--- Introduction to Geophysical Fluid Dynamics

1. --- Introduction to Geophysical Fluid Dynamics Ch. 6 Fundamentals of Atmospheric/Ocean Modeling

4. Variables and Units Independent Variables Values are independent of each other x increases eastward y increases northward z increases upward t time Later we can use other coordinate systems p decreases upward latitude, longitude

5. Variables and Units Dependent Variables Values depend on other variables wind speeds u > 0 for eastward motion v > 0 for northward motion w > 0 for upward motion Temperature T = T(x,y,z,t) Pressure p = p(x,y,z,t) Density  = (x,y,z,t)

6. SI prefixes -- Factor Name  Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da   Factor Name  Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p  SI base units Base quantity Name Symbol length meter m mass kilogram    kg time second s temperature       kelvin K Part II - The International Unit System (SI) So, for Length… 1000 m = 1 km 1m = 1000 mm And so forth. Much simpler!

7. As of 2005, only three countries hang on to the messy Imperial Units, Myanmar, Liberia, and the United States.

8. Part II - The International Unit System (SI) SI prefixes -- Factor Name  Symbol 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da   Factor Name  Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p  SI base units Base quantity Name Symbol length meter m mass kilogram    kg time second s temperature       kelvin K SI derived units Derived quantity Name Symbol area square meter m2 volume cubic meter m3 speed, velocity meter per second m/s acceleration meter per second squared   m/s2 mass density kilogram per cubic meter kg/m3 specific volume cubic meter per kilogram m3/kg

9. In meteorology/ocean, we almost always use SI units, journals require it. Force - Newtons (kg m/s) Pressure - We still use millibars (mb) 1 mb = 100 Pa = 1 hPa (PASCALS N/m2) (hpa: hecto-pascal) Pressure = force / unit area; Must use correct (SI) units in calculations Temperatures - Always use Kelvin in calculations T(K) = T( C ) +273

10. Dimensions and Units All physical quantities can be expressed in terms of basic dimensions Mass M (Kg) Length L (m) Time T (s) Temperature K (K) Velocity = Distance / Time, so it has dimensions L/T, or m/s Acceleration = Velocity / Time, so it has dimensions L/T2, or m/s2 Force = Mass x Acceleration, so it has dimensions M LT-2, or Kg m/s2 Pressure, density

25. Pressure GradientForce(PGF) • pressure gradient: high pressure  low pressure • pressure differences exits due to unequal heating of Earth’s surface • spacing between isobars indicates intensity of gradient • flow is perpendicular to isobars Figure 6.7

26. Pressure Gradient Force (PGF) Figure 6.8a

41. Coriolis effect seen on a rotating platform, as 1 person throws a ball to another person.

42. Coriolis Force • Due to the rotation of the Earth • Objects appear to be deflected to the right (following the motion) in the Northern Hemisphere • Speed is unaffected, only direction Fig. 6-9, p. 165

43. The Coriolis Effect • -The Coriolis force causes the wind to deflect to the right of its intended path in the Northern Hemisphere and to the left of its intended path in the Southern Hemisphere. It acts at a right angle to the wind. • - The Coriolis force is largest at the pole and zero at the equator • - The stronger the wind speed, the greater the deflection • - The Coriolis force changes only wind direction, not wind speed. • - We measure motion on the rotating Earth. Thus, we need to be concerned with the Coriolis force