[理学]大气静力学.pptVIP

Newtons Laws The fundamental law used to try and determine motion in the atmosphere is Newtons 2nd Law Force = Mass x Acceleration Meteorology is a science that likes the KISS principle, and to further simplify matters we shall consider only a unit mass. i.e. Force = Acceleration Frame of Reference If we were to consider absolute acceleration relative to “fixed” stars (i.e. a non-rotating Earth ) Then our equation would read something like this; “The rate of change of velocity with time is equal to the sum of the forces acting on the parcel” Frame of Reference For a non-rotating Earth, these forces are: Pressure gradient force (Pgf) Gravitational force (ga) and Friction force (F) Frame of Reference However, we don’t live on a non-rotating Earth, and we have to consider the additional forces which arise due to this rotation, and these are: Centrifugal Force (Ce) and Coriolis Force (Cof) Equation of Motion We now have a new equation which states that: i.e. The relative acceleration relative to the Earth is equal to the real forces (Pressure gradient, Gravity and Friction) plus the “apparent forces” Centrifugal force and Coriolis force A Useable form If we now consider the centrifugal force we can combine it with the gravitational force (ga) to produce a single gravitational force (g), since the centrifugal force depends only on position relative to the Earth. Hence, g = ga + Ce A Useable form We can now write our equation as: We now look at the equation in its component forms, since we are considering the atmosphere as a 3-Dimensional entity Conventions In Meteorology, the conventions for the components in the horizontal and vertical are; x = E-W flow y = N-S flow Z = Vertical motion Also, the conventions for velocity are u = velocity E-W v = velocity N-S w = Vertical velocity Pressure Gradient Force “Force acting on air by virtue of spatial variations of pressure” These changes in pressure (or Pressure Gradient) are given by; Pressure Gradient Force If we