Lower bound for transient growth of inclined buoyancy layer

The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of energy stability is solved with the method of descending exponentials. The disturbance energy is found to be able to grow to 11.62 times as large as the initial disturbance energy for Pr = 0.72 when the Grashof number is between the critical Grashof numbers of the energy stability and the linear stability. We prove that, with a weighted energy method, the basic flow of the vertical buoyancy boundary layer is stable to finite-amplitude streamwise-independent disturbances.

Nonlinear saturation amplitude of cylindrical Rayleigh Taylor instability

The nonlinear saturation amplitude （NSA） of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface （r0） and the Atwood number （A） play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ（λ is the perturbation wavelength）, the larger the NSA of the fundamental mode. When ro/λ is large enough （r0 〉〉 λ）, the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

Viscous Rayleigh-Taylor instability with and without diffusion effect

The approximate but analytical solution of the viscous Rayleigh-Taylor insta- bility （RTI） has been widely used recently in theoretical and numerical investigations due to its clarity. In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate method. Its accuracy is verified numerically to be significantly improved in comparison with the previous one in the whole wave number range for different viscosity ratios and Atwood numbers. Fur- thermore, this solution is expanded for viscous RTI including the concentration-diffusion effect.

A dislocation-based model for cyclic plastic response of lath martensitic steels

Softening behavior of lath martensitic steels is related to the coarsening of laths and dislocation evolution during cyclic deformation.Involving the physical mechanism,we developed a dislocation-based model to study the cyclic plastic response for lath martensitic steels.For a block,we proposed an interfacial dislocation evolution model to physically present the interaction between mobile dislocations in the block and interfacial dislocations by considering the coarsening mechanism of the laths.Moreover,the evolution behavior of backstress caused by dislocation pile up at the block boundary has been considered.Then,a hierarchical model based on the elastic-viscoplastic self-consistent(EVPSC)theory is developed,which can realize the scale transition among representative volume element(RVE),prior austenite grains(PAGs)and blocks.According to the proposed model,the effective mechanical responses including the cyclic hysteretic loop and peak stress at different cycles for lath martensitic steel have been theoretically predicted and investigated.

A comparative study of cluster-based methods at finite strain

Virtual clustering analysis(VCA)is a reduced-order method for numerical homogenization.We formulate VCA for finite strain problems,illustrate its implementation,and provide numerical codes for free download and perusal.Comparison for four test examples shows that both VCA and Self-consistent clustering analysis(SCA)excellently approximate FFT-based direct numerical simulation(DNS)results,yet at much reduced numerical expenses.VCA is actually even faster in the online stage.