Nonmodal nonlinear route of transition to two-dimensional turbulence

Abstract

Turbulence has remained an unsolved problem in physics, despite the availability of some numerical results. The onset and growth of disturbances leading to two-and three-dimensional turbulence have been theoretically and computationally shown for wall excitation with the response having modal and nonmodal components in the spectrum. The nonmodal component is seen to be dominant. Here, we conclusively show the nonmodal growth for a transition to turbulence, with the same equilibrium flow excited from the free stream with results from linearized and nonlinear two-dimensional Navier-Stokes equations. We establish that transition to turbulence definitely requires nonlinearity, even if the onset process is similar to a linear mechanism. Thus, the transition to turbulence in wall-bounded flows is due to a nonmodal nonlinear mechanism for any disturbance.

Direct numerical simulations of three-dimensional surface instability patterns in thin film-compliant substrate structures

“…Furthermore, instability in solid structures under compression is frequently referred to as the onset of buckling, as opposed to its definition in fluid mechanics as the onset of development of turbulence. Nevertheless, apparent similarities exist and one may draw analogies between the present surface instability analysis in solid materials and the studies of receptivity 39 or non-modal disturbance growth 40 in fluid mechanics.…”

On the stability of a pair of vortex rings

“…Furthermore, integrating these growth rates in time fully characterizes the modal content of the perturbation spectrum, on top of which additional instabilities and nonlinearities develop and cause the flow to transition to a turbulent state. Future studies may therefore examine these nonlinear dynamics in the context of the present CI-modulated flow and utilize non-modal analysis to determine what similarities, if any, exist between transition in more thoroughly studied wall-bounded flows (Schmid 2007; Sengupta, Sundaram & Sengupta 2020) and vortex core interactions.…”

Optimizing control of stationary cross-flow vortices excited by surface roughness

“…Stationary cross-flow disturbances are excited by setting the boundary condition (11) for u e = (u e , v e , w w ) as…”

“…( 9). Alternatively, the amplitude A of the linear perturbation q can be computed by coupling (8) with the Lagrange identity (16) and boundary conditions (11). On integrating over the wall-normal direction y ∈ [0, ∞) and the streamwise interval x ∈ [x 1 , x 2 ], the following formula for the amplitude A of the linear disturbance is derived…”

“…Nonmodal stability theory suggests that the superposition of linearly stable non-orthogonal perturbations can lead to a shorttime transient amplification of the energy contained within the initial flow conditions and establish transition to turbulence 8,9 . Numerous studies on the nonmodal mechanism for transition have been undertaken, including the flow within a duct of square cross section 10 and the flow over a flat plate 11,12 . In addition, a recent review by Kerswell 13 presents an optimisation technique based on nonlinear nonmodal analysis.…”