Buckling of Turbulent Jets.

The stability of round turbulent jets is examined for two different cases. The first case concerns the static buckling of a downward-flowing jet confined by a flexible duct. The equilibrium shape of the duct is found to be approximately sinusoidal with a wavelength which is inversely proportional to both flow velocity and distance from the fixed end of the duct. The amplitude of the buckled shape is found to be governed by the magnitude of the shear stress caused by slight deflection of the fluid stream as it leaves the free end of the duct. Experimental measurements confirm the buckling wavelength predicted analytically. The second case considered in the present study is that of a free jet surrounded by an annular shear layer. The mean jet velocity profile is assumed to be a curvilinear trapezoid which approximates the mean profile in the developing region of round turbulent jets. The radial dependence of the amplitudes of growing disturbances are examined in order to illustrate the extent to which the disturbance penetrates into the jet. It is shown that at constant shear layer thickness, the radial penetration depth of each disturbance is directly proportional to the wavelength of the disturbance. It is also shown that the radial penetration depth of disturbances with constant relative rates of amplification is directly proportional to the thickness of the shear layer. These results are used to explain the radial variation of the Strouhal number of the most amplified mode. In addition, it is found that amplified disturbance waves exhibit a phase lag across the shear layer; it is suggested that this phase lag may be responsible for the spade-like structures evident in flow visualizations of turbulent jets. Finally, it is shown that the influence of the velocity of the fluid surrounding the jet upon stability characteristics can be accounted for by multiplying the group and phase velocities of the disturbance waves by the appropriate contraction factor.