BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies

A methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18, with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features

WMO Global Annual to Decadal Climate Update A Prediction for 2021-25

Under embargo until: 2022-10-01As climate change accelerates, societies and climate-sensitive socioeconomic sectors cannot continue to rely on the past as a guide to possible future climate hazards. Operational decadal predictions offer the potential to inform current adaptation and increase resilience by filling the important gap between seasonal forecasts and climate projections. The World Meteorological Organization (WMO) has recognized this and in 2017 established the WMO Lead Centre for Annual to Decadal Climate Predictions (shortened to “Lead Centre” below), which annually provides a large multimodel ensemble of predictions covering the next 5 years. This international collaboration produces a prediction that is more skillful and useful than any single center can achieve. One of the main outputs of the Lead Centre is the Global Annual to Decadal Climate Update (GADCU), a consensus forecast based on these predictions. This update includes maps showing key variables, discussion on forecast skill, and predictions of climate indices such as the global mean near-surface temperature and Atlantic multidecadal variability. it also estimates the probability of the global mean temperature exceeding 1.5°C above preindustrial levels for at least 1 year in the next 5 years, which helps policy-makers understand how closely the world is approaching this goal of the Paris Agreement. This paper, written by the authors of the GADCU, introduces the GADCU, presents its key outputs, and briefly discusses its role in providing vital climate information for society now and in the future.publishedVersio

Stochastic Parameterization Toward a New View of Weather and Climate Models

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Recent applications and potential of near-term (interannual to decadal) climate predictions

Following efforts from leading centres for climate forecasting, sustained routine operational near-term climate predictions (NTCP) are now produced that bridge the gap between seasonal forecasts and climate change projections offering the prospect of seamless climate services. Though NTCP is a new area of climate science and active research is taking place to increase understanding of the processes and mechanisms required to produce skillful predictions, this significant technical achievement combines advances in initialisation with ensemble prediction of future climate up to a decade ahead. With a growing NTCP database, the predictability of the evolving externally-forced and internally-generated components of the climate system can now be quantified. Decision-makers in key sectors of the economy can now begin to assess the utility of these products for informing climate risk and for planning adaptation and resilience strategies up to a decade into the future. Here, case studies are presented from finance and economics, water management, agriculture and fisheries management demonstrating the emerging utility and potential of operational NTCP to inform strategic planning across a broad range of applications in key sectors of the global economy

Recovery of fluid mechanical modes in unsteady separated flows

© 2010 Dr. Vassili KitsiosCompleted under a Cotutelle arrangement between the University of Melbourne and the Universite de PoitiersThis study is concerned with the recovery of fluid mechanical modes that can be used to describe the physical properties of unsteady separated flows. The flow configuration of interest is a spanwise homogeneous NACA 0015 airfoil with leading edge laminar separation and turbulent recirculation. An in-depth understanding of the unsteady flow dynamics and fluid mechanical stability properties, can assist in the future development of more efficient separation control strategies. In order to provide a richer understanding of the physics, the flow fields are numerically generated, and characterised at various key Reynolds numbers leading up to the target turbulent case. Proper Orthogonal Decomposition modes are recovered to most efficiently represent the unsteady scales of motion, and linear stability modes are sought to identify how a perturbation will evolve in this unsteady environment. The generation of the Proper Orthogonal Decomposition modes can require very large amounts of data, and the current study presents a means of recovering these modes using parallel computation. To enable the stability analysis, a means of performing the calculation in steady two-dimensional flows of semi-complex geometry has been developed. The corrections required to perform the stability analysis in unsteady turbulent flows has also been identified by using a non-linear eddy viscosity model to close the triple decomposition stability equations. It is intended that the means of recovering these fluid mechanical modes can assist in the future development of reduced order models necessary for the control of unsteady separated flows

