The Impacts of Sub-grid Scale Parameterization of Large-Eddy Simulations on Real Hurricane Dynamics and Forecasts

The irreversible mixing efficiency is studied using large-eddy simulations (LES) of stratified turbulence, where three different subgrid-scale (SGS) parameterizations are employed. For comparison, direct numerical simulations (DNS) and hyperviscosity simulations are also performed. In the regime of stratified turbulence where$Fr_{v}\sim 1$, the irreversible mixing efficiency$\unicode[STIX]{x1D6FE}_{i}$in LES scales like$1/(1+2Pr_{t})$, where$Fr_{v}$and$Pr_{t}$are the vertical Froude number and turbulent Prandtl number, respectively. Assuming a unit scaling coefficient and$Pr_{t}=1$,$\unicode[STIX]{x1D6FE}_{i}$goes to a constant value$1/3$, in agreement with DNS results. In addition, our results show that the irreversible mixing efficiency in LES, while consistent with this prediction, depends on SGS parameterizations and the grid spacing$\unicode[STIX]{x1D6E5}$. Overall, the LES approach can reproduce mixing efficiency results similar to those from the DNS approach if$\unicode[STIX]{x1D6E5}\lesssim L_{o}$, where$L_{o}$is the Ozmidov scale. In this situation, the computational costs of numerical simulations are significantly reduced because LES runs require much smaller computational resources in comparison with expensive DNS runs.

In this thesis, parameterizations of non-linear interactions in quasigeostrophic (QG) flows for severely truncated models (STM) and Large Eddy Simulations (LES) are studied. Firstly, using Direct Numerical Simulations (DNS), atmospheric barotropic flows over topography are examined, and it is established that such flows exhibit multiple equilibrium states for a wide range of parameters. A STM is then constructed, consisting of the large scale zonal flow and a topographic mode. It is shown that, qualitatively, this system behaves similarly to the DNS as far as the interaction between the zonal flow and topography is concerned, and, in particular, exhibits multiple equilibrium states. By fitting the analytical form of the topographic stationary wave amplitude, obtained from the STM, to the results obtained from DNS, renormalized dissipation and rotation parameters are obtained. The usage of renormalized parameters in the STM results in better quantitative agreement with the DNS. In the second type of problem, subgrid-scale parameterizations in LES are investigated with both atmospheric and oceanic parameters. This is in the context of two-level QG flows on the sphere, mostly, but not exclusively, employing a spherical harmonic triangular truncation at wavenumber 63 (T63) or higher. The methodology that is used is spectral, and is motivated by the stochastic representation of statistical closure theory, with the ‘damping’ and forcing covariance, representing backscatter, determined from the statistics of DNS. The damping and forcing covariance are formulated as 2 × 2 matrices for each wavenumber. As well as the transient subgrid tendency, the mean subgrid tendency is needed in the LES when the energy injection region is unresolved; this is also calculated from the statistics of the DNS. For comparison, a deterministic parameterization scheme consisting of 2× 2 ‘damping’ parameters, which are calculated from the statistics of DNS, has been constructed. The main difference between atmospheric and oceanic flows, in this thesis, is that the atmospheric LES completely resolves the deformation scale, the energy and enstrophy injection region, and the truncation scale is spectrally distant from it, being well in the enstrophy cascade inertial range. In oceanic flows, however, the truncation scale is in the vicinity of the injection scale, at least for the parameters chosen, and is therefore not in an inertial range. A lower resolution oceanic LES at T15 is also examined, in which case the injection region is not resolved at all. For atmospheric flows, it is found that, at T63, the matrix parameters are practically diagonal so that stratified atmospheric flows at these resolutions may be treated as uncoupled layers as far as subgrid-scale parameterizations are concerned. It is also found that the damping parameters are relatively independent of the (vertical) level, but the backscatter parameters are proportional to the subgrid flux in a given level. The stochastic and deterministic parameterization schemes give comparably good results relative to the DNS. For oceanic flows, it is found that the full matrix structure of the parameters must be used. Furthermore, it is found that there is a strong injection of barotropic energy from the subgrid scales, due to the unresolved, or partially resolved, baroclinic instability injection scales. It is found that the deterministic parameterization is too numerically unstable to be of use in the LES, and instead the stochastic parameterization must be used

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.

