## What is/are Spatially Developing?

Spatially Developing - For such spatially developing she.^{[1]}The compressibility effects on the transition to turbulence in a spatially developing, compressible plane free shear layer are investigated via direct numerical simulation using a high-order discontinuous spectral element method for three different convective Mach numbers of 0.

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## turbulent boundary layer

In this study, numerical simulations of spatially developing incompressible turbulent boundary layers (SDTBLs) with adverse pressure gradient (APG) over two-dimensional smooth curved ramps have bee.^{[1]}We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer.

^{[2]}Visualization of the thermal field in highly accelerated spatially developing turbulent boundary layers is carried out.

^{[3]}Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed.

^{[4]}Three-dimensional distribution of microbubbles dispersed in a turbulent boundary layer spatially developing along a flat plate is investigated experimentally.

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## direct numerical simulation

The compressibility effects on energy exchange mechanisms in a three-dimensional, spatially developing plane free shear layer are investigated via data produced by direct numerical simulation.^{[1]}By direct numerical simulations, the effects of heat release on turbulence characteristics are systematically investigated in a three-dimensional spatially developing supersonic droplet-laden mixing layer with the convective Mach number of 1.

^{[2]}Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damkohler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames.

^{[3]}Direct numerical simulations of a spatially developing Ma 2.

^{[4]}Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer.

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## spatially developing boundary

In this context, this work aims to extend the ZIBC framework, initially adapted to reproduce blockage effects, to take into account configurations where the influence of spatially developing boundary layers has to be accurately predicted.^{[1]}In this study, the effect of natural convection affected by gas radiation on a spatially developing boundary layer was investigated through large-eddy simulations to evaluate the interaction between natural convection and thermal radiation in an open environment, wherein Tollmien–Schlichting instabilities dominate.

^{[2]}The two mechanisms by which the outer irrotational flow can be entrained into the turbulent region and their relative contribution to the growth of the spatially developing boundary layer are evaluated: (i) nibbling is the enstrophy transport across the turbulent/non-turbulent interface (TNTI), and (ii) engulfment is the entrapment of pockets of irrotational flow inside the TBL prior to finally breaking apart.

^{[3]}An analytic expression for the sensitivity is derived for parallel and spatially developing boundary layers, the latter using linear parabolized stability equations and their adjoint.

^{[4]}Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations.

^{[5]}Large eddy simulations are performed to investigate the possibility of bypass transition delay in spatially developing boundary layers.

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## spatially developing turbulent

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damkohler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames.^{[1]}Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer.

^{[2]}Visualization of the thermal field in highly accelerated spatially developing turbulent boundary layers is carried out.

^{[3]}Second, the optimal parameter values of AFP obtained from the inviscid Taylor-Green vortex tests are validated on a series of test configurations with increasing complexity, that include an inviscid 1D advection problem involving a thermal contact discontinuity, an inviscid 2D Kelvin-Helmholtz instability test and 3D experimental unheated and heated spatially developing turbulent round jets.

^{[4]}Direct numerical simulation of a spatially developing turbulent boundary layer over a compliant wall with anisotropic wall material properties is performed.

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## spatially developing supersonic

By direct numerical simulations, the effects of heat release on turbulence characteristics are systematically investigated in a three-dimensional spatially developing supersonic droplet-laden mixing layer with the convective Mach number of 1.^{[1]}The effects of static surface deformations on a spatially developing supersonic boundary layer flow at Mach number M = 4 and Reynolds number R e δ i n ≈ 49300 , based on inflow boundary layer thickness ( δ i n ), are analyzed by performing large eddy simulations.

^{[2]}Direct numerical simulation of a spatially developing supersonic mixing layer with a convective Mach number of 1.

^{[3]}Two and three dimensional large eddy simulations of a spatially developing supersonic mixing layer are performed using an in-house hybrid finite volume code that combines a fourth order non-dissipative MacCormack scheme for capturing turbulence and a second order SLAU2 upwind scheme for capturing shocks and other discontinuities in the flow.

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## spatially developing shear

Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing.^{[1]}Direct numerical simulation is conducted for a spatially developing shear mixing layer to investigate the spatial transition of the dissipation coefficient of the turbulent kinetic energy, Cϵ.

^{[2]}Numerical studies of droplet-laden spatially developing shear layers are conducted with a high convective Mach number (Mc = 1.

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## spatially developing transitional

Numerical simulations of a spatially developing transitional flow in a vertical channel with one side uniformly heated and subjected to random velocity fluctuations at the inlet have been performed.^{[1]}A spatially developing transitional flow in a vertical channel with one side heated uniformly and subjected to random velocity fluctuations at the inlet is investigated in this experimental and numerical study.

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## spatially developing flow

In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.^{[1]}This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.

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