An axisymmetric cyclonic vortex is in cyclostrophic balance (f = 0) with a tan- gential velocity profile given by V Vo(r/ro)", where Vo is the tangential velocity component at a distance ro from the vortex center. = (a) Compute the circulation and vorticity about a streamline at radius r. What is special about the cases n = 1 and n = -1? Sketch V(r) for both cases. (b) Using cyclostrophic balance and assuming that density p is constant, show that the pressure at radius r is given by P - Po = —— (V²_V²), Р 2n where Po is the pressure at radius ro. HINTS: The radial pressure gradient force is p-¹0p/ar, and the vertical vorticity in cylindrical polar coordinates is given by ¢ = V/ar + V/r when there is no radial velocity component. [~ Holton 4.11]
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![An axisymmetric cyclonic vortex is in cyclostrophic balance (f = 0) with a tan-
gential velocity profile given by V = Vo(r/ro)", where Vo is the tangential velocity
component at a distance ro from the vortex center.
(a) Compute the circulation and vorticity about a streamline at radius r. What is
special about the cases n = 1 and n = -1? Sketch V(r) for both cases.
(b) Using cyclostrophic balance and assuming that density p is constant, show that
the pressure at radius r is given by
р
P - Po = (V² - V²),
2n
where Po is the pressure at radius ro.
HINTS: The radial pressure gradient force is p-¹0p/ar, and the vertical vorticity in
cylindrical polar coordinates is given by av/ar + V/r when there is no radial
velocity component. [~ Holton 4.11]
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