Direct numerical simulation of laminar–turbulent flow over a flat plate at hypersonic flow speeds

Linear, nonlinear and transitional regimes of second-mode instability

“…This location also matches the streamwise station beyond which the spanwise spectra switch over from a narrowband form (peak energy near or ) to one where a wide range of low wavenumbers are energized (discussed previously in figure 12 a ). By the end of the domain, , the value is , which is consistent with the turbulent skin-friction value reported in Egorov & Novikov (2016) for identical free stream conditions (marked with a solid circle). The wall-normal profile of streamwise velocity in terms of wall units () and friction velocity () at this location are provided in figure 16( b ).…”

“…The pressure perturbation contours in figure 6( a ) indicate waves accumulating behind the shock wave, as well as amplifying within the boundary layer. Unlike the linear scenario, pressure perturbations here show occasional extensions into the free stream, as was also observed in the nonlinear behaviour of second-mode by Egorov & Novikov (2016). The region marked by the rectangle (in figure 6 a ) is magnified in figure 6( b ) for a detailed representation of the pressure perturbation contours.…”

“…However, the nonlinear field is asymmetric, with the negative deviations being spatially dominant. The interlacing is also pronounced in the nonlinear response (Egorov & Novikov 2016), with the braided pattern becoming more evident. This is seen, for instance, in the experiments of Laurence et al.…”

“…The actuator used to excite instabilities in the HBL is modelled as a blowing–suction slot, which introduces harmonic perturbations in wall-normal momentum, . Following Egorov & Novikov (2016), this is defined as The amplitude of the spanwise homogeneous wave, , depends on whether the analysis is linear or nonlinear, and is defined in the relevant sections below. The frequency of forcing, , and its upstream and downstream limits, and , respectively, are obtained from linear stability analysis, as described in the following section.…”

Closed vortex lines in fluid and gas

“…In some cases, it is possible a priori (before making calculations) to state that vortex lines and tubes will be closed (for example, a flow behind a detached shock wave [22]) and checking the closure of vortex lines can serve to verify the calculations. In other cases, closed vortex tubes are detected as a result of a calculation (for example, [23][24][25][26][27][28]), and checking the regularities specific to vortex tubes would allow verification of the calculation. This article is devoted to the search for such regularities in the general 3D case for continuous flows of fluid and gas, hereinafter called as fluid flows.…”