PSI - Issue 40

Natalya V. Burmasheva et al. / Procedia Structural Integrity 40 (2022) 82–89 Natalya V. Burmasheva, Evgeniy Yu. Prosviryakov / Structural Integrity Procedia 00 (2019) 000 – 000

88

7

In this case, the presence of a zero point for the velocity component U can lead to the appearance of a zero point for the velocity V x , which is determined by the interaction of two components: the homogeneous component U and the inhomogeneous component uy . However, in certain sections (i.e. at certain values of the longitudinal coordinate y ) the linear (along the vertical coordinate Z ) term uy can prevail over the nonlinear term U (Fig. 3).

Fig. 3. The horizontal velocity V x profile.

Finally, let us analyze the stress field (Gershuni et al., 1976), the components of which are determined on the basis of Newton's law (Dytnersky et al., 1995; Kochin et al., 1964):

V

         



         

  

 

V

V

x V V         z x +  z





y

2

p − +





  

+

x

x

x

y x



 

V

V

V







     

  

  

  

V

V





y

y

y

2

p − +

=  

+

+





x

z

.

y x V V     

y

z  

y



V



 

  

V

V





y

2

p − +

+

+







x

z

z

z



z  

y

y z

z

 



 

Here, p is hydrostatic pressure. For the considered class (5) of exact solutions, all the three off-diagonal components will be nonzero,

y x y x       V V    

u  ,

= =   

+ =

xy

yx

( V V U u y z x   + = +  x z

         

)

,

= =   

xz

zx