<p>Halogen halides emitted by volcanoes are known to rapidly convert within plumes into BrO while depleting ozone, as clearly shown by observations and models over the past 2 decades (e.g. review by Gutmann et al., 2018). So far, most of the modelling studies have focused on the plume processes occurring in the first few hours after the emission. The only study at the regional scale is that of Jourdain et al. (2016). They assessed the impact of volcanic halogens for a period of strong degassing of the Ambrym volcano, showing in particular its effect on the atmospheric oxidizing capacity and methane lifetime.</p><p>A step further would be to quantify the impact of volcanic halogens at the global scale using global chemistry models. This type of model uses a horizontal resolution (greater than 50 km) that is much coarser than the plume size. This raises the issue of, whether at this resolution, it is possible to represent the chemistry occurring under high concentrations within the plume. To assess this, a sub-grid scale parameterization is proposed. It has been tested in the 1D version of MOCAGE global and regional chemistry transport model for a short eruption of Mt Etna on the 10<sup>th</sup> of May 2008. The results show that while using the subgrid-scale plume parameterization or not does change the timing of when the maximum BrO occurs but does not affect the predicted maximum concentration. The same finding is made when using a range of different settings in the parameterization regarding dilution of the plume with its environment. The 1D model results show a sensitivity of BrO formation to parameters other than the sub-grid scale effects: composition of the plume at the vent, injection height of the emissions, and time of the day when the eruption takes place.</p>

The effect of the model for the lengthscale in sub-grid scale (SGS) parameterizations used in large-eddy simulations (LES) of atmospheric flows is considered. SGS models that carry predictive equations for SGS energy (i.e., T models) are more susceptible to the model for the SGS lengthscale than are models that diagnose SGS energy, this is because in T models most of the SGS buoyancy flux in the entrainment zone is found to be associated with Richardson numbers greater than unity, i.e., regimes where the equilibrium value of SGS energy is zero. The sensitivity of LES to the model of the lengthscale depends on the type of flow, and details of the flow solver. The lengthscale sensitivity ofTmodels is fruitfully interpreted using analytic solutions to the SGS energy equation for conditions of no transport and fixed forcing.KeywordsPlanetary Boundary LayerConvective Boundary LayerRichardson NumberBuoyancy FluxEntrainment RateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Accurate representation of turbulent processes remains a critical challenge in atmospheric modelling. Large Eddy Simulations (LES) serve as valuable tools for understanding atmospheric turbulence by explicitly resolving energy-containing eddies while parameterizing smaller-scale motions through subgrid-scale (SGS) models. In their most complex forms, these SGS parameterizations can significantly influence LES performance and computational efficiency, making their improvement useful for advancing atmospheric modelling capabilities. Neural Network based emulation of such parametrizations have proven effective in reducing the computational cost, while maintaining accuracy and stability.Building upon recent advances in physics-informed neural networks (NN) for atmospheric modelling and emulation of physics-based processes, we present a physics-guided NN architecture for emulation of the SGS turbulence parameterizations that introduces several key innovations. Our approach uniquely combines scale-specific normalization with multi-scale feature extraction through parallel convolutional paths, distinguishing it from existing physics-guided machine learning frameworks. The deep learning-based (DL) model also incorporates physically-motivated constraints across different spatial scales while simultaneously ensuring conservation of momentum and energy.Unlike earlier studies that focus on single aspects of physical conservation, our architecture implements a comprehensive physics-informed framework that combines Richardson number gradient handling for stability constraints, with explicit treatment of diffusion and viscosity coefficients, and scale-specific normalization for different atmospheric variables. The model was trained on limited high-resolution Radiative-Convective Equilibrium (RCE) simulations from the Met Office-Natural Environment Research Council (NERC) Cloud model (MONC), employing physics-based loss functions that enforce both conservation laws and stability constraints.The training dataset consisted of 3-D diagnostics data from the RCE simulations, with a 64x64 km2 domain and 1 km grid spacing in the horizontal. While the original simulations had 99 vertical levels with varying vertical resolution, the DL model was trained on random slices (vertical levels) chosen from the original data volume. The inputs consisted of the resolved state variables like velocity components (u, v, w) from the previous time step, the perturbations to potential temperature, mixing ratios and Richardson number, whereas the targets for the DL model were the SGS tendencies of the model prognostic fields resulting from the Smagorisnky parameterization and the coefficients of viscosity and diffusion.The DL model's cross-regime applicability was evaluated through multiple independent test cases: (200-second sampling frequency) and different atmospheric conditions from the Atmospheric Radiation Measurement (ARM) program. The simulations from ARM atmospheric settings were mainly targeted at simulating shallow convection, with different grid/domain configurations. Results from the off-line tests demonstrate promising performance in predicting SGS and transport coefficients (viscosity and diffusion) across these varied conditions, particularly in maintaining physical consistency during regime transitions.Our preliminary findings indicate that this enhanced multi-scale, physics-informed architecture can effectively learn SGS parameterizations from limited training data while maintaining physical fidelity across different atmospheric conditions and spatio-temporal resolutions. This approach demonstrates the potential for the development of high-fidelity, generalizable parameterizations for weather and climate models, suggesting a route forward for reducing the greater computational costs associated with more complex SGS parameterization schemes.