Subgrid parameterisations for high resolution atmospheric flows

Numerical and computational methods are developed for the Large Eddy Simulation of atmospheric flows on a sphere with a spectral quasigeostrophic model. The subgrid scales of motion are parameterised using a net eddy viscosity that is derived from a high resolution reference Direct Numerical Simulation with $504$~zonal and total wavenumbers or $1536 \times 768$ grid points (longitude by latitude). Simulations are undertaken for a wide range of truncation wavenumbers to determine the influence of resolution on the net eddy viscosity. A universal scaling law for these coefficients is established for application to large eddy simulations of more general geophysical flows. References J. S. Frederiksen. Precursors to blocking anomalies: the tangent linear and inverse problems. J. Atmos. Sci., 55:2419--2436, 1998. doi:10.1175/1520-0469(1998)055<2419:PTBATT>2.0.CO;2 J. S. Frederiksen. Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity and stochastic backscatter for flow over topography. J. Atmos. Sci, 56:1481--1493, 1999. doi:10.1175/1520-0469(1999)056<1481:SSPOET>2.0.CO;2 J. S. Frederiksen and A. G. Davies. Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models. J. Atmos. Sci, 54:2475--2492, 1997. doi:10.1175/1520-0469(1997)054<2475:EVASBP>2.0.CO;2 J. S. Frederiksen and S. M. Kepert. Dynamical subgrid-scale parameterizations from {Direct Numerical Simulations}. J. Atmos. Sci., 63:3006--3019, 2006. doi:10.1175/JAS3795.1 C. E. Leith. Stochastic backscatter in a subgrid-scale model: Plane shear mixing layer. Phys. Fluids, 2(3):297--299, 1990. doi:10.1063/1.857779 J. Smagorinsky. General circulation experiments with the primitive equations: I. the basic experiment. Mon. Wea. Rev., 91(3):99--164, 1963. doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 M. J. Zidikheri and J. S. Frederiksen. Stochastic subgrid parameterizations for simulations of atmospheric baroclinic flows. J. Atmos. Sci., 66:2844--2858, 2009. doi:10.1175/2009JAS303

Subgrid parameterisation of the eddy-meanfield interactions in a baroclinic quasi-geostrophic ocean

We present parameterisations of the subgrid eddy-eddy and eddy-meanfield interactions in a baroclinic ocean representative of the Antarctic Circumpolar Current. Benchmark direct numerical simulations were undertaken using a quasi-geostrophic spectral spherical harmonic code of maximum zonal and total truncation wavenumber of $T=252\,$. The eddy-eddy interactions are represented by both stochastic and deterministic parameterisations, with model coefficients determined from the direct numerical simulations truncated back to the large eddy simulation truncation wavenumber $T_R$ less than $T$. Coefficients of the deterministic eddy-meanfield model are determined by a new least squares regression method. Truncations were repeated for various $T_R$, with the dependence of the coefficients on $T_R$ identified. Kinetic energy spectra from the large eddy simulations using these coefficients agree with the direct numerical simulations. References K. Bryan and J. L. Lewis. A water mass model of the global ocean. J. Geophys. Res., 84:2503--2517 (1979). doi:10.1029/JC084iC05p02503 J. S. Frederiksen. Precursors to blocking anomalies: the tangent linear and inverse problems. J. Atmos. Sci., 55:2419--2436 (1998). doi:10.1175/1520-0469(1998)055<2419:PTBATT>2.0.CO;2 J. S. Frederiksen. Self-energy closure for inhomogeneous turbulence and subgrid modeling. Entropy, 14:769--799 (2012). doi:10.3390/e14040769 J. S. Frederiksen and S. M. Kepert. Dynamical subgrid-scale parameterizations from direct numerical simulations. J. Atmos. Sci., 63:3006--3019 (2006). doi:10.1175/JAS3795.1 P. R. Gent and J. C. McWilliams. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20:150--155 (1990). doi:10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2 S. M. Griffies, A. Gnanadesikan, K. W. Dixon, J. P. Dunne, R. Gerdes, M. J. Harrison, A. Rosati, J. L. Russell, B. L. Samuels, M. J. Spelman, M. Winton, and R. Zhang. Formulation of an ocean model for global climate simulations. Ocean Science, 1:45--79 (2005). doi:10.5194/os-1-45-2005 V. Kitsios, J. S. Frederiksen, and M. J. Zidikheri. Scaling laws for parameterisations of subgrid eddy-eddy interactions in simulations of oceanic circulations. Ocean Modelling, in print (2013). J. N. Koshyk and K. Hamilton. The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere-stratosphere-mesosphere GCM. J. Atmos. Sci., 58:329--348 (2001). doi:10.1175/1520-0469(2001)058<0329:THKESA>2.0.CO;2 M. H. Redi. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12:1154--1158 (1982). doi:10.1175/1520-0485(1982)012<1154:OIMBCR>2.0.CO;2 M. J. Zidikheri and J. S. Frederiksen. Stochastic modelling of unresolved eddy fluxes. Geophysical and Astrophysical Fluid Dynamics, 104:323--348 (2010). doi:10.1080/03091921003694701 M. J. Zidikheri and J. S. Frederiksen. Stochastic subgrid-scale modelling for non-equilibrium geophysical flows. Phil. Trans. Royal Soc. A, 368:145--160 (2010). doi:10.1098/rsta.2009.019

