The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

Abstract

Abstract

Vorticity generation and conservation on generalised interfaces in three-dimensional flows

“…Of particular interest is the viscous term (), often referred to as the ‘boundary vorticity flux’. This term describes the rate at which vorticity diffuses across , under the action of viscous forces, and is generally understood to indicate the rate of vorticity creation on solid boundaries (Lighthill 1963; Panton 1984; Wu & Wu 1993; Terrington, Hourigan & Thompson 2021), free surfaces (Rood 1994 b ; Lundgren & Koumoutsakos 1999; Peck & Sigurdson 1999) and fluid–fluid interfaces (Wu 1995; Brøns et al. 2014; Terrington et al.…”

“…There is no obvious physical argument to prefer either Lighthill's or Lyman's definition (Terrington et al. 2021), and we are free to take either definition. Lyman's definition is used in this article, as it offers several compelling advantages over the Lighthill–Panton definition (Terrington et al.…”

“…Lyman's definition is used in this article, as it offers several compelling advantages over the Lighthill–Panton definition (Terrington et al. 2021). This approach differs from previous formulations of interfacial and free-surface vorticity dynamics, which have used the Lighthill–Panton definition (Lugt & Ohring 1992; Rood 1994 a , b ; Wu 1995; Sarpkaya 1996; Peck & Sigurdson 1998, 1999; Lundgren & Koumoutsakos 1999).…”

“…The first benefit of Lyman's definition is that it allows Morton's (1984) inviscid description of vorticity generation to be directly applied to three-dimensional flows (Lyman 1990; Terrington et al. 2021). Under the Lighthill–Panton definition, an additional viscous contribution to the creation of vorticity must be included, which is difficult to accommodate under Morton's interpretation.…”

“…Lyman's definition also more clearly explains the mechanism that enforces the kinematic condition that vortex lines do not end inside the fluid (Terrington et al. 2021). In the reconnection of antiparallel vortex pairs, for example, the cutting of vortex filaments and the reconnection of broken vortex lines are described by the same term under Lyman's definition (Terrington et al.…”