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The finite-thickness effect of two superimposed fluids on harmonics in the Richtmyer-Meshkov instability (RMI) for arbitrary Atwood numbers is investigated by using weakly nonlinear analysis up to the third order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitudes of the first three harmonics compared with those in classical RMI. On the one hand, the thickness effect encourages or reduces the amplitudes of the first three harmonics, and on the other hand, it changes the phases of the second and the third harmonics.The finite-thickness effect of two superimposed fluids on harmonics in the Richtmyer-Meshkov instability (RMI) for arbitrary Atwood numbers is investigated by using weakly nonlinear analysis up to the third order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitudes of the first three harmonics compared with those in classical RMI. On the one hand, the thickness effect encourages or reduces the amplitudes of the first three harmonics, and on the other hand, it changes the phases of the second and the third harmonics.

Theoretical study on finite-thickness effect on harmonics in Richtmyer-Meshkov instability for arbitrary Atwood numbers