Here we make the following assumptions : — 



(1) Let H be the height of the friction layer in the atmosphere, and 

 U the wand velocity at that height. H and U are constant. 



(2) Let A be the Austausch coefficient of the air above the inversion 

 layer. A is constant. 



(3) Let H' be the height" of the inversion. H' increases through the 

 upward transfer of cooling effect from below, as the air moves over cold 

 water. Denote the wind velocity at H' b}'" u' . 



(4) . Let A' be the Austausch coefficient of the air in the inversion 

 layer. A' is constant. This means that the air proceeds over the area 

 where the water temperature of sea surface decreases rapidly leeward 

 so that the steepness of the inversion is kept constant, for A' depends 

 closely on lapse-rate. 



(5) The motion of the air in the friction layer is caused by the eddy 

 transfer of momentum from the steady current of the air above the 

 friction layer. 



(6) The air is in steady motion. 



(7) Frictional force at the sea surface is apiiQ'-^ , where p is density of 

 the air, zip wind velocity at the surface, and o- constant. For the ground 

 a will be nearly 0-004, but for the sea surface we shall take it as 0-0005 

 on account of its smoothness. 



Now we shall consider the variation of wind velocity with height, 

 when warm air has moved some distance over cold water and the inversion 

 is present. 



According to the assumptions wind velocity increases linearly with 

 height in each layer from surface to H' and from H' to H. 



Therefore the boundary condition at the sea surface is 



H' 



and at H' 



^ U — :Z<' ^ ^, w' — Ho 



H - H' H' 



From these equations we obtain 



,. - 1 + v/TTlMU „,,_ ,, _ _ /H' ■ , H - H' 



2M 



^ ^, /H' , H-H'\ 

 , where M. = ap i \- " i 



Va' a J 



and , , H' 



A' 



Now we shall calculate vertical distributions of wind velocity at two 

 points where, for example, H' = 400 m. and H' = 500 m. respectively. 



We take here H = 1,500 m., U = 10m./sec., A = 100 g./cm.sec'., 

 A' = lOg./cm.sec, and p = 0-0012 g./cm.^. Then it follows that 

 for H' = 400 m. 



Wq =4-31 m./sec, u' =8-77 m./sec, 

 and for H' = 500 m. 



Wo =4-07 m./sec, u' = 9 -04 m./sec. 



Therefore, we are now able to draw the vertical distribution of wind 

 velocity at these points in a diagram. 



76 



