Dynamics I: Basic forces METR 2413 22 February 2004 Dynamics I: Basic forces

Review Synoptic meteorology “Synoptic” refers to the spatial and temporal scale of the systems Length scale is of the order of 1000 km (106 m) time scale is of the order of several days (105 s) Typical weather features at the synpotic scale are Surface cyclones and anticyclones Upper level troughs and ridges Fronts Hurricanes

Pressure gradient force A main concept of synoptic meteorology is the Pressure Gradient Force (PGF). The PGF can be defined as: the change in pressure measured across a given distance. In mathematical terms:

Pressure gradient force So Hence, the total pressure gradient is defined as the change in pressure measured in the “x” direction plus the change in pressure measured in the “y” direction plus the change in pressure measured in the “z” direction. But why do we call it a Force? Is it really a force? A closer look reveals that pressure is actually a “momentum flux” (recall from the kinetic theory of gases).

Pressure gradient force Force, F = m a Pressure, or So pressure is momentum (mv) per unit area per unit time, or momentum flux. Hence, the pressure gradient force is a force per unit mass, or an acceleration.

Pressure gradient force Now, let’s consider PGF in the atmosphere. Consider regions of high and low pressure. Air will tend to move in the direction of low pressure due to the PGF.

Pressure gradient force In the absence of any other “forces”, air tends to move away from regions of high pressure and toward regions of low pressure. However, if you look at a weather map, you never see wind blowing in this direction, (except maybe in the tropics). That’s because air parcels that are moving experience other “forces”.

Coriolis force The Coriolis force deflects moving objects to the right in the Northern Hemisphere (NH). Why? Because the earth is rotating, and we are on the that rotating reference frame. The Coriolis force arises because the earth is an acccelerating frame of reference. It can be defined as Fcor = v f = v 2Ω sinφ, where Coriolis parameter, f = 2Ω sinφ, with angular speed of the Earth’s rotation, Ω =2π/86,400s = 7.3×10-5 s-1 and latitude φ.

Coriolis force If we look at the scales for the Coriolis force, it has scales of velocity/time = acceleration = F/m So the Coriolis force is really a force per unit mass or an acceleration, just like the pressure gradient force. The Coriolis force is a function of velocity, so as the wind speed increases, the Coriolis force on air parcels also increases.

Coriolis force Initially an air parcel (A) responds to the PGF by moving toward low pressure. As it accelerates, the Coriolis force increases. Eventually, the PGF and the Coriolis force balance each other.

Coriolis force For typical synoptic scale winds, the flow is fairly steady, so the net force on an air parcel is zero. The Coriolis force (to the right of the velocity vector in the NH) balances the pressure gradient force (from high to low pressure).

Coriolis force In the NH, the Coriolis force ALWAYS acts to the right of the wind vector!!! Coriolis Force PGF Wind Vector Wind Vector Coriolis Force PGF

Geostrophic wind In the absence of any other “forces”, the Coriolis force balances the PGF and the flow is steady. This is called the Geostrophic Wind. On a weather map, say at 500 mb, the wind vectors are usually parallel to the contours, and the flow around a cyclone is anticlockwise in the NH.

Geostrophic wind What about in the Southern Hemisphere? In the SH, the sense of the Earth’s rotation is opposite to the NH and the Coriolis parameter, f, is negative. So, the Coriolis force is in the opposite direction in the SH and points to the left of the wind vector. Coriolis Force The geostrophic wind in the SH is still a balance between the PGF and the Coriolis force, but the flow around a cyclone is clockwise in the SH. High pressure Wind Vector PGF Low pressure

Frictional effects Near the earth’s surface, friction opposes motion, so the flow is not longer geostrophic. So what happens? PGF does not change Velocity decreases Coriolis force decreases The wind no longer behaves geostrophically, and there is “cross-contour” flow toward lower pressure The vector sum of the Coriolis force and friction balances the PGF 1000 hPa Wind Vector PGF 1004 hPa Friction Coriolis Force 1008 hPa

Summary PGF acts in the direction of low pressure Coriolis force due to the Earth’s rotation, Fcor = f v, acts to the right (left) of the wind vector in the NH (SH) For geostrophic flow, PGF balances the Coriolis force, the flow is parallel to the pressure contours, and the flow around a cyclone is anticlockwise in the NH (clockwise in the SH) For flow near the surface, where friction is important, geostrophic balance does not hold, and there is cross-isobar flow towards low pressure