Waves and shear flows
The exact analytical solution of the extended Rayleigh equation for the case of periodic compressible shear flow is found. The dispersion relation of the problem is the Hill determinant. It is found that the sound waves in shear flow have a dispersion and its velocity field contains a solenoidal part. Besides the sound waves, new wave modes, namely phonon, waveguide and vortex wave modes, are revealed. The phonon mode is similar to phonons in the crystal lattice but they are not connected to heat transfer. The vortex mode is a singular solenoidal mode. The vortex modes are negative-energy waves and it is possible that they possess dissipative instability. The absolute phonon-vortex instability appears for a Mach number Ma ≳ 0.4. The interplay of waves and solar granulation is considered.
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