Turbulence is ubiquitous in geophysical flows. There are hardly any situations in the dynamics of natural waters and the atmosphere that do not involve turbulent effects at some point, and only little insight can be gained in the dominant processes, if turbulence is not taken into account. Thus, the modelling of this phenomenon has attracted a great many researchers and more and more advanced models, suitable for the description of a large variety of geophysical flows, evolved over the last decades. A general model embracing all aspects of turbulence is still out of reach. Nevertheless, there has been an enormous progress in the understanding of turbulence in the past. More recently, Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) provided data that were previously only available by high-precision laboratory setups (or not at all) and had a large impact on the development of new turbulence models. It seems likely that, especially in oceanography and meteorology, LES will take a position equitable to the ensemble averaged methods in the near future. At present, however, in spite of the development of larger and faster computers, LES is still too expensive for standard simulations of geophysical interest. In this chapter, we will mainly investigate a simple parameterization of the subgrid-scale turbulent closure which is based on the Reynolds Averaged Navier-Stokes Equations (RANS) and the subgrid-scale eddy viscosity parameterizations. We employ the three-dimensional, hydrodynamic, semi-implicit, finite difference model, developed by Song and Haidvogel and extended for the TVD treatment of the advection terms by Y. Wang. Subgrid-Scale Parameterization in Numerical Simulations of Lake Circulation are used and Smagorinsky’s formulation and Mellor–Yamada ’s level-2.5 model are used to parameterize the horizontal and vertical eddy viscosities. Numerical results in an assumed rectangular basin with constant depth and in Lake Constance are displayed and discussed. A comparison is made with prescribed constant eddy viscosities; it clearly shows the importance of subgrid-scale parameterizations in numerical simulations of lake circulation. We do not claim that such subgrid-scale parameterizations are the best choice of possible closure conditions, but only show that suitable parameterizations of the small-scale (subgrid-scale) turbulent motions are needed.

