A shear layer between two fluids. Assume the following velocity distribution between two shear layers:

\[v_{x}(y)=v_{0} \tanh (y / \delta)\]

This is known as the Betchov and Criminale form. Calculate the stability analysis using the Rayleigh equation for the following parameters: \(v_{0}=1\) and \(\delta=1\). Set \(\alpha=0.8\). Betchov and Criminale obtained \(c_{\mathrm{I}}=0.1345\) and \(c_{\mathrm{R}}=0\).