Important aspects of the basic structure of a mature tropical cyclone can be deduced from two (2) simple equations that express an exact balance of forces in the vertical and radial directions. These equations enable one to develop a theory for the primary circulation. Let us assume steady flow (a/at = 0) and let us ignore the secondary circulation, i.e. we assume that the radial velocity is identically zero. This reduces to the gradient wind equation which could be obtained from the exact differential equation 2v +f dv- dr = 0 where f is the Coriolis parameter. Find the gradient wind equation when v and r are and r = f2 where p is the air density (another parameter). Rotation axis Low pressure contre Primary circulation Pressure gradient force Centrifugal force and Coriolis force Gradient wind balance A.........
Important aspects of the basic structure of a mature tropical cyclone can be deduced from two (2) simple equations that express an exact balance of forces in the vertical and radial directions. These equations enable one to develop a theory for the primary circulation. Let us assume steady flow (a/at = 0) and let us ignore the secondary circulation, i.e. we assume that the radial velocity is identically zero. This reduces to the gradient wind equation which could be obtained from the exact differential equation 2v +f dv- dr = 0 where f is the Coriolis parameter. Find the gradient wind equation when v and r are and r = f2 where p is the air density (another parameter). Rotation axis Low pressure contre Primary circulation Pressure gradient force Centrifugal force and Coriolis force Gradient wind balance A.........
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
EQUATIONS OF ORDER ONE – EXACT
complete solution.
Transcribed Image Text:Important aspects of the basic structure of a mature tropical cyclone can be deduced from two (2) simple
equations that express an exact balance of forces in the vertical and radial directions. These equations
enable one to develop a theory for the primary circulation. Let us assume steady flow (a/at = 0) and let
us ignore the secondary circulation, i.e. we assume that the radial velocity is identically zero. This
reduces to the gradient wind equation which could be obtained from the exact differential equation
2v
+f
dv-
dr = 0
where f is the Coriolis parameter. Find the gradient wind equation when v and r are
and
r =
f2
where p is the air density (another parameter).
Rotation axis
Low pressure
contre
Primary
circulation
Pressure
gradient
force
Centrifugal force
and
Coriolis force
Gradient wind balance
A.........
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