Large Eddy Simulation (LES) has become an increasingly attractive option for turbulence modeling due to the rise in computing power and the improvement in sub-grid scale (SGS) parameterizations. This study tests the improvements in simulations of wall-bounded flows over heterogeneous surfaces attained by the implementation of three improvements in the eddy-viscosity SGS closure: the dynamic model by Germano et al. [1], the Lagrangian model by Meneveau et al. [2], and the scale-dependent approach by Porte´-Agel et al. [3]. The dynamic model consists of using the resolved scales to ‘measure’ the model coefficient during the simulation; therefore, no a-priori knowledge of the coefficient or the flow physics is needed. The traditional dynamic approach averages the coefficient over statistically homogeneous directions to numerically stabilize the simulations. The Lagrangian model relaxes the need for homogeneous directions by averaging the coefficient over pathlines, hence allowing local determination of the coefficient and facilitating applications to complex-geometry flows. The scale-dependent approach uses the dynamic formulation but does not assume that the SGS coefficients are scale-invariant, as is the case in traditional dynamic formulations. The deficiencies of the traditional Smagorinsky model are confirmed. Implementation of a dynamic model treats some of these deficiencies but is found to be under-dissipative close to the wall in high Reynolds number LES that does not resolve the viscous layer. The sensitivity of the model coefficient to the wall roughness is demonstrated thus confirming the need for a local SGS model such as the Lagrangian model used here. Finally, when the Lagrangian-dynamic model is implemented with the scale-dependent formulation, the results improve significantly.

Atmospheric flows and many fluid flows of engineering interest feature a multitude of characteristic length and time scales and associated scale-dependent processes. In theoretical investigations, quantitativemeteorological forecasts, or in engineering design, the ensuing complexity is often handled by employing techniques of computational fluid dynamics. Yet, in a typical application, even the most powerful computer available today would not allow us to resolve all the scales of a flow in detail. At the same time, we are mostly not interested in all these details anyway, but rather in a flow’s larger-scale features and effects. As a consequence, in practical flow simulations, we have to introduce a minimal spatiotemporal resolution as represented, e.g., by the size of a computational grid cell and by theminimal allowed time step. The effects of processes not resolved in space and time on the space-time grid are then approximately represented by “closure schemes” or “parameterizations”. For decades, practitioners in numerical weather forecasting proceeded as follows in this context: A target grid resolution was decided upon, depending on the expected available compute power. Then, subgrid scale process parameterizations were developed and implemented in an up-to-date flow solver (dynamical core) operating on the chosen grid. Finally, any free constants in the parameterizations were tuned for the entire simulation system to achieve the highest-possible weather prediction skill scores. It was common sense that any sizeable increase in grid resolution would necessarily have to be followed up by a re-tuning or even a partial rewrite of the subgrid scale process parameterizations. The situation is similar for engineering turbulent flow simulation using “large eddy simulation” approaches. In recent years, however, meteorologists as well as fluids engineers have become aware of the potential benefits of dynamically adaptive computational grids, and major meteorological centers and engineering research groups are incorporating grid adaptivity in their next-generation dynamical cores. Dynamically adaptive grids come with a caveat, though, as regards subgrid scale parameterizations. Because the spatiotemporal resolution that would be found in a simulation at any given point in space and time is not known in advance in an adaptive simulation, it is no longer possible to “tune” one’s parameterizations to perfection and then perform all production runs with the optimal parameter setting. Rather, one now needs adaptive parameterizations as well, which dynamically move particular processes from the realm of “grid resolved features” to the realm of the subgrid scales, and do so smoothly in the intermediate regimes, where the relevant processes are only partially resolved at the current resolution. Similarly, intelligent refinement and coarsening criteria are needed that place high resolution where it produces the largest benefit given some overall goal for the simulation. Needless to say that the development of such adaptive parameterizations requires to account for the subtle competition of (partially resolved) subgridscale processes with truncation errors of the underlying computational flow solver and that this necessitates balanced cooperations between physical/mathematical modellers and numerical analysts.

