scholarly journals The evaporatively driven cloud-top mixing layer

2010 ◽  
Vol 660 ◽  
pp. 5-36 ◽  
Author(s):  
JUAN PEDRO MELLADO
Keyword(s):  
Mixture Fraction ◽  
Evaporative Cooling ◽  
Mixing Layer ◽  
Molecular Transport ◽  
Buffer Zone ◽  
Turbulent Convection ◽  
Constant Thickness ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
Entrainment Velocity

Direct numerical simulations of the turbulent temporally evolving cloud-top mixing layer are used to investigate the role of evaporative cooling by isobaric mixing locally at the stratocumulus top. It is shown that the system develops a horizontal layered structure whose evolution is determined by molecular transport. A relatively thin inversion with a constant thickness h = κ/we is formed on top and travels upwards at a mean velocity we ≃ 0.1(κ |bs|χc2)1/3, where κ is the mixture-fraction diffusivity, bs < 0 is the buoyancy anomaly at saturation conditions χs and χc is the cross-over mixture fraction defining the interval of buoyancy reversing mixtures. A turbulent convection layer develops below and continuously broadens into the cloud (the lower saturated fluid). This turbulent layer approaches a self-preserving state that is characterized by the convection scales constructed from a constant reference buoyancy flux Bs = |bs|we/χs. Right underneath the inversion base, a transition or buffer zone is defined based on a strong local conversion of vertical to horizontal motion that leads to a cellular pattern and sheet-like plumes, as observed in cloud measurements and reported in other free-convection problems. The fluctuating saturation surface (instantaneous cloud top) is contained inside this intermediate region. Results show that the inversion is not broken due to the turbulent convection generated by the evaporative cooling, and the upward mean entrainment velocity we is negligibly small compared to the convection velocity scale w* of the turbulent layer and the corresponding growth rate into the cloud.

scholarly journals Compressible mixing layer in shock-induced separation

2019 ◽  
Vol 863 ◽  
pp. 620-643 ◽  
Author(s):  
P. Dupont ◽  
S. Piponniau ◽  
J. P. Dussauge
Keyword(s):  
Turbulent Transport ◽  
Mixing Layer ◽  
Spreading Rate ◽  
Turbulent Shear ◽  
Free Shear Layer ◽  
Mean Velocity ◽  
Entrainment Velocity ◽  
Spatial Growth ◽  
Turbulent Shear Stress ◽  
High Mach

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

Large-scale structure and entrainment in the supersonic mixing layer

1995 ◽  
Vol 284 ◽  
pp. 171-216 ◽  
Author(s):  
N. T. Clemens ◽  
M. G. Mungal
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Layer ◽  
Mie Scattering ◽  
Planar Laser ◽  
The Cross ◽  
Convective Mach Number ◽  
Stream Direction

Experiments were conducted in a two-stream planar mixing layer at convective Mach numbers,Mc, of 0.28, 0.42, 0.50, 0.62 and 0.79. Planar laser Mie scattering (PLMS) from a condensed alcohol fog and planar laser-induced fluorescence (PLIF) of nitric oxide were used for flow visualization in the side, plan and end views. The PLIF signals were also used to characterize the turbulent mixture fraction fluctuations.Visualizations using PLMS indicate a transition in the turbulent structure from quasi-two-dimensionality at low convective Mach number, to more random three-dimensionality for$M_c\geqslant 0.62$. A transition is also observed in the core and braid regions of the spanwise rollers as the convective Mach number increases from 0.28 to 0.62. A change in the entrainment mechanism with increasing compressibility is also indicated by signal intensity profiles and perspective views of the PLMS and PLIF images. These show that atMc= 0.28 the instantaneous mixture fraction field typically exhibits a gradient in the streamwise direction, but is more uniform in the cross-stream direction. AtMc= 0.62 and 0.79, however, the mixture fraction field is more streamwise uniform and with a gradient in the cross-stream direction. This change in the composition of the structures is indicative of different entrainment motions at the different compressibility conditions. The statistical results are consistent with the qualitative observations and suggest that compressibility acts to reduce the magnitude of the mixture fraction fluctuations, particularly on the high-speed edge of the layer.

scholarly journals On the scaling of shear-driven entrainment: a DNS study

2013 ◽  
Vol 732 ◽  
pp. 150-165 ◽  
Author(s):  
Harm J. J. Jonker ◽  
Maarten van Reeuwijk ◽  
Peter P. Sullivan ◽  
Edward G. Patton
Keyword(s):  
Reynolds Number ◽  
Lower Boundary ◽  
Square Root ◽  
Simulation Design ◽  
Self Similarity ◽  
Original Experiment ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Constant Shear Stress ◽  
Self Similar

AbstractThe deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as$R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

Turbulence, waves and mixing at shear-free density interfaces. Part 1. A theoretical model

1997 ◽  
Vol 347 ◽  
pp. 197-234 ◽  
Author(s):  
H. J. S. FERNANDO ◽  
J. C. R. HUNT
Keyword(s):  
Theoretical Model ◽  
Critical Frequency ◽  
Lower Layer ◽  
Breaking Waves ◽  
Turbulent Motion ◽  
Interfacial Wave ◽  
Full Spectrum ◽  
Turbulent Layer ◽  
Entrainment Velocity ◽  
Linear Waves

