Abstract
Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.
Highlights
The nonlinear advection term in the Navier–Stokes equations controls the stretching of vortex lines in turbulence, which is thought to be the basic mechanism of energy 930 R2-1K.P
How does the vortex stretching mechanism, which depends on the nonlinear character of the Navier–Stokes dynamics, change with decreasing viscosity or increasing Reynolds numbers? An exposition of these issues is the thrust of this paper
Using a direct numerical simulation (DNS) database of isotropic turbulence that spans more than two orders of magnitude in box size, we study regions with depleted nonlinearity for their energy cascade characteristics
Summary
The nonlinear advection term in the Navier–Stokes equations controls the stretching of vortex lines in turbulence, which is thought to be the basic mechanism of energy. It has been widely reported that local depletion of nonlinearity occurs in developed turbulence (Pelz et al 1985; Kit et al 1987; Kraichnan & Panda 1988; Shtilman & Polifke 1989; Shtilman 1992; Tsinober, Ortenberg & Shtilman 1999; Bos & Rubinstein 2013) Based on this notion, it has been conjectured that turbulent flows spend a large proportion of time in neighbourhoods of Euler solutions, which are without dissipation and are weakly Beltrami in nature, i.e. velocity u and vorticity ω (≡ ∇ × u) are aligned with each other (Levich 1987; Moffatt & Tsinober 1992; Moffatt 2014). Our main findings are as follows: (i) we confirm previous low-Reynolds-number results that dissipation fluctuations are not influenced by local ‘Beltramization’ of the flow.
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