Geostrophic and Gradient Wind Questions and Answers

Answer: A

Agreement indicates that neither curvature nor friction is contributing appreciably, which means straight flow in the free atmosphere. The strength of the gradient does not affect whether the approximation holds, temperature is irrelevant on a pressure surface, and proximity to the equator would make the agreement worse rather than better. Using the comparison as a diagnostic of the flow regime is a good habit when examining observations. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

Curvature changes the speed required for balance without introducing any cross-contour component, so a subgeostrophic wind flowing along the contours indicates cyclonic curvature. Friction, by contrast, produces both a speed reduction and a cross-isobaric component towards low pressure. Distinguishing the two signatures allows the cause of a discrepancy to be identified from the observation alone.

Answer: A

In the Ekman limit the two directions are the same.

Two Ekman layers act in turn (Northern Hemisphere). In the atmospheric boundary layer, friction slows the wind and the pressure gradient turns it, so in the Ekman limit the surface wind blows 45° to the left of the geostrophic wind above. In the ocean's surface Ekman layer, the wind stress drives a surface current 45° to the right of the surface wind.

The two 45° turns cancel, so the ocean surface current flows parallel to, and in the same direction as, the geostrophic wind. The options with a single 45° turn count only one of the two layers, and 'exactly opposite' has no basis.

Answer: C

This is the Thermal wind.

The thermal wind is the vertical shear of the geostrophic wind: the difference between the geostrophic winds at two levels. It arises because horizontal temperature gradients make the pressure gradient change with height, and it blows parallel to the mean isotherms with cold air to the left in the Northern Hemisphere.

The isallobaric wind is the ageostrophic part driven by pressure changing with time. The gradient wind adds curvature (centripetal) effects to the geostrophic balance, and the cyclostrophic wind is the balance of pressure gradient and centripetal force alone, as in tornadoes. None of these describes a change with height.

Answer: B

The key gives The speed remains constant for a geostrophic flow and changes for a cyclostrophic flow.

In geostrophic balance the pressure gradient force is balanced by the Coriolis force:

\[ V_{g} = \frac{1}{\rho f}\frac{\partial p}{\partial n} \]

Along a fixed latitude the Coriolis parameter \(f\) is the same, so for a given pressure gradient the speed does not depend on the position across the isobars. In cyclostrophic balance the pressure gradient is balanced by the centripetal acceleration of curved flow:

\[ \begin{aligned} \frac{V^{2}}{r} &= \frac{1}{\rho}\frac{\partial p}{\partial n} \\ \Rightarrow V &= \sqrt{\frac{r}{\rho}\frac{\partial p}{\partial n}} \end{aligned} \]

The speed depends on the radius \(r\), which changes as one moves across the circular isobars, so the speed changes. The other options reverse this or treat both balances alike.

Answer: A

The net Ekman transport is southward.

A westerly wind blows from the west towards the east. In the Northern Hemisphere the Coriolis effect deflects the depth-integrated Ekman transport 90 degrees to the right of the wind direction. Ninety degrees to the right of eastward is southward.

Northward transport would be the Southern Hemisphere result, where deflection is to the left. North-eastward and south-westward correspond to 45-degree deflections, which describe the surface current, not the net transport over the Ekman layer.

Answer: C

The correct matching is P - Y; Q - Z; R - X.

1. A balance of pressure gradient, centrifugal and Coriolis forces in curved flow is the gradient wind; anticlockwise rotation in the Northern Hemisphere is cyclonic, so P describes cyclones (Y).
2. A balance of pressure gradient and centrifugal force alone is cyclostrophic flow, found in small, intense vortices where the Coriolis force is negligible and either sense of rotation is possible: tornadoes (Q-Z).
3. A balance of pressure gradient and Coriolis force in straight, uniform flow is geostrophic flow (R-X).

The other options assign geostrophic flow to curved or cyclostrophic balances, or tornadoes to the gradient balance, which mismatch the forces involved.

Answer: D

The system is in cyclostrophic balance.

Compare the centrifugal and Coriolis terms through the Rossby number, using the radius R = 0.5 km:

\[ Ro = \frac{V}{fR} = \frac{100}{10^{-4} \times 500} = 2000 \]

The centrifugal acceleration \(V^{2}/R\) is two thousand times the Coriolis acceleration \(fV\), so the Coriolis force is negligible and the pressure gradient force is balanced by the centrifugal force alone. That is cyclostrophic balance, typical of tornadoes and dust devils.

Geostrophic balance needs \(Ro \ll 1\), and gradient wind balance matters when both terms are comparable. A cyclostrophic vortex always has low pressure at its centre, since the pressure gradient must point inward, so it cannot be a high-pressure system.

Answer: B

In cyclostrophic motion the pressure gradient and centrifugal forces balance.

Cyclostrophic balance applies to small, intense vortices such as tornadoes and dust devils, and to flow near the equator, where the Rossby number is large: the Coriolis force is negligible compared with the centrifugal force of the tight, fast rotation. The inward pressure gradient force is balanced by the outward centrifugal force alone.

Including all three forces describes gradient wind balance; pressure gradient against Coriolis is geostrophic balance; and centrifugal against Coriolis without a pressure gradient describes inertial motion.

Answer: B

Widely spaced isobars indicate a weak pressure gradient and light winds.

Isobars join places of equal pressure. When they are far apart, pressure changes little over distance, so the pressure gradient force is weak and the wind it drives is light. Closely packed isobars mean a steep gradient and strong winds, as around a cyclone.

Options A and C pair wide spacing with a steep gradient, which reverses the relationship, and option D pairs a weak gradient with strong winds, which contradicts the gradient being what drives the wind.