Nature of turbulence and its energy-transfer mechanisms
Characterize the nature of turbulence and elucidate the energy-transfer mechanisms in industrially and scientifically relevant turbulent flows governed by the Navier–Stokes equations.
References
Although turbulent flows have been widely studied for over 140 years, the nature of turbulence and its energy-transfer mechanisms remain unclear for most of the industrial and scientific flows.
While the detailed physical origin of the delay remains unclear, the present results demonstrate that its magnitude plays a central role in controlling the transition between intermittent and dynamically equilibrated turbulence. By incorporating this delayed dissipation response into the outer-layer energetics, we developed a low-dimensional delay-differential system with MKE and TKE as the state variables. When the prescribed delay is varied, the system reproduces the DNS transition from strongly oscillatory behaviour at low $Re_0$ to weakly oscillatory or sustained turbulence at higher $Re_0$. The delay system also suggests that larger $\hat{Ri_f}$, corresponding to stronger stratification, is associated with intermittency and stronger burst events. The DNS further indicates that stronger stratification allows larger amounts of MKE to accumulate during quiescent phases. Once turbulence develops, this energy is rapidly transferred to turbulence and, in combination with the delayed dissipation response, produces more intense burst events.
The role of the density ratio in this exchange is not fully understood.
In conclusion, the framework established here seem to provide a nice theoretical foundation for understanding and exploiting anisotropic turbulence (polarization, directionality and acoustic directivity) and the helicity effects within. And, we anticipate that it will stimulate further developments in both fundamental turbulence theory and practical acoustic diagnostics. But, as a theoretical approach, several caveats should be pointed out: first, as always, the absolute equilibrium only indicates the possible trend(s) of the relevant physical properties in turbulence (with dissipation),32 here the CWDRF turbulence, so it must be iterated that our results indicate only that the corresponding turbulence may tend to have such aeroacoustic directivities; second, anisotropy, specifically here the truncations of the modes of some velocity component(s) down to 𝑘𝑖 = 0 for particular component(s) 𝑘𝑖 of the wavevector k, can introduce additional time scale(s) that may deteriorate the relevance of the thermalization (whose time scale is supposed to be comparable to the eddy turn-over time of isotropic turbulence); third, the CWDRF relevance to realistic flow dynamics, such as the 331RSF to stratification, is not very clear yet;16 and, fourth, the Lighthill-type acoustic analogy is but an analogy our calculation has so far been restricted to the source strength (power spectrum), not directly the object that is heard/measured.
Despite grid resolutions of up to $20483$ points the Reynolds numbers accessible are not sufficiently large to distinguish conclusively between a weak and a strong dissipative anomaly.