Natural coordinate: Gradient wind in natural coordinate system In natural coordi
ID: 106255 • Letter: N
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Natural coordinate: Gradient wind in natural coordinate system In natural coordinate system, we can write the acceleration of the wind (dv/dt) as follows: dv/dt = dv t cap/dt = t cap dv/dt + V dt/dt (Eq.1), where V vector =v t cap and t cap is the unit vector parallel to the V vector with the horizontal wind speed can be written as V = ds/dt. With the aid of the figure below, we can get delta psi = |delta t cap|, implying change in the angle delta psi is equivalent to the magnitude of delta t cap. If delta s rightarrow 0, delta t cap is directed parallel to n vector and dt cap/ds = n cap/R. Then, dt cap/dt = dt cap/ds ds/dt = n cap/R V. Finally, d v vector/dt = t cap dv/dt + n v^2/R (Eq.2). What are the physical meaning of the first and the second terms in the equation 1 and 2: dv vector/dt = t cap dv/dt + V dt cap/dt = t cap dv/dt + n v^2/R? (Use 1 -2 sentences) The Corilois force is always normal to the direction of motion, we can write it simply - f k cap times V vector = - fV n cap. On the other hand, the pressure gradient force can be expressed as = nabla phi = -(t cap partial phi/partial s + n cap partial phi/partial n). Then the equation of motion parallel and normal to the direction of flow can be written as follows dv/dt = -partial phi/partial s V^2/R + fV = -partial phi/partial n Let's imagine a situation that the 1st equation. acceleration parallel to the flow, is zero and we only have the 2nd equation. This is called the gradient wind approximation. Let's find the solution for V. In the Northern hemisphere, please link the following four cases to the case in the above table.Explanation / Answer
a. The meaning of the equation is that the velocity change with respect to the time period is inversely proportional to each other.
b.The common formula for acceleration in units is m/s2. It is also denoted as velicity multiplied twice. When acceleration is parallel to the flow,the velocity will also change its direction parallel to te flow.
c.V<0,the root is negative and hence the flow is unanomalous.
V>0,for positive root again the root is anomalous as R is always lesser than zero and hence it will not attain a satble state.For negative root also the root is unanomalous.
d.a->for negative root when V<0
b->for positive root when V>0
c->for positive root when V>0
d->for negative root when V<0
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