Daniel Chung

Large-eddy simulation of large-scale structures in long channel flow

We investigate statistics of large-scale structures from large-eddy simulation (LES) of turbulent channel flow at friction Reynolds numbers Re_τ = 2K and 200K (where K denotes 1000). In order to capture the behaviour of large-scale structures properly, the channel length is chosen to be 96 times the channel half-height. In agreement with experiments, these large-scale structures are found to give rise to an apparent amplitude modulation of the underlying small-scale fluctuations. This effect is explained in terms of the phase relationship between the large- and small-scale activity. The shape of the dominant large-scale structure is investigated by conditional averages based on the large-scale velocity, determined using a filter width equal to the channel half-height. The conditioned field demonstrates coherence on a scale of several times the filter width, and the small-scale–large-scale relative phase difference increases away from the wall, passing through π/2 in the overlap region of the mean velocity before approaching π further from the wall. We also found that, near the wall, the convection velocity of the large scales departs slightly, but unequivocally, from the mean velocity.

On the Fidelity of Large-Eddy Simulation of Shallow Precipitating Cumulus Convection

AbstractThe present study considers the impact of various choices pertaining to the numerical solution of the governing equations on large-eddy simulation (LES) prediction and the association of these choices with flow physics. These include the effect of dissipative versus nondissipative advection discretizations, different implementations of the constant-coefficient Smagorinsky subgrid-scale model, and grid resolution. Simulations corresponding to the trade wind precipitating shallow cumulus composite case of the Rain in Cumulus over the Ocean (RICO) field experiment were carried out. Global boundary layer quantities such as cloud cover, liquid water path, surface precipitation rate, power spectra, and the overall convection structure were used to compare the effects of different discretization implementations. The different discretization implementations were found to exert a significant impact on the LES prediction even for the cases where the process of precipitation was not included. Increasing nume...

Large-eddy simulation and wall modelling of turbulent channel flow

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Karman-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Re_τ based on the friction velocity u_τ and the channel half-width δ in the range 2 × 10^3 to 2 × 10^7. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jimenez (2006) at Re_τ = 2003 and maintain an O(1) grid dependence on Re_τ.

A Unified Model for Moist Convective Boundary Layers Based on a Stochastic Eddy-Diffusivity/Mass-Flux Parameterization

AbstractA single-column model (SCM) is developed for representing moist convective boundary layers. The key component of the SCM is the parameterization of subgrid-scale vertical mixing, which is based on a stochastic eddy-diffusivity/mass-flux (EDMF) approach. In the EDMF framework, turbulent fluxes are calculated as a sum of the turbulent kinetic energy–based eddy-diffusivity component and a mass-flux component. The mass flux is modeled as a fixed number of steady-state plumes. The main challenge of the mass-flux model is to properly represent cumulus clouds, which are modeled as moist plumes. The solutions have to account for a realistic representation of condensation within the plumes and of lateral entrainment into the plumes. At the level of mean condensation within the updraft, the joint pdf of moist conserved variables and vertical velocity is used to estimate the proportion of dry and moist plumes and is sampled in a Monte Carlo way creating a predefined number of plumes. The lateral entrainment ...

Steady-State Large-Eddy Simulations to Study the Stratocumulus to Shallow Cumulus Cloud Transition

AbstractThis study presents a series of steady-state large-eddy simulations (LESs) to study the stratocumulus to shallow cumulus cloud transition. To represent the different stages of what can be interpreted as an Eulerian view of the transition, each simulation is assigned a unique sea surface temperature (SST) and run until statistically steady. The LES runs are identical in every other aspect. These idealized boundary-driven steady-state LESs allow for a simple parametric assessment of cloud-controlling factors in isolation from initial conditions and time-lag effects inherent in the Lagrangian view of the transition. The analysis of the thermodynamic energy budget reveals that, as the cloud regime transitions from stratocumulus to shallow cumulus, changes in the cloud radiative cooling term are balanced by changes in the subsidence warming term. This leads to a linear regression between the cloud fraction (CF) and an integral that scales, to a first-order approximation, as the lower-tropospheric stabi...

