Kelvin-Helmholtz Instability for Air-Water System

Example 5.6 Kelvin-Helmholtz Instability for Air-Water System 

Calculate the critical velocity and wavenumber for air at 1 atm and 25°C blowing over water. 

We have y= 72 mN/m, Pa = 1 g/cm, pg = pMIRT by the ideal gas law equals 0.00119 glcw . At marginal stability, the expression in brackets in Equation 5.139 vanishes. Inspection of Equation 5.139 shows that for a given value of V/ - Vgl, this condition occurs whenever the stabilizing quantity y a + (pa - 9 )glo. is minimized. Thus at marginal stability we have 

Hence = 3.69/cm (A, ,= 1.70 cm) when the instability first develops. The critical value of the velocity difference is given by 

The speed e of the traveling wave can be found from the first term of Equation 5.139  

---