A 1D "Navier-Stokes Machine" and its application to turbulence studies

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear term are presented and discussed. The calculations take the full 4D flow as its starting point and continuously projects the forces acting on the fluid at a fixed Eulerian point onto the direction of the instantaneous velocity. Pressure is included through modeling. Adhering to the requirement that time must in general be considered an independent variable, the time development of the time records and power spectra of the velocity fluctuations are studied. It is found that the actions of the nonlinear term in the Navier-Stokes equation manifests itself by generating sharp pulses in the time traces, where the sharpness is bounded by the finite viscosity. In the spectral domain, the sharp gradients in the pulses generate energy contributions at high frequencies that yields a $-2$ slope across the inertial range. The $-2$ (or $-6/3$) slope is explained through a simple example and the classically expected $-5/3$ slope in the inertial range can be recovered from the pressure fluctuations from the full flow field that can be considered a noise contribution at the point considered. We also observe that the spectrum can in principle keep spreading to higher frequencies or wavenumbers without upper bound, as the viscosity is approaching the zero limit

Statistical Description Of The Turbulent Round Jet Developing Region Along Its Centerline

Due to the technical measurement difficulties, analysis on the developing region of a turbulent round jet has been omitted despite its vast significance in explaining the establishment of the fully developed counterpart. With a self-developed novel and sophisticated laser Doppler system that can accurately measure high turbulence intensity flow with high spatial resolution and dynamics range, a turbulent round jet is mapped in terms of statistical moments along the centerline throughout and beyond the developing region. About 25-30 jet exit diameters downstream, turbulence begins to approach the fully developed state where the mean velocity and variance develop in parallel in a seeming equilibrium. Turbulence intensity is consequently observed to initially increase before levelling out when approaching the fully developed state. The downstream development of the measured spatial energy spectra and second-order structure functions further support these observations in that they begin to develop the Kolmogorov characteristic-5/3 and 2/3 slopes in the inertial subrange within the downstream distance of 25-30 jet exit diameters. The dissipation can be to a reasonable approximation extracted from the third-order structure functions from about 20 jet exit diameters and further downstream. The results should be useful for development of analytic and numerical turbulence models

Alteration of helical vortex core without change in flow topology

The abrupt expansion of the slender vortex core with changes in flow topology is commonly known as vortex breakdown. We present new experimental observations of an alteration of the helical vortex core in wall bounded turbulent flow with abrupt growth in core size, but without change in flow topology. The helical symmetry as such is preserved, though the characteristic parameters of helical symmetry of the vortex core transfer from a smooth linear variation to a different trend under the influence of a non-uniform pressure gradient, causing an increase in helical pitch without changing its sign