Direct numerical simulation and large-eddy simulation of stationary buoyancy-driven turbulence

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgridscale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off.

Large-Eddy Simulation of Stratified Turbulence. Part II: Application of the Stretched-Vortex Model to the Atmospheric Boundary Layer

AbstractThe buoyancy-adjusted stretched-vortex subgrid-scale (SGS) model is assessed for a number of large-eddy simulations (LESs) corresponding to diverse atmospheric boundary layer conditions. The cases considered are free convection, a moderately stable boundary layer [first Global Energy and Water Exchanges (GEWEX) Atmospheric Boundary Layer Study (GABLS)] case, shallow cumulus [Barbados Oceanographic and Meteorological Experiment (BOMEX)], shallow precipitating cumulus [Rain in Cumulus over the Ocean (RICO)] and nocturnal stratocumulus [Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS-II) field study RF01]. An identical LES setup, including advection discretization and SGS model parameters, is used for all cases, which is a stringent test on the ability of LES to accurately capture diverse conditions without any flow-adjustable parameters. The LES predictions agree well with observations and previously reported model results. A grid-resolution convergence study is carried out, and fo...

Vertical natural convection: application of the unifying theory of thermal convection

Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 1.0×10 5 –1.0×10 9 and Prandtl number 0.709 support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh–Benard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl–Blasius–Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the −1/2 -power of a wind-based Reynolds number, where the ‘wind’ of the GL theory is interpreted as the maximum mean velocity. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the ‘bulk’ or ‘background’ dissipation of the GL theory, is found to obey the Kolmogorov–Obukhov–Corrsin scaling for fully developed turbulence. In contrast to Rayleigh–Benard convection, the direction of gravity in vertical natural convection is parallel to the mean flow. The orientation of this flow presents an added challenge because there no longer exists an exact relation that links the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux that produces the kinetic energy, also exhibits both laminar and turbulent scaling behaviours, consistent with the GL theory. The present results suggest that, similar to Rayleigh–Benard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics.

Large-Eddy Simulation of Stratified Turbulence. Part I: A Vortex-Based Subgrid-Scale Model

AbstractThe stretched-vortex subgrid-scale (SGS) model is extended to enable large-eddy simulation of buoyancy-stratified turbulence. Both stable and unstable stratifications are considered. The extended model retains the anisotropic form of the original stretched-vortex model, but the SGS kinetic energy and the characteristic SGS eddy size are modified by buoyancy subject to two constraints: first, the SGS kinetic energy dynamics is determined by stationary and homogeneous conditions, and second, the SGS eddy size obeys a scaling analogous to the Monin–Obukhov similarity theory. The SGS model construction, comprising an ensemble of subgrid stretched-vortical structures, naturally limits vertical mixing but allows horizontal mixing provided the alignment of the SGS vortex ensemble is favorable, even at high nominal gradient Richardson numbers. In very stable stratification, the model recovers the z-less limit, in which a vortex-based Obukhov length controls the SGS dynamics, while in very unstable stratif...

A fast direct numerical simulation method for characterising hydraulic roughness

We describe a fast direct numerical simulation (DNS) method that promises to directly characterise the hydraulic roughness of any given rough surface, from the hydraulically smooth to the fully rough regime. The method circumvents the unfavourable computational cost associated with simulating high-Reynolds-number flows by employing minimal-span channels (Jimenez & Moin 1991). Proof-of-concept simulations demonstrate that flows in minimal-span channels are sufficient for capturing the downward velocity shift, that is, the Hama roughness function, predicted by flows in full-span channels. We consider two sets of simulations, first with modelled roughness imposed by body forces, and second with explicit roughness described by roughness-conforming grids. Owing to the minimal cost, we are able to conduct DNSs with increasing roughness Reynolds numbers while maintaining a fixed blockage ratio, as is typical in full-scale applications. The present method promises a practical, fast and accurate tool for characterising hydraulic resistance directly from profilometry data of rough surfaces.