Subgrid parameterisations for primitive equation atmospheric models

Dynamical and thermodynamical subgrid-scale parameterisations of eddy drain, net dissipation and stochastic backscatter are calculated for a multi-level primitive equation atmospheric general circulation model. The parameterisations have only moderate variability with height and a cusp behaviour with peaks near the largest retained wavenumber. Vertically integrated net dissipation functions for vorticity and temperature are very similar to corresponding results for barotropic simulations while the divergence dissipation is nearly four times stronger. Atmospheric general circulation model simulations with the new subgrid model improve kinetic energy spectra and zonal flows compared with control simulations. References J. S. Frederiksen. Self-energy closure for inhomogeneous turbulence and subgrid modelling. Entropy 14:769–799, 2012. doi:10.3390/e14040769 J. S. Frederiksen and A. G. Davies. Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models. J. Atmos. Sci 54:2475–2492, 1997. doi:10.1175/1520-0469(1997)054<2475:EVASBP>2.0.CO;2 J. S. Frederiksen and S. M. Kepert. Dynamical subgrid-scale parameterizations from direct numerical simulations. J. Atmos. Sci. 63:3006–3019, 2006. doi:10.1175/JAS3795.1 J. S. Frederiksen, T. J. O'Kane and M. J. Zidikheri. Stochastic subgrid parameterizations for atmospheric and oceanic flows. Phys. Scripta 85:068202, 2012. doi:10.1088/0031-8949/85/06/068202 J. S. Frederiksen, M. R. Dix and S. M. Kepert. Systematic energy errors and the tendency toward canonical equilibrium in atmospheric circulation models. J. Atmos. Sci. 53:887–904, 1996. doi:10.1175/1520-0469(1996)053<0887:SEEATT>2.0.CO;2 I. M. Held, and M. J. Suarez. A proposal for the intercomparison of the dynamical cores of atmospheric general circulation models. Bull. Am. Met. Soc. 75:1825–1830, 1994. doi:10.1175/1520-0477(1994)075<1825:APFTIO>2.0.CO;2 V. Kitsios, J. S. Frederiksen and M. J. Zidikheri. Scaling laws for parameterisations of subgrid eddy-eddy interactions in simulations of oceanic circulations. Ocean Model. 68:88–105, 2013. doi:10.1016/j.ocemod.2013.05.001 V. Kitsios, J. A. Sillero, J. S. Frederiksen and J. Soria. Proposed stochastic parameterisations of subgrid turbulence in large eddy simulations of turbulent channel flow. J. Turbulence 16:729–741, 2015. doi:10.1080/14685248.2015.1026970 J. L. McGregor, H. B. Gordon, I. G. Watterson, M. R. Dix and L. D. Rotstayn. The csiro 9-level atmospheric general circulation model. csiro Division of Atmospheric Research, Technical Report 26, 1993. https://publications.csiro.au/rpr/pub?list=BRO&pid=procite:d73112b4-4d15-481b-84c5-f488501e7e07 I. N. Smith, M. R. Dix and R. J. Allen. The effect of greenhouse SSTs on ENSO simulations with an agcm. J. Climate 10:342–352, 1997. doi:10.1175/1520-0442(1997)010<0342:TEOGSO>2.0.CO;