Chapter 4
2.5D Vertical Slice Modelling
Abstract This chapter introduces the reader to 2.5-dimensional modelling in a vertical ocean slice which allows for inclusion of the Coriolis force. Exercises address
geostrophic adjustment of density fronts, coastal upwelling and Ekman pumping.
The last exercise of this chapter explains the curiosity that winds can create flows in
the ocean running opposite to the wind direction.
4.1 The Basis
4.1.1 Adding Another Half Dimension
Elongated dynamical features being influenced by the Coriolis force, such as oceanic
fronts, can be described to first-order approximation by the dynamics in a vertical
ocean slice with vanishing gradients of all variables normal to this slice (Fig. 4.1).
This approach is called the 2.5-dimensional vertical ocean-slice model.
4.1.2 The Geostrophic Balance
Processes considered in this section involve the Coriolis force. Therefore, we briefly
revisit the fundamentals of flows dominated by a balance between the Coriolis
force and the horizontal pressure-gradient force; that is, the geostrophic balance.
The momentum equations for pure geostrophic flow in Cartesian coordinates are
given by:
− f v geo = −
1
ρ
∂ P
∂ x
(4.1)
+ f u geo = −
1
ρ
∂ P
∂ y
(4.2)
where f is the Coriolis parameter (see Sect. 2.1). Geostrophic flows run along lines
of constant pressure, called isobars. With inclusion of the hydrostatic balance, which
J. K¨ ampf, Advanced Ocean Modelling, DOI 10.1007/978-3-642-10610-1 4,
C
Springer-Verlag Berlin Heidelberg 2010
97
2.5D Vertical Slice Modelling
Abstract This chapter introduces the reader to 2.5-dimensional modelling in a vertical ocean slice which allows for inclusion of the Coriolis force. Exercises address
geostrophic adjustment of density fronts, coastal upwelling and Ekman pumping.
The last exercise of this chapter explains the curiosity that winds can create flows in
the ocean running opposite to the wind direction.
4.1 The Basis
4.1.1 Adding Another Half Dimension
Elongated dynamical features being influenced by the Coriolis force, such as oceanic
fronts, can be described to first-order approximation by the dynamics in a vertical
ocean slice with vanishing gradients of all variables normal to this slice (Fig. 4.1).
This approach is called the 2.5-dimensional vertical ocean-slice model.
4.1.2 The Geostrophic Balance
Processes considered in this section involve the Coriolis force. Therefore, we briefly
revisit the fundamentals of flows dominated by a balance between the Coriolis
force and the horizontal pressure-gradient force; that is, the geostrophic balance.
The momentum equations for pure geostrophic flow in Cartesian coordinates are
given by:
− f v geo = −
1
ρ
∂ P
∂ x
(4.1)
+ f u geo = −
1
ρ
∂ P
∂ y
(4.2)
where f is the Coriolis parameter (see Sect. 2.1). Geostrophic flows run along lines
of constant pressure, called isobars. With inclusion of the hydrostatic balance, which
J. K¨ ampf, Advanced Ocean Modelling, DOI 10.1007/978-3-642-10610-1 4,
C
Springer-Verlag Berlin Heidelberg 2010
97