Atmospheric Forces, Balances and Weather Systems. Nili Harnik DEES, Lamont-Doherty Earth Observatory

Transcription

1 Atmospheric Forces, Balances and Weather Systems Nili Harnik DEES, Lamont-Doherty Earth Observatory

2 Newtons second law of motion The relationship between forces and motion: F = m a F- force, m- mass, a- acceleration If a net force different than zero is acting on a body (an air parcel in our case), it will accelerate at a rate proportional to the net force.

3 Mass Balance / Continuity Another important principle that controls air flow: In a continuous fluid (with no walls or partitions) one can not empty out a region from its mass - when fluid is taken out from one place, surrounding fluid rushes in to take up that space. Convergence and divergence of the flow at any level of the atmosphere and ocean will result in, among other things, vertical motion.

4 Horizontal Forces: Sea Breeze

5 Horizontal Forces: Sea Breeze Land warms (or cools) faster than ocean. Warm air expands. This results in different vertical pressure and density profiles over land and over ocean, leading to horizontal pressure gradients. The gradients are opposite at the ground and aloft, with air blowing from cool to warm near the surface. The direction reverses between day and night.

6 Horizontal Forces: Sea Breeze

7 Horizontal Forces: Sea Breeze The motion of the sea breeze is governed by two physical laws: 1. Newton's 2nd law of motion: F = m a = F_pressure + F_friction Responsible for the horizontal flow from cold to warm at the surface and from warm to cold aloft. 2. The law of the mass continuity: No empty spaces are tolerated in a fluid. This completes the cycle by creating the vertical motion of the air, up in the warm side of the coast, and down in the cold side.

8 Sea Breeze /Monsoon Seasonal cycle of heating produces the monsoon winds akin to the daily occurring sea-breeze.

9 Dynamic Meteorology The study of atmospheric motion is referred to as Dynamic Meteorology. To handle the physics of motion we need to consider a coordinate system, or a frame of reference. That is because forces and velocities are vectors so both magnitude and direction are important. In meteorology we define an x, y, z coordinate system which has an origin somewhere on the Earth's surface (say at the equator and the Greenwich meridian), and we measure the three directions in the following way: x: is the zonal (East-West) direction; positive eastward y: is the meridional (North-South) direction; positive northward z: is the vertical (up-down) direction; positive upward. u: is the velocity in the zonal direction; positive eastward v: is the velocity in the meridional direction; positive northward w: is the velocity in the vertical direction; positive upward.

10 The pressure gradient force Pressure, is the force per unit area exerted by the air molecules on any imaginary surface within the atmosphere. Consider an air parcel suspended in the atmosphere in hydrostatic balance. If pressure on one side of parcel exceeds that on other side, the parcel will experience a net force from high toward low pressure. The force per unit mass acting on the parcel (in Newtons/kg) is given by: F px = - ( p / x) / ρ F py = - ( p / y) / ρ p+ p x direction of motion p

11 The pressure gradient force F px = - ( p / x) / ρ

12 The pressure gradient force F px = - ( p / x) / ρ

13 The pressure gradient force Thus to the weather forecaster or an observer of motion on Earth, the horizontal distribution of pressure is extremely important. Pressure is routinely measured and plotted on maps and isobars (contours of constant pressure) are drawn.

14 Isobars strong gradient strong gradient weak gradient

15 Friction The physical laws governing atmospheric friction are too complex to be explained here. However, one very simple way of describing the friction in a layer close to the ground is to express it as a force proportional to the velocity of the air and acting to reduce it down. Thus the frictional force per unit mass is: F fx = - α u F fy = - α v Where u and v are the zonal and meridional wind (in units of m/sec), and α is a constant equal to about 2 x10-5 1/sec.

16 Friction Combining the forces we find that when an air parcel is subjected to the forces of pressure gradient and friction the equation describing the motion (per unit mass) can be written as: a x = F px + F fx = - ( p / x) / ρ - α u a y = F py + F fy = - ( p / y) / ρ - α v Here a x and a y are the acceleration of a unit mass in the west-to-east and south-to-north directions. If a balance is achieved between friction and pressure, the left hand terms in these equations are replaced by 0.

17 Apparent (inertial) forces To study of body movement under force we use a frame of reference. A frame of reference is called inertial if it is at rest or if it moves with constant velocity (that is, constant speed and direction). If the reference frame is moving under acceleration it is non-inertial. Examples for non inertial frames of references are an accelerating car, a rotating platform (even if the angular velocity is constant), and our planet Earth. All non-inertial systems are under the influence of a force either acting linearly or by exerting a torque on the system to cause rotation. If we want to use such system as a reference we need to introduce a fictitious reaction to balance that force into our considerations. This reaction is called an apparent force. A relatively simple example of an apparent force is the centrifugal force. Another such force, which may be new to many, is the Coriolis force, named after the French engineer, mathematician, and physicist G. de Coriolis ( ). It is of utmost importance in meteorology and oceanography.

