Vertically bounded double diffusive convection in the fingering regime: comparing no-slip vs free-slip boundary conditions

TL;DR

This study compares no-slip and free-slip boundary conditions in vertically bounded double diffusive convection, revealing similar global scaling laws but different local dissipation behaviors, with implications for natural and laboratory fluid dynamics.

Contribution

It provides a detailed numerical comparison of boundary conditions in double diffusive convection, highlighting their effects on flow structures and dissipation rates.

Findings

Flow is dominated by fingers in both boundary conditions.

Scaling laws are similar, with free-slip having larger prefactors.

Local dissipation near free-slip boundaries can exceed no-slip cases.

Abstract

Vertically bounded fingering double diffusive convection (DDC) is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e. the no-slip condition which is inevitable in the lab-scale experimental research, and the free-slip condition which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of fingers and sheet structures near the free-slip boundaries. This counter intuitive result might be relevant for properly estimating and modelling the mixing and entrainment phenomena at free-surfaces and interfaces.