Onset of Turbulence from the Receptivity Stage of Fluid Flows

Abstract

The traditional viewpoint of fluid flow considers the transition to turbulence to occur by the secondary and nonlinear instability of wave packets, which have been created experimentally by localized harmonic excitation. The boundary layer has been shown theoretically to support spatiotemporal growing wave fronts by Sengupta, Rao, and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] by a linear mechanism, which is shown here to grow continuously, causing the transition to turbulence. Here, we track spatiotemporal wave fronts to a nonlinear turbulent state by solving the full 2D Navier-Stokes equation, without any limiting assumptions. Thus, this is the only demonstration of deterministic disturbances evolving from a receptivity stage to the full turbulent flow. This is despite the prevalent competing conjectures of the event being three-dimensional and/or stochastic in nature.

Precursor of transition to turbulence: Spatiotemporal wave front

“…Figure 2(b) identifies the three elements of response, as was shown in Refs. [8,9,11] for the creation of 2D turbulence. Following the local solution, planar and a pair of oblique TS wavepackets are seen in Fig.…”

“…STWF has 77 never been reported by either temporal or spatial instability 78 theories. Actual structure of the STWF was also shown to 79 be similar by solving full 2D NSE [8], which helped track 80 the nonlinear growth of the STWF to intermittent turbulent 81 flow stage. However, to follow the nonlinear evolution of the 82 STWF by NSE, the computational domain has to be long 83 enough.…”

“…1, where a representative disturbance field obtained for a zero-pressure-gradient boundary layer perturbed by timeharmonic excitation is noted at a particular height. The growing * swagata@iitk.ac.in † http://spectral.iitk.ac.in STWF originating from the solution of OSE and by solving full 53 2D NSE is seen to be responsible for 2D transition [6,8]. In this 54 respect, it is pertinent to distinguish the STWF from TS waves, 55 the latter has been predominantly discussed in the literature.…”

“…The instability theory only predicts the asymptotic wave-packet in a qualitative manner. To replicate the experimental observations, one can follow the above linearized receptivity study [7] or solve the nonlinear NSE by direct numerical simulation (DNS) [6,8]. The results of a DNS is shown in Fig.…”

“…For the 2D turbulence simulation in Ref. [8], 86 the computational domain is 12 times longer than that used in 87 Ref. [10].…”