Tham khảo tài liệu 'kundu fluid mechanics 2 episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 244 tiruvity Itưivn We shall see in the next section that it has the significance of being the frequency of oscillation if a fluid particle is vertically displaced. After substitution of Eq. the equations of motion - become du 1 dp dt Pữ dx dv _ 1 dp dt Po dy dw 1 dp1 p g dt Pữ dz Po 9p -7- w 0 flr g du dv dw n In deriving this set we have also used Eq. and replaced the density equation by its linearized form . Comparing the sets - and - we see that the equations satisfied by the perturbation density and pressure are identical to those satisfied by the total p and p. In deriving the equations for a stratified fluid we have assumed that p is a function of temperature T and concentration 5 of a constituent but not of pressure. At first this docs not seem to be a good assumption. The compressibility effects in the atmosphere are certainly not negligible even in the ocean the density changes due to the huge changes in the background pressure are as much as 4 which is 10 times the density changes due to the variations of the salinity and temperature. The effects of compressibility however can be handled within the Boussinesq approximation i f we regard p in the definition of N as the background potential density that is the density distribution from which the adiabatic changes of density due to the changes of pressure have been subtracted out. The concept of potential density is explained in Chapter 1. Oceanographers account for compressibility effects by converting all their density measurements to the standard atmospheric pressure thus when they report variations in density what they call sigma tee they arc generally reporting variations due only to changes in temperature and salinity. A useful equation for stratified flows is the one involving only w. The u and V can be eliminated by taking the time derivative of the continuity equation and using the horizontal momentum .
