Formation of spikes and bubbles in the linear phase of Rayleigh-Taylor instability in elastic-plastic media

The generation of spikes and bubbles, a typical characteristic of the nonlinear regime in the Rayleigh-Taylor instability, is found to occur as well during the linear regime in an elastic-plastic solid medium caused, however, by a very different mechanism. This singular feature originates in the differential loads at different locations of the interface, which makes that the transition from the elastic to the plastic regime takes place at different times, thus producing an asymmetric growth of peaks and valleys that rapidly evolves in exponentially growing spikes, while bubbles can also grow exponentially at a lower rate.

Figure 1

Schematic of the perturbed interface between an elastic-plastic ($y<0$) medium and a massless ideal fluid ($y>0$).

Figure 2

Boundaries for stability (full line) and for the elastic-plastic transition (dotted line).

Figure 3

Interface profile at different times for ${\lambda }^{*}>1$.

Figure 4

Amplitude of the perturbation as a function of time for different locations on the interface for ${\lambda }^{*}>1$.

Figure 5

Interface profile at different times for ${\lambda }^{*}<1$.

Figure 6

Amplitude of the perturbation as a function of time for different locations on the interface for ${\lambda }^{*}<1$.