This paper presents a theoretical model of turbulence and mixing at a shear-free stable density interface. In one case (single-sided stirring) the interface separates a layer of fluid of density ρ in turbulent motion, with r.m.s. velocity uH and lengthscale LH, from a non-turbulent layer with density ρ+Δρ, while in the second case (double-sided stirring) the lower layer is also in turbulent motion. In both cases, the external Richardson number Ri=ΔbLH/ u2H (where Δb is the buoyancy jump across the interface) is assumed to be large. Based on the hypotheses that the effect of the interface on the turbulence is as if it were suddenly imposed (which is equivalent to generating irrotational motions) and that linear waves are generated in the interface, the techniques of rapid distortion theory are used to analyse the linear aspects of the distortion of turbulence and of the interfacial motions. New physical concepts are introduced to account for the nonlinear aspects.To describe the spectra and variations of the r.m.s. fluctuations of velocity and displacements, a statistically steady linear model is used for frequencies above a critical frequency ωr/μc, where ωr(=Δb/2uH) is the maximum resonant frequency and μc<1. As in other nonlinear systems, observations below this critical frequency show the existence of long waves on the interface that can grow, break and cause mixing between the two fluid layers. A nonlinear model is constructed based on the fact that these breaking waves have steep slopes (which determines the form of the displacement spectrum) and on the physical argument that the energy of the vertical motions of these dissipative nonlinear waves should be comparable to that of the forced linear waves, which leads to an approximately constant value for the parameter μc. The model predictions of the vertical r.m.s. interfacial velocity, the interfacial wave amplitude and the velocity spectra agree closely with new and published experimental results.An exact unsteady inviscid linear analysis is used to derive the growth rate of the full spectrum, which asymptotically leads to the growth of resonant waves and to the energy transfer from the turbulent region to the wave motion of the stratified layer. Mean energy flux into the stratified layer, averaged over a typical wave cycle, is used to estimate the boundary entrainment velocity for the single-sided stirring case and the flux entrainment velocity for the double-sided stirring case, by making the assumption that the ratio of buoyancy flux to dissipation rate in forced stratified layers is constant with Ri and has the same value as in other stratified turbulent flows. The calculations are in good agreement with laboratory measurements conducted in mixing boxes and in wind tunnels. The contribution of Kelvin–Helmholtz instabilities induced by the velocity of turbulent eddies parallel to the interface is estimated to be insignificant compared to that of internal waves excited by turbulence.

LES and Hybrid RANS/LES of a Fundamental Trailing Edge Slot

2014 ◽  
Author(s):  
Elizaveta Ivanova ◽  
Gregory M. Laskowski
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Numerical Study ◽  
Mixing Layer ◽  
Detached Eddy Simulation ◽  
Trailing Edge ◽  
Adiabatic Wall ◽  
Mean Velocity ◽  
Eddy Simulation ◽  
Delayed Detached Eddy Simulation

This paper presents the results of a numerical study on the predictive capabilities of Large Eddy Simulation (LES) and hybrid RANS/LES methods for heat transfer, mean velocity, and turbulence in a fundamental trailing edge slot. The geometry represents a landless slot (two-dimensional wall jet) with adjustable slot lip thickness. The reference experimental data taken from the publications of Kacker and Whitelaw [1] [2] [3] [4] contains the adiabatic wall effectiveness together with the velocity and the Reynolds-stress profiles for various blowing ratios and slot lip thicknesses. The simulations were conducted at three different lip thickness and several blowing ratio values. The comparison with the experimental data shows a general advantage of LES and hybrid RANS/LES methods against unsteady RANS. The predictive capability of the tested LES models (dynamic ksgs-equation [5] and WALE [6]) was comparable. The Improved Delayed Detached Eddy Simulation (IDDES) hybrid method [7] also shows satisfactory agreement with the experimental data. In addition to the described baseline investigations, the influence of the inlet turbulence boundary conditions and their implication for the initial mixing layer and heat transfer development were studied for both LES and IDDES.

Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate

2000 ◽  
Vol 421 ◽  
pp. 229-267 ◽  
Author(s):  
JONATHAN B. FREUND ◽  
SANJIVA K. LELE ◽  
PARVIZ MOIN
Keyword(s):  
Growth Rate ◽  
Mach Number ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Velocity Difference ◽  
Mean Velocity ◽  
The Mean ◽  
Mach Numbers ◽  
High Mach ◽  
Compressibility Effects

