(Q_{kd}\) at u,v-points.

Notes

Definition of the Q-vector due to kinematic deformation (following [R8], see also [R9]):

\[\begin{split}\mathbf{Q}^g_{kd} = - \begin{pmatrix} \partial_x u \,\partial_x b + \partial_x v_g \,\partial_y b \\ \partial_y u \,\partial_x b + \partial_y v_g \,\partial_y b \end{pmatrix}\end{split}\]

References

[R8]	(1, 2) Hoskins, B.J., Bretherton, F.P., 1972. Atmospheric Frontogenesis Models: Mathematical Formulation and Solution. J. Atmos. Sci. 29, 11-37.

[R9]	(1, 2) Giordani, H., Prieur, L., Caniaux, G., 2006. Advanced insights into sources of vertical velocity in the ocean. Ocean Dynamics 56, 513-524.