Precursor of transition to turbulence: Spatiotemporal wave front

Abstract

To understand transition to turbulence via 3D disturbance growth, we report here results obtained from the solution of Navier-Stokes equation (NSE) to reproduce experimental results obtained by minimizing background disturbances and imposing deterministic excitation inside the shear layer. A similar approach was adopted in Sengupta and Bhaumik [Phys. Rev. Lett. 107, 154501 (2011)], where a route of transition from receptivity to fully developed turbulent stage was explained for 2D flow in terms of the spatio-temporal wave-front (STWF). The STWF was identified as the unit process of 2D turbulence creation for low amplitude wall excitation. Theoretical prediction of STWF for boundary layer was established earlier in Sengupta, Rao, and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] from the Orr-Sommerfeld equation as due to spatiotemporal instability. Here, the same unit process of the STWF during transition is shown to be present for 3D disturbance field from the solution of governing NSE.

Combined effects of amplitude, frequency and bandwidth on wavepackets in laminar turbulent transition

“…Interestingly, at high frequency, the front of the wavetrain could exhibit N-type characteristics while the main body of the wave undergoes K-type transition, as investigated in Section 3.2. K-type transition for higher-frequency disturbances had also been reported by Bhaumik and Sengupta (2014). 3.…”

“…More recently, the mechanism of genesis and evolution of the spatio-temporal wavepacket in a linear framework was explored in Sengupta et al (2006b) and Sengupta et al (2006a), and the influence of frequency in determining either K-type or H-type transition in wavepackets was described in Bhaumik andSengupta (2014, 2015); ; Sharma et al (2018), who used the synonymous term "spatio-temporal wave front" (STWF) for a wavepacket. This spatio-temporal wavepacket is a modulated and bandlimited combination of spatio-temporal eigenmodes of the Orr-Sommerfeld equation as described by Equation 1 in Bhaumik and Sengupta (2014).…”

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

“…Lele 7 then presented a detailed analysis of compact schemes up to fourth derivatives, including their boundary closures. The small stencil and spectral-like resolution of compact schemes are highly desirable in CFD methods with structured meshes, 8 especially for direct numerical simulation (DNS) [9][10][11][12] or large-eddy simulation 13,14 of turbulence and computational aeroacoustics, [15][16][17][18] in which small-scale flow structures need to be resolved. Compact schemes have advantages regarding high accuracy, small truncation error, low dissipation, and a compact stencil.…”

Nonmodal nonlinear route of transition to two-dimensional turbulence

“…Researchers [18,19] have shown the existence of STWF from the solution of 2D NSE and its role in the creation of 2D turbulence [20,21] with the typical dependence of the energy spectrum on the wave number as E (α) ∼ α −3 . These computations require high accuracy dispersion relation preserving numerical methods [22], which have been subsequently used to show the three-dimensional (3D) routes of transition [23,24].…”