Fundamental Forces in the Atmosphere Questions and Answers

Answer: A

The pressure gradient force per unit mass is minus the gradient of pressure divided by density, so it points from high towards low pressure and is the only force that can set still air into motion. Coriolis acts only on air already moving and does no work on it, centrifugal appears only where the path is curved, and friction can only oppose existing motion. Because every other force in the horizontal equation either turns the flow or slows it, the pressure gradient is the origin of all atmospheric motion, and tracing a wind back to the heating that created its pressure field is the standard way of explaining any circulation.

Answer: B

Closely spaced isobars mean a large change of pressure over a short distance, and it is that spatial rate of change, not the pressure value itself, that produces the force. A uniform pressure of any magnitude produces no force at all. Temperature enters only through density in the denominator, and the local time tendency describes how the field is evolving rather than how hard it pushes. This is why forecasters read wind speed directly from isobar spacing on a surface chart, and why the same spacing implies a stronger wind aloft where the density is lower.

Answer: C

Coriolis is not a physical interaction between bodies but an artefact of describing motion in a rotating frame, and it vanishes entirely when the motion is described from an inertial frame in space. Pressure gradient, friction and gravitation are all real forces with identifiable sources. Calling Coriolis apparent does not make it negligible: on the scales of weather systems it is comparable with the pressure gradient force, and no useful description of large-scale flow can omit it. The centrifugal force shares the same apparent character for the same reason.

Answer: D

In the northern hemisphere the deflection is always ninety degrees to the right of the instantaneous velocity, and in the southern hemisphere always to the left. Because it acts perpendicular to the motion it changes direction without changing speed and does no work. The rule explains why northern hemisphere lows circulate anticlockwise: air drawn inward by the pressure gradient is turned right until it flows nearly along the isobars. Fixing the hemispheric sense firmly is essential, since almost every subsequent result in this subject depends on it.

Answer: A

The latitude enters through the vertical component of the Earth's rotation vector, so \( f \) vanishes at the equator and reaches its greatest magnitude at the poles. With \( \Omega \) about \( 7.29 \times 10^{-5} \) per second, \( f \) is roughly \( 10^{-4} \) per second in mid-latitudes, a value worth committing to memory because it appears in every scale estimate in this subject. Longitude does not enter, and the angle of the velocity is irrelevant since the deflection is always perpendicular to whatever direction the parcel moves.

Answer: B

Taking a latitude of about 45 degrees gives \( f = 2\Omega\sin 45^{\circ} \), close to \( 1 \times 10^{-4} \) per second. The Earth's own rotation rate is smaller by a factor of about 1.4, the acceleration due to gravity is a different quantity entirely, and the last value belongs to boundary layer drag. This single number underlies the Rossby number estimate, the geostrophic wind formula and the deformation radius, so carrying it in mind makes most order of magnitude arguments in this subject immediate.

Answer: C

Because \( f \) is proportional to the sine of the latitude, its horizontal effect disappears at the equator and is greatest at the poles. This is why tropical cyclones cannot form within a few degrees of the equator and why tropical dynamics is dominated by different balances from those of mid-latitudes. The stratosphere is no exception to the rule, and the direction of the wind relative to the isobars affects the balance rather than the force. Note that the full Coriolis force does not vanish at the equator, only the component acting horizontally.

Answer: D

A force at right angles to the displacement contributes nothing to the rate of working, so Coriolis changes the direction of a parcel but never its kinetic energy. This is why it cannot generate or destroy the energy of a circulation and why energy arguments in this subject concern the pressure gradient and buoyancy instead. The force is proportional to the first power of the speed, not the square, and it is defined by the instantaneous velocity rather than by the history of the parcel's journey.

Answer: A

In a frame following the curving parcel, an apparent centrifugal force of magnitude \( V^2/R \) acts outward along the radius of curvature, and it must be included whenever the flow is strongly curved, as in a tropical cyclone or a sharply curved jet. Coriolis and friction depend on the velocity itself rather than on the curvature, and the pressure gradient depends only on the mass field. The gradient wind balance is exactly the three-way balance obtained when this term is retained alongside the other two.

Answer: B

Gradient wind balance sets the pressure gradient force against the sum of Coriolis and centrifugal terms, and it is the appropriate approximation wherever the isobars are strongly curved. Geostrophic balance is its straight-flow limit, hydrostatic balance is vertical, and Ekman balance describes the frictional boundary layer. The practical consequence is that around a low the gradient wind is subgeostrophic while around a high it is supergeostrophic, which explains why intense lows are common but intense highs are not.