Internal shear layers in rotating fluids : asymptotic and numerical analyses
Internal shear layers in rotating fluids are fine viscous structures, associated with underlying inviscid singularities. We tried to build asymptotic descriptions of internal shear layers inside three-dimensional spherical shells and two-dimensional cylindrical annuli forced by time-harmonic viscous and inviscid forcings, in the small-Ekman-number limit.
The asymptotic solutions are compared to numerical results obtained by integrating the harmonic linearised equations for small Ekman numbers relevant to geophysical applications (such as 1e-11). Efficient spectral codes are thus developed based on the block Thomas algorithm typical to a block tridiagonal system.
The asymptotic solutions are based on the viscous self-similar solutions of Moore and Saffman function. Different singularities of the critical latitude and attractors lead to two similarity solutions, differing in singularity strength and amplitudes. They are applied to building asymptotic solutions of two wave patterns of
internal shear layers, namely periodic orbits and attractors.
It is found that the asymptotic solutions yield satisfactory results, some of which are excellent. More importantly, all the asymptotic predictions on the Ekman number scalings of the amplitudes are recovered in numerical results.
Contact Pierre Augier for more information or to schedule a discussion with the seminar speaker.