<p><span>Land-surface heterogeneity is known to play an important role in land-surface hydrology, which drives the bottom boundary condition for atmospheric models in numerical weather prediction (NWP) applications. However, the ultimate impact of land-surface heterogeneity on atmospheric boundary layer (ABL) development is still an open problem with implications for sub-grid scale (SGS) parameterizations for both NWP and climate modeling. Large-eddy simulation (LES) is often used to study the effects of land-surface heterogeneity on ABL development, most typically via specified surface fields which are not influenced by the atmosphere (i.e. semi-coupled). Heterogeneous land surfaces have been seen in previous studies to have a significant influence on ABL dynamics, particularly cloud production, in certain cases when semi-coupled to the atmosphere. </span></p><p><span>Here we use the Weather Research and Forecasting (WRF) model as an LES with both semi-coupled and fully-coupled land surfaces to investigate the impact of two-way coupling on the interaction between heterogeneous land surfaces and daytime ABLs. For semi-coupled simulations, the HydroBlocks land-surface model is run offline, drive</span><span>n by 4-km NLDAS-2 meteorology with Stage-IV radar rainfall data, and then used to specify the bottom boundary in WRF. The WRF-Hydro model is used for cases where the land surface is fully coupled to the WRF model. Both land-surface models use the Noah-MP model as their underlying physics package and add both subsurface and overland flow routing. </span><span>The WRF model uses a 100-m horizontal resolution, and the land-surface models use </span><span>high resolution (30 m) datasets that were upscaled to match the LES resolution for elevation, landcover, and soil type using NED, NLCD, and POLARIS respectively. </span><span>These LES experiments are performed over the ARM Southern Great Plains Site</span><span> atmospheric observatory in Oklahoma during the Summer of 2017 with a grid size of 100 km x 100 km to imitate a single cell in a modern climate model. </span><span>The impact of land-surface heterogeneity on the atmosphere is evaluated by comparing simulations using the fully heterogeneous land surfaces with simulations where the land surface is homogenized at each timestep, taking a domain-wide spatial mean value at every grid cell. </span><span>Results are evaluated primarily by the differences in the development of clouds and evolution of turbulent kinetic energy in the ABL. </span></p>

The effect of small-scale forcing on large-scale structures in two-dimensional flows

LES models for subgrid scale transport of momentum and mixture fraction are assessed using DNS and LES data of a turbulent round variable density jet. The closure models evaluated are the dynamic variable density extensions of the mixed nonlinear or Clark model and an eddy diffusivity-type model for both momentum and mixture fraction. The work is focused on understanding the coupling between momentum and scalar models. The ability to reproduce means and Reynolds stresses is used to determine model performance. To aid in understanding the coupling between models, SGS dissipation is computed, and it is demonstrated that the choice of SGS scalar model alters the SGS dissipation properties of the momentum closure. Results show that the predictive ability of the simulation depends on the model chosen, with the mixed model in general outperforming the eddy diffusivity type models. The combination of a dynamic mixed model for momentum and a fixed eddy diffusivity for scalar is a cost effective approach for variable density LES problems. I. Introduction. The low-Mach number equations provide a computationally attractive set of conservation equations for implementation in direct numerical simulation (DNS) and large-eddy simulation (LES) of low speed, complex flows with large density and temperature gradients, including for reacting flow applications. LES of reacting flow requires numerous modelling decisions including how to model the unclosed momentum, scalar, and combustion terms. Accurately predicting the scalar concentration fields is essential for the development of precise combustion simulations. Assessment of the subgrid scale (SGS) models for the incompressible momentum equation 1–3 as well as combustion models 4, 5 have seen considerable effort. Previous investigations of SGS models in compressible flows 6–8 focused primarily on higher Mach number regimes and SGS models for the energy equation. There has been some analysis 9–11 of the models used to close the scalar equations. These studies demonstrate the superiority of mixed model closures for momentum in free shear flows, and that for small density gradients the choice of scalar closure has less influence. In this work, we seek to elucidate what effects different subgrid scale (SGS) stress and scalar flux models have on both the mixing properties and turbulent statistics of the flow. Additionally, we aim to understand how the coupling between the SGS stress and scalar flux models alters the predictive abilities of LES. To isolate these effects, we restrict the study to an isothermal axi-symmetric turbulent jet governed by the lowMach number equations. This canonical flow was chosen for both its abundance of available experimental data and its lack of a wall region that requires additional treatment in LES. We study different permutations of two common SGS models. The first is the ubiquitous dynamic Smagorinsky model and its scalar analog, and the other is a dynamic mixed model combining the nonlinear or Clark model with an eddy diffusivity term, for a total of five LES cases. A methane/air jet is selected for the investigation. In addition to its practical importance, this flow has ∂

