## What is/are Spatially Evolving?

Spatially Evolving - The primary object of this study is to derive new scaling laws for passive scalar statistical quantities in temporally and spatially evolving plane turbulent jet flows.^{[1]}The theoretical framework is based on the exact equation for the second-order moment of the two-point velocity increment and allows us to trace, for the first time, the spatially evolving cascade processes at the basis of turbulence mixing and entrainment.

^{[2]}Studies have shown that under rainfall conditions, some temporally and spatially evolving transient saturated zones will form inside the slope, which will cause the continuous degradation of the rock and soil mechanical properties of the slope in this zone, and eventually cause the slope to instability.

^{[3]}They originate from the out-of-plane flexibility of 2D materials introducing spatially evolving electronic structure and friction behavior.

^{[4]}As well as being able to compute time-dependent spatially evolving solutions numerically, the resulting model allows steady-state solutions to be constructed for the height, width and depth-averaged velocity profile across a leveed channel, which are in good quantitative agreement with small scale analogue experiments using monodisperse dry sand.

^{[5]}Cities are spatially evolving complex systems.

^{[6]}With the Eulerian–Lagrangian point-source method, turbulence modulation by dispersed particles is systematically investigated in a three-dimensional spatially evolving compressible mixing layer with the convective Mach number up to 1.

^{[7]}We investigate the properties of the velocity gradient tensor for spatially evolving turbulent flows (a near-wake, two axisymmetric jets and a planar mixing layer).

^{[8]}We investigate this observation and provide a possible explanation for the disparity between the results of local and global receptivity analysis in spatially evolving flows.

^{[9]}We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition.

^{[10]}First experimental detection of spatially evolving TS wave-packets were reported by Schubauer and Skramstad (J Aeronaut Sci, 14(2), 69–78, [16]), who essentially perturbed the ZPGBL boundary layer by vibrating a ribbon at a fixed frequency inside it.

^{[11]}The DE analysis is applied to a set of spatially evolving premixed jet flames at different Reynolds numbers.

^{[12]}In this paper, direct numerical simulation (DNS) of spatially evolving flat plate hypersonic turbulent boundary layer with free-stream Mach number 8 is used to study the effects of wall temperature on compressibility and Reynolds stress contribution.

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