Presentation on theme: "physics. curtin. edu. au/teaching/units/2003/Avp201/"— Presentation transcript:
1http://www. physics. curtin. edu. au/teaching/units/2003/Avp201/ Lec03.ppt Using the Equation of Motion
2Objectives Revision of last weeks lecture Applying Equation of motion to derive wind models“Anomalous” wind flowsImpact of friction on air flowThermal wind
3RevisionLast week we obtained a complete equation of motion which incorporated both “real” and “apparent” forces.Stated that the total rate of change of velocity with time (acceleration) was due to a combination of Pressure Gradient Force, Gravity, Centrifugal Force, Coriolis Force and Friction.
4RevisionWe simplified matters further by combining Gravity and Centrifugal force into a single Gravity force.We also eliminated friction by assuming flow in a friction free environment, e.g. 3000ft above the Earth’s surface.
5RevisionBy resolving into the different components of a 3-dimensional system and using scale analysis we obtained the general equation of motion as below.
6Hydrostatic EquationThe final term of the equation can be further simplified to give us the following result;
7Hydrostatic EquationThis equation tells us that as gravity is a constant, then the rate of change of pressure with height is greater for cold dense air than for warm less dense air.We can say therefore that the rate of change of pressure with height is dependent on temperature.
8Use of Hydrostatic Equation Main use is in measurement of height above groundIf a ‘standard’ atmosphere is assumed whereby mean sea level temperature is 15°C and the lapse rate is 6.5°C/km, then a ‘standard’ distribution of pressure with height resultsThis ‘standard’ is used in pressure altimeters, which sense pressure but read out height.
9Wind EquationsThe horizontal components of Newton’s 2nd law are sometimes called the wind equations.For both N-S and E-W flow the only forces we need consider are the Pressure gradient force, the Coriolis force and Friction.We can neglect friction if we assume flow in a friction free environment, i.e. above 3000ft.
10Wind EquationsWe have also seen from our scale analysis that we have an acceleration which is an order of magnitude less than the forces which cause it.Therefore we can disregard these accelerations, and if we have no local curvature effects such as those found around lows and highs we can state the following.
11Geostrophic WindGeostrophic motion occurs when there is an exact balance between the HPGF and the Cof, and the air is moving under the the action of these two forces only.It impliesNo accelerationeg Straight, parallel isobarsNo other forceseg frictionNo vertical motioneg no pressure changes
12Geostrophic WindAs geostrophic conditions imply no acceleration or friction, we can set these terms to zero in the simplified equations of motion to get the Geostrophic wind equations
13Geostrophic WindWe can combine these results to give an equation for the geostrophic wind on a surface chart if we know the perpendicular distance n between isobars.The equation is as follows;
14An ExampleWhat is the Geostrophic wind speed for a pressure gradient of 2hPa/Km and density of 1.2kgm-3 at a latitude of 20° ? ( = x 10-5 ,2 = 1.45x10-4)
15The Nature of Vg Geostrophic wind acts Parallel to the Isobars If you have your back to the wind then Low Pressure is on your RIGHT1016hPaCoVgPGF1012hPa
17Upper level chartsIt can be shown that the geostrophic argument works for upper level charts as well as for surface charts.The equation for geostrophic wind at upper levels loses the density term and becomes;
18Gradient Wind VgrWind which results when the Centrifugal Force resulting from curved flow is exactly balanced by the Coriolis and Pressure Gradient ForcesCe= Co- PGF3 Cases of Vgr existAnti-clockwise flow (a High)Clockwise flow (A Low)Straight Flow (Vgr=Vg which is a special case)
19Gradient Wind Equations The equations for the gradient wind depend on whether the flow is cyclonic or anti-cyclonic, but it can be shown they are as follows;
20Gradient WindThere are some limiting factors to gradient flow around high pressure systems when we look at the equation closely.
21Gradient WindThis tells us that there is a limit to how fast the wind can move around an anti-cyclone, and that limit is twice the speed of the Geostrophic wind.There is no limit to the speed a cyclonic circulation can achieve.
23Gradient WindThis tells us that when the radius of curvature is small, then so must the rate of change of pressure with distance.In other words the isobars must get further apart the closer you get towards the centre of the anticyclone.There is no limit to the spacing of the isobars around the centre of cyclonic flow.
