Question

Consider a discrete fluid-solid mechanical system (for instance a wing profile with two degrees of freedom). Solutions of the form V

⃗ 

e

λt

 are looked for, V

⃗ 

 being a two components vector. On the figure below the real and imaginary parts of λ

 are plotted as function of the Cauchy number. Give an estimate of the critical value of the Cauchy number at which an instability occurs.

Answer 1

figure is missing in this and we can not solve this without figure

i am giving approach related to this question.

Cauchy number is dimensionless number in continuum mechanics. It is represented by

$C_a=\frac{\rho u^2}{K}$

where,$\rho=$ density of fluid, u=local velocity,K= bulk modulus