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We demonstrate that numerical solutions of Burgers' equation can be obtainedby a scale-totality algorithm for fluids of small viscosity (down to onebillionth). Two sets of initial data, modelling simple shears and wall boundarylayers, are chosen for our computations. Most of the solutions are carried outwell into the fully turbulent regime over finely-resolved scales in space andin time. It is found that an abrupt spatio-temporal concentration in shearconstitutes an essential part during the flow evolution. The vorticity surgehas been instigated by the non-linearity complying with instantaneous enstrophyproduction, while ad hoc disturbances play no role in the process. Inparticular, the present method predicts the precipitous vorticityre-distribution and accumulation, predominantly over localised regions ofminute dimension. The growth rate depends on viscosity and is a strong functionof initial data. Nevertheless, the long-time energy decay ishistory-independent and is inversely proportional to time. Our results providedirect evidence of the vorticity proliferation embedded in the equations ofmotion. The non-linear intensification is a robust feature, and is ultimatelyresponsible for the drastic succession in boundary layer profiles over theintrinsic laminar-turbulent transition (Schubauer and Klebanoff 1955). Thedynamical inception of turbulence can be decrypted by solving the fulltime-dependent Navier-Stokes equations which ascribe no instability stages.

Non-linear vorticity upsurge in Burgers' flow