25Gradient WindThe previous slide shows us the balance of forces required to make Gradient flow occur.From our knowledge we can now say that gradient flow around a cyclone is sub-geostrophic, and that gradient flow around an anti-cyclone is super-geostrophic.
26CofPgfCefWind directionIn this situation, it is impossible to achieve balanced flow, as all the forces are acting in the same direction. Therefore it is impossible for clockwise flow to exist around a high in the Southern Hemisphere.
27Cyclostrophic FlowAs mentioned previously there are no restrictions to the strength of the pressure gradient around low pressure systems.This can lead to situations whereby if the radius of curvature is very small (such as found around tornadoes), then the centrifugal force and pressure gradient forces balance each other.This is Cyclostrophic flow.
28CefWind directionPgfCofIn order for balanced flow to occur, the Cef must balance the Cof and PGF. This can only happen with large amounts of Cef, eg small radius of curvature and large speeds. Therefore can only occur with small scale systems such as dust devils and tornadoes.
29FrictionSo far we have chosen to ignore the effects that friction has on air in motion, by looking at motion above 3000ft.However, we have to take it into account when looking at motion closer to the surface.
30Frictional Effects Wind veers as Coriolis is reduced Frictional effects reduce Wind speedCross Isobar flow towards Low Pressure RegionFlow outwards from High PressureFlow inwards to Low PressureAs friction reduces with height, wind flow will BACK with height
31Frictional Effects 1012 Vgr (3000ft) Sfc wind 1010 Friction at Surface is greatest and we get a reduction in speed, which in turn leads to a reduction in Cof. PGF becomes dominant and so wind blows towards LP.Vgr = W’ly SFC = NW’lyFrom Vgr to SFC, winds have veered.From SFC to Vgr, winds have backed.
32Effects of Friction Balanced Gradient flow HighLowVgrCePGFCof
33Effects of Friction Low Vf High CePGFCofVVfFFriction [F] reduces gradient Speed [V]Cof now reducedPGF becomes dominant force and so wind VEERS
34Effect of Friction Cross - Isobar Flow HLCoPGFWind speed reduced by friction and so Co decreases. PGF>Co
36Diurnal Variation of Wind Wind shows a marked diurnal variationPeak during daytime and lull overnightVariation more marked with existence of low level temperature inversion.During night inversion acts as “lid” and prevents energy transfer downwards and thus have (relatively) stronger winds above inversion.During day convective currents break inversion down allowing sfc winds to increase and transfer turbulence aloft to decrease upper winds.
38Terrain Induced Turbulence Varying terrain will cause changes in the depth of the turbulenceBe aware of changes in turbulence depth with changes in surface featuresi.e. Sea surfaces will have a lesser depth of turbulence than land surfaces
39Wind Shear The variation of wind between 2 points Vertical wind shear is the variation in the wind between 2 layersIn particular it is theWind at top of layer minus wind at bottom of layer
40Wind Shear 270/60 10000 FT Wind Shear 270/25 5000 FT = 270/35
41Thermal Wind This shear is given the name Thermal wind. Use of the Hydrostatic assumption and gradient wind equation can show us how the vertical shear will vary due to horizontal temperature gradients.
42ABWARMCOLDP = 1013 hPaEquatorPoleTwo columns of air, A and B exert the same pressure (1013hPa) at the surface
43ABWARMCOLDConstant Height AGLEquatorPoleHowever, because A is warmer and therefore less dense than B, the pressure at the constant height surface at A is greater than at B.(By using the hydrostatic assumption and remembering that pressure drops more rapidly in cold air than warm air)
44PgfABWARMCOLDConstant Height AGLEquatorPoleThis sets up a Pressure Gradient Force between A and B
45CoPgfABWARMCOLDConstant Height AGLEquatorPoleCoriolis force now acts on the moving air to deflect it to the left in the Southern Hemisphere to achieve balanced Geostrophic flow
46Resultant Wind A B WARM COLD Constant Height AGL Equator Pole This shows us that upper level westerlies are a direct result of horizontal temperature differences.We can now go one step further and show that we can determine the direction and strength of upper level winds if we know the direction and strength of the lower level wind and the direction and strength of the thermal wind.[Remember that upper-lower = thermal lower + thermal = upper]Giving us the upper level westerly which we observe as being the pre-dominant wind in the upper atmosphere