Chapter 9

Question 1

Inertial waves

Answer 1

are a type of mechanical wave possible in rotating fluids.

Question 2

Inertial waves are a type of mechanical wave possible in rotating fluids. Unlike surface gravity waves commonly seen at the beach, inertial waves flow

Answer 2

through the interior of the fluid, not at the surface.

Question 3

. Like any other kind of wave, an inertial wave is caused by

Answer 3

a restoring force and characterized by its wavelength and frequency.

Question 4

. Like any other kind of wave, an inertial wave is caused by a restoring force and characterized by its wavelength and frequency. The restoring force for inertial waves is the

Answer 4

the Coriolis force. Inertial waves are transverse.

Question 5

Inertial waves are restored to equilibrium by the Coriolis force. To be precise, the Coriolis force

Answer 5

arises (along with the centrifugal force) in a rotating frame.

Question 6

Inertial waves, therefore, cannot exist without

Answer 6

rotation

Question 7

Inertial waves are possible only when

Answer 7

a fluid is rotating, and exist in the bulk of the fluid, not at its surface.

inertial waves are transverse, which means that their vibrations occur perpendicular to the direction of wave travel.

Question 8

One peculiar geometrical characteristic of inertial waves is that their phase velocity, which describes the movement of the crests and troughs of the wave, is

Answer 8

perpendicular to their group velocity, which is a measure of the propagation of energy.

Question 9

Whereas a sound wave or an electromagnetic wave of any frequency is

Answer 9

possible

Question 10

Whereas a sound wave or an electromagnetic wave of any frequency is possible, inertial waves can exist only over

Answer 10

the range of frequencies from zero to twice the rotation rate of the fluid.

Question 11

Whereas a sound wave or an electromagnetic wave of any frequency is possible, inertial waves can exist only over the range of frequencies from zero to twice the rotation rate of the fluid. Moreover, the frequency of the wave is determined by

Answer 11

its direction of travel.

Question 12

Waves traveling perpendicular to the axis of rotation have

Answer 12

zero frequency and are sometimes called the geostrophic modes.

Question 13

Waves traveling perpendicular to the axis of rotation have zero frequency and are sometimes called the geostrophic modes. Waves traveling parallel to the axis have

Answer 13

maximum frequency (twice the rotation rate), and waves at intermediate angles have intermediate frequencies.

Question 14

Inertial waves are observed most commonly

Answer 14

in planetary atmospheres (Rossby waves, geostrophic winds) and in oceans and lakes (geostrophic currents), where they are responsible for much of the mixing that takes place

Question 15

Inertial-gravity waves occur when the flow is

Answer 15

statically stable

Question 16

Inertial-gravity waves occur when the flow is statically stable. They are essentially

Answer 16

gravity waves that have a large enough wavelength to be affected by the earth’s rotation.

Question 17

for inertial-gravity waves the group velocity and phase velocity are

Answer 17

orthogonal

Question 18

Thus, for inertial-gravity waves the group velocity and phase velocity are orthogonal, and upward propagating waves transport energy

Answer 18

downward

Question 19

The parcel trajectories for inertial-gravity waves are

Answer 19

ellipses

Question 20

K•V = 0.

This means that the

Answer 20

velocity is always perpendicular to the wave number vector; i.e., there is no component of particle motion along the direction of the phase propagation. Therefore, the ellipses are always at 90° to the direction of phase propagation.

Question 21

The particles move along these ellipses in an ……………….. fashion (in the Northern Hemisphere), regardless makes sense, since the Coriolis force must be directed toward the ………….

Answer 21

anticyclonic

the inside of the ellipse