Dynamical subgrid scale parameterizations of stochastic backscatter and eddy dissipation have been calculated for typical atmospheric turbulent flows on the sphere. A methodology based on a stochastic model representation of the subgrid scale eddies in direct numerical simulations, and with wide applicability to fluid flows, has been employed. Large eddy simulations incorporating these subgrid scale parameterizations are found to have energy spectra that compare closely with the results of higher resolution direct numerical simulations for both barotropic and baroclinic turbulent flows. References O'Kane, T.J. and J.S. Frederiksen, Statistical dynamical subgrid-scale parameterizations for geophysical flows, Physica Scripta , 78 , 2008, in press. Frederiksen, J.S., Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity, and stochastic backscatter for flow over topography, J. Atmos. Sci. 56 , 1999, 1481--1494. 2.0.CO;2>doi:10.1175/1520-0469(1999)056 2.0.CO;2 Frederiksen, J.S., and A.G. Davies, Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models, J. Atmos. Sci. , 54 , 1997, 2475--2492. 2.0.CO;2>doi:10.1175/1520-0469(1997)054 2.0.CO;2 Frederiksen, J.S. and S.M. Kepert, Dynamical subgrid-scale parameterizations from direct numerical simulations, J. Atmos. Sci. , 63 , 2006, 3006--3019. doi:10.1175/JAS3795.1 Frederiksen, J.S. and M.R. Dix and A.G. Davies, The effects of closure-based eddy diffusion on the climate and spectra of a GCM, Tellus A , 55 , 2003, 31--44. doi:10.1034/j.1600-0870.2003.201329.x

A Preliminary Study of the Burgers Equation with Symbolic Computation

We extend the idea of multiscale large-eddy simulation (LES), the underresolved fluid dynamical simulation that is augmented with a physical description of subgrid-scale (SGS) dynamics. Using a vortex-based SGS model, we consider two areas of specialization: active (buoyant) scalar mixing and wall-bounded turbulence. First, we develop a novel method to perform direct numerical simulation (DNS) of statistically stationary buoyancy-driven turbulence by using the fringe-region technique within a triply periodic domain, in which a mixing region is sandwiched between two fringes that supply the flow with unmixed fluids---heavy on top of light. Spectra exhibit small-scale universality, as evidenced by collapse in inner scales. A comparison with high-resolution DNS spectra from Rayleigh--Taylor turbulence reveals some similarities. We perform LES of this flow to show that a passive scalar SGS model can also be used in an unstably stratified environment. LES spectra, including subgrid extensions, show good agreement with DNS data. For stably stratified flows, we develop an active scalar SGS model by performing a perturbation expansion in small Richardson numbers of the passive scalar SGS model to obtain an expression for the SGS scalar flux that contains buoyancy corrections. We then develop a wall model for LES in which the near-wall region is unresolved. A special near-wall SGS model is constructed by averaging the streamwise momentum equation together with an assumption of local--inner scaling, giving an ordinary differential equation for the local wall shear stress that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stresses due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the off-wall LES boundary conditions. A Karman-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for friction-velocity Reynolds numbers $Rey_ au=2, extrm{k}$--$20, extrm{M}$. Results, including SGS-extended spectra, compare favorably with DNS at Rey_ au=2, extrm{k}$, and maintain an $O(1)$ grid dependence on $Rey_ au$. Finally, we apply the wall model to LES of long channels to capture effects of large-scale structures. Computed correlations are found to be consistent with recent experiments.