List of top Atmospheric and Ocean Science Questions

Acceleration due to Coriolis force of a water parcel at a location P (67°E, 20°N) moving with a speed of \(0.35~\mathrm{m/s}\) is ____________ \(\times 10^5~\mathrm{m/s^2}\). (Round off to two decimal places) 
[Assume the angular velocity of the Earth is \(7.3\times 10^{-5}~\mathrm{s^{-1}}\).]

Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid? 
[In the given equations, \(\rho\) is the density and \(\mathbf{V}\) the three-dimensional velocity vector of the fluid.] 
(i) \(\dfrac{\partial \rho}{\partial t} + \nabla \times (\rho \mathbf{V}) = 0\) 
(ii) \(\dfrac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{V}) = 0\) 
(iii) \(\dfrac{\partial \mathbf{v}}{\partial t} + \rho \, \nabla \cdot \mathbf{v} = 0\) 
(iv) \(\dfrac{\partial \rho}{\partial t} + \mathbf{v} \cdot \nabla \rho = 0\) 
 

In the figures given below, L and H indicate low and high pressure centers, respectively; PGF, CoF and CeF indicate Pressure Gradient Force, Coriolis Force and Centrifugal Force, respectively; \( V \) is Velocity. [The arrows indicate only the directions but not the magnitudes of the forces and velocity.]

Which of the following is/are the correct representation(s) of the directions of various forces and velocity in the gradient wind balance in the northern hemisphere?
 

Which of the following is the correct form of the mass divergence form of the continuity equation for a compressible fluid? [In the given equations, \( \rho \) is the density and \( \nabla \) the three-dimensional velocity vector of the fluid.] 
[(i)] $\displaystyle \frac{\partial \rho}{\partial t} + \nabla \times (\rho \mathbf{v}) = 0$
[(ii)] $\displaystyle \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0$ 
[(iii)] $\displaystyle \frac{\partial \mathbf{v}}{\partial t} + \rho \cdot \nabla \mathbf{v} = 0$ 
[(iv)] $\displaystyle \frac{\partial \rho}{\partial t} + \mathbf{v} \cdot \nabla \rho = 0$