Divergence and Vertical Motion Questions and Answers

Answer: A

The mass flux of the meridional overturning is expressed as a streamfunction in the latitude-height plane, whose maximum value gives the strength of the cell in units of kilograms per second. Typical winter values reach about \( 2 \times 10^{11} \) kilograms per second. Velocity potential describes the divergent circulation in the horizontal, and precipitation and pressure differences are indirect indicators at best. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: D

The flow is clockwise in nature.

The vertical component of relative vorticity is the zonal gradient of the meridional current minus the meridional gradient of the zonal current:

\[ \begin{aligned} \zeta &= \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y} \\ &= (-0.3 - 0.3) \times 10^{-3} = -0.6 \times 10^{-3}\ \text{s}^{-1} \end{aligned} \]

Negative vorticity means clockwise rotation; at 15 °N this is anticyclonic flow.

The flow is clearly rotational, since \(\zeta \ne 0\). Counter-clockwise rotation would need positive vorticity. Divergence needs the gradients \(\partial u/\partial x\) and \(\partial v/\partial y\), which are not given, so nothing can be said about it from these data.

Answer: B

The mass divergence form is equation (ii) only.

Conservation of mass for a compressible fluid states that the local rate of change of density is balanced by the divergence of the mass flux:

\(\dfrac{\partial \rho}{\partial t} + \nabla \cdot (\rho\mathbf{v}) = 0\)

Equation (i) uses the curl instead of the divergence, and a curl is a vector while \(\partial\rho/\partial t\) is a scalar, so it cannot be a mass balance. Equation (iii) describes the time change of velocity, not of density. Equation (iv) says that density does not change following a fluid parcel, \(D\rho/Dt = 0\), which is the condition for incompressible flow; the full advective form of continuity is \(D\rho/Dt + \rho\nabla \cdot \mathbf{v} = 0\).

Answer: D

A net outflow of air is called Divergence.

Where more air leaves a region than enters it, the air is diverging. At the surface this happens under high pressure, where sinking air spreads out; in the upper troposphere divergence above a low draws air up from below.

Convergence is the opposite, a net inflow of air. Advection is horizontal transport of a property such as heat or moisture by the wind, and convection is vertical transfer of heat by rising and sinking air, so neither names a net outflow.