Abstract
Shear flows are ubiquitous in astrophysical objects including planetary and stellar interiors, where their dynamics can have significant impact on thermo-chemical processes. Investigating the complex dynamics of shear flows requires numerical calculations that provide a long time evolution of the system. To achieve a sufficiently long lifetime in a local numerical model the system has to be forced externally. However, at present, there exist several different forcing methods to sustain large-scale shear flows in local models. In this paper we examine and compare various methods used in the literature in order to resolve their respective applicability and limitations. These techniques are compared during the exponential growth phase of a shear flow instability, such as the Kelvin-Helmholtz (KH) instability, and some are examined during the subsequent non-linear evolution. A linear stability analysis provides reference for the growth rate of the most unstable modes in the system and a detailed analysis of the energetics provides a comprehensive understanding of the energy exchange during the system's evolution. Finally, we discuss the pros and cons of each forcing method and their relation with natural mechanisms generating shear flows.
Highlights
The relative difficulty of observing most astrophysical shear regions, such as those in the Sun, in detail makes it imperative to use analytical and numerical techniques to shed light on the motions present there
Turbulent motions driven by a shear flow instability are subject to occur in a wide range of physical systems, where numerical calculations can provide a comprehensive insight to the physical processes
Direct numerical calculations in two- and threedimensional Cartesian domains are used to analyse different forcing methods, which were exploited in the past to maintain a background shear flow
Summary
The relative difficulty of observing most astrophysical shear regions, such as those in the Sun, in detail makes it imperative to use analytical and numerical techniques to shed light on the motions present there. A variety of classical studies of shear driven turbulence exploit a method where a decoupled background shear flow is present (for example used by Holt, Koseff & Ferziger 1992; Jacobitz, Sarkar & van Atta 1997; Barker et al 2012). This method requires a change of variables to incorporate a mean shear profile and does not allow for a back-reaction of the actual flow on the forcing.
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