This work uses direct numerical simulations of time evolving annular mixing layers, which correspond to the early development of round jets, to study compressibility effects on turbulence in free shear flows. Nine cases were considered with convective Mach numbers ranging from Mc = 0.1 to 1.8 and turbulence Mach numbers reaching as high as Mt = 0.8.Growth rates of the simulated mixing layers are suppressed with increasing Mach number as observed experimentally. Also in accord with experiments, the mean velocity difference across the layer is found to be inadequate for scaling most turbulence statistics. An alternative scaling based on the mean velocity difference across a typical large eddy, whose dimension is determined by two-point spatial correlations, is proposed and validated. Analysis of the budget of the streamwise component of Reynolds stress shows how the new scaling is linked to the observed growth rate suppression. Dilatational contributions to the budget of turbulent kinetic energy are found to increase rapidly with Mach number, but remain small even at Mc = 1.8 despite the fact that shocklets are found at high Mach numbers. Flow visualizations show that at low Mach numbers the mixing region is dominated by large azimuthally correlated rollers whereas at high Mach numbers the flow is dominated by small streamwise oriented structures. An acoustic timescale limitation for supersonically deforming eddies is found to be consistent with the observations and scalings and is offered as a possible explanation for the decrease in transverse lengthscale.

A laboratory study of stratified accelerating shear flow over a rough boundary

1984 ◽  
Vol 138 ◽  
pp. 185-196 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Shear Flow ◽  
Internal Waves ◽  
Mixing Layer ◽  
Internal Gravity Waves ◽  
Rough Boundary ◽  
Turbulent Layer ◽  
Near Surface ◽  
Rate Of Spread ◽  
Vertical Scale ◽  
The Waves

Experiments are made in which a stratified shear flow, accelerating from rest and containing a level where the direction of flow reverses, is generated over a rough floor. The roughness elements consist of parallel square bars set at regular intervals normal to the direction of flow. Radiating internal gravity waves are generated in the early stages of flow, whilst flow separation behind the bars produces turbulent mixing regions which eventually amalgamate and entirely cover the floor. This turbulent layer spreads vertically less rapidly than the internal waves. Observed features of the waves are compared with those predicted by a model in which the floor is assumed to be sinusoidal, and fair agreement is found for the amplitude, phase and vertical wavenumber of the waves, even when the latter becomes large.The rate of spread of the turbulent layer depends on the separation of the bars. Some interaction between the turbulence and the internal waves occurs near the edge of the turbulent layer. Wave-breaking is prevalent and the vertical scale of the waves is affected by turbulent eddies. The radiating internal waves are suppressed by replacing the bars by an array of square cubes, but there is continued evidence of features resembling internal waves near the boundary of the turbulent region. Structures are observed which bear some similarities to those found at the foot of the near-surface mixing layer in a lake.

Effect of viscosity gradients on mean velocity profile in temporal mixing layer

2016 ◽  
Vol 17 (5) ◽  
pp. 491-517 ◽  
Author(s):  
N. Taguelmimt ◽  
L. Danaila ◽  
A. Hadjadj
Keyword(s):  
Velocity Profile ◽  
Mixing Layer ◽  
Mean Velocity ◽  
Temporal Mixing Layer

Simplified theory of the near-wall turbulent layer of Newtonian and drag-reducing fluids

1982 ◽  
Vol 119 ◽  
pp. 423-441 ◽  
Author(s):  
M. A. Goldshtik ◽  
V. V. Zametalin ◽  
V. N. Shtern
Keyword(s):  
Velocity Profile ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Outer Boundary ◽  
Viscous Sublayer ◽  
Viscous Layer ◽  
Mean Velocity ◽  
Turbulent Layer ◽  
The Mean ◽  
Near Wall

We propose a simplified theory of a viscous layer in near-wall turbulent flow that determines the mean-velocity profile and integral characteristics of velocity fluctuations. The theory is based on the concepts resulting from the experimental data implying a relatively simple almost-ordered structure of fluctuations in close proximity to the wall. On the basis of data on the greatest contribution to transfer processes made by the part of the spectrum associated with the main size of the observed structures, the turbulent fluctuations are simulated by a three-dimensional running wave whose parameters are found from the problem solution. Mathematically the problem reduces to the solution of linearized Navier-Stokes equations. The no-slip condition is satisfied on the wall, whereas on the outer boundary of a viscous layer the conditions of smooth conjunction with the asymptotic shape of velocity and fluctuation-energy profiles resulting from the dimensional analysis are satisfied. The formulation of the problem is completed by the requirement of maximum curvature of the mean-velocity profile on the outer boundary applied from stability considerations.The solution of the problem does not require any quantitative empirical data, although the conditions of conjunction were formulated according to the well-known concepts obtained experimentally. As a result, the near-wall law for the averaged velocity has been calculated theoretically and is in good agreement with experiment, and the characteristic scales for fluctuations have also been determined. The developed theory is applied to turbulent-flow calculations in Maxwell and Oldroyd media. The elastic properties of fluids are shown to lead to near-wall region reconstruction and its associated drag reduction, as is the case in turbulent flows of dilute polymer solutions. This theory accounts for several features typical of the Toms effect, such as the threshold character of the effect and the decrease in the normal fluctuating velocity. The analysis of the near-wall Oldroyd fluid flow permits us to elucidate several new aspects of the drag-reduction effect. It has been established that the Toms effect does not always result in thickening of the viscous sublayer; on the contrary, the most intense drag reduction takes place without thickening in the viscous sublayer.

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