18 Coriolis Effect on a Merry-Go-Round

19 The Coriolis Force This force "results from" the fact that we view the movement of air masses on Earth from a point of reference attached to its surface. The Earth is a rotating sphere. As the entire sphere spins around its axis, from west to east, every point on its surface moves in circular motion around the radius connecting it to the Earth's center. This circular motion is largest at the poles where the Earth's angular velocity is equal to one rotation around the Earth's axis in a day or: Ω = 2π /84600 = 7.27 x 10-5 rad/sec

20 R d Ω Ω Φ For Earth: Ω = 2π /84600 = 7.27 x 10-5 rad/sec Ω The Coriolis Force on Earth ΩsinΦ How does the situation on Earth resemble the rotating disk? The planet rotates around its axis with an angular velocity Ω pointing to the north. At the North and South Poles Ω is vertical to the surface and anywhere else it is slanted to the surface. The local angular velocity component vertical to the surface is ΩsinΦ. It describes the rotation of the local surface around the radius connecting it to the center of the Earth, just like the disk, with an angular velocity that decreases from the North Pole (Ω) to the equator (0) and then reversing sign in the Southern Hemisphere and continuing to decrease to the South Pole (-Ω).

21 Coriolis force The Coriolis Force On Earth

22 The Coriolis Force Coriolis force per unit mass of air is expressed as follows: F cx = + 2 Ω v sin φ = + f v F cy = - 2 Ω u sin φ = - f u f = 2 Ω sin φ is known in meteorology and oceanography as the Coriolis parameter. Note that this force is only important on large spatial scales and time intervals (distances on the order of hundreds to thousand of kilometers and times of at least close to the Earth's rotation period). Note also that the x-component of the Coriolis force depends on the y-component of the velocity, and vice versa. It thus acts perpendicular to the direction of motion.

23 The Coriolis Force Coriolis force F cx = + 2 Ω v sin φ = + f v

24 Geostrophic balance The balance between the pressure gradient force and the Coriolis force is the most important balance in dynamics of the climate system. Expressed in mathematical terms it is written as follows: 2 Ω sin φ v = f v = ( p / x) / ρ 2 Ω sin φ u = f u = - ( p / y) / ρ The geostrophic balance gives us the means to calculate wind speed and direction given the pressure gradient. It also tells us that in the large scale atmospheric motion of the Northern Hemisphere, the air flows along the isobars so that the low pressure is to the left of an observer standing with his face in the direction of the wind.

25 Geostrophic balance Geostrophic Balance: f u = - ( p / y) / ρ Pressure Gradient Force (PGF) = Coriolis Force (CF)

26 Geostrophic flow and friction At the surface, friction must be considered in the balance of forces acting on an air parcel. In general the surface flow wind arrows are not perpendicular nor are they parallel to the isobars. To understand why that is so, remember two facts: 1. Friction slows down the flow speed, and 2. Coriolis force depends on the flow speed. This means that a new balance is achieved in which friction and Coriolis forces together counter the pressure gradient force. The effect is known as the Ekman balance (after the German hydrodynamicist V. W. Ekman).

27 Geostrophic flow and friction This means that a new balance is achieved in which friction and Coriolis forces together counter the pressure gradient force.

28 Geostrophic flow and friction That is why low pressure systems generally bring stormy weather, while high pressure systems bring sun.

29 Midlatitude weather systems /Fronts. In the middle latitudes the flow is broken into sequences of low and high pressure cells moving from west to east. As we discussed above, these lows and highs affect the local vertical motion through convergence and divergence induced by surface friction. They also sweep air masses of different temperature from north and south bringing alternations in temperature to the regions they pass by in their eastward procession. The moving air masses collide and at their boundaries fronts are created in the low pressure centers. A passage of a front indicates an imminent change of temperature and also a change in weather. There are two kinds of fronts: Warm fronts and cold fronts.

30 Midlatitude weather systems /Fronts. Warm fronts and cold fronts.

31 Midlatitude weather systems /Fronts. Midlatitude weather systems "storms" transport heat poleward and upward and are thus contribute to the large scale equator to pole heat transport.

32 Tropical cyclones (or hurricanes or typhoons) Tropical cyclone, also called hurricane and typhoon, is the names given to an intense low pressure region that forms and migrates in the tropical ocean regions and is associated with intense winds and a very strong convection activity which brings thunderstorms and large amounts of rainfall

33 Tropical cyclones (or hurricanes or typhoons)

34 Hurricane Vertical Cross Section The massive disturbances that sometimes grow in a time frame of a week or so, need specific and favorable conditions to occur, such as high sea surface temperatures (at lease 26 C) and weak vertical wind shears. Once they do, they spreads over a radius of a few hundred kilometers. Hurricanes are surrounded by rings of towering thunder clouds spiraling up to a small circle at the center of the storm, with a radius of km. Here the winds can reach a speed of 100 km/hour and more and the most intense rainfall occurs. Inside this ring lies the eye of the storm, where the air is still and the convection is suppressed by slow downward motion (subsidence).

35 Regions of Hurricane Activity Hurricanes are active in the "trade wind" belts - the regions just north or south of the equator where the winds blow quite steadily from east to west (easterlies). Here tropical disturbances generally form, initiated by weak pressure perturbations that exist all the time in the tropics. They move west with the trade winds in a steady, relatively slow motion (10-20 km/hour). During this phase they intensify mainly through the release of latent heat in the surrounding clouds and a small percentage reach full hurricane intensity. Hurricanes tracks curve eastward and they speed up north of ~30 N