New instability mode in a grooved channel

It is known that longitudinal grooves may stabilize or destabilize the travelling wave instability in a channel flow depending on the groove wavenumber. These waves reduce to the classical Tollmien–Schlichting waves in the absence of grooves. It is shown that another class of travelling wave instability exists if grooves with sufficiently high amplitude and proper wavelengths are used. It is demonstrated that the new instability mode is driven by the inviscid mechanism, with the disturbance motion having the form of a wave propagating in the streamwise direction with phase speed approximately four times larger than the Tollmien–Schlichting wave speed and with its streamwise wavelength being approximately twice the spanwise groove wavelength. The instability motion is concentrated mostly in the middle of the channel and has a planar character, i.e. the dominant velocity components are parallel to the walls. A significant reduction of the corresponding critical Reynolds number can be achieved by increasing the groove amplitude. Conditions that guarantee the flow stability in a grooved channel, i.e. the grooved surface behaves as a hydraulically smooth surface, have been identified.