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Papers by Sebastian Remmler

High Performance Computing in Science and Engineering ‘14, 2014

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and cor... more As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study.

The differentially heated rotating annulus is a classical experiment for the investigation of bar... more The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure. Both models employ an implicit parameterization of the subgrid-scale turbulence by the Adaptive Local Deconvolution Method (ALDM). One part of the laboratory procedure, which is commonly neglected in simulations, is the annulus spin-up. During this phase the annulus is accelerated from a state of rest to a desired angular velocity. We use a simple modelling approach of the spin-up to investigate whether it increases the agreement between experiment and simulation. The model validation compares the azimuthal mode numbers of the baroclinic waves and does a principal component analysis of time series of the temperature field. The Eady model of baroclinic instability provides a guideline for the qualitative understanding of the observations.

Fluid Mechanics and Its Applications, 1994

ABSTRACT

Dynamics of Atmospheres and Oceans, 1996

... Sci., 41: 2202-2216. Nieuwstadt, FTM, Mason, PJ, Moeng, C.-H. and Schumann, U., 1993. ... Lar... more ... Sci., 41: 2202-2216. Nieuwstadt, FTM, Mason, PJ, Moeng, C.-H. and Schumann, U., 1993. ... Large-eddy simulation of turbulent convection over flat and wavy terrain. In: B. Galperin and SA Orszag (Editors), Large Eddy Simulation of Complex Engineering and Geophysi-cal Flows. ...

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric iner... more A systematic approach to the direct numerical simulation (DNS) of breaking upper
mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is
presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase
velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and
structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional
velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is
then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to
three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the
computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to
breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day
computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave,
a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity
wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of
the wave and generation of turbulence is faster in three dimensions, but the results are otherwise
qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the
domain and initial condition are chosen properly.

The dynamics of three-dimensional turbulence under the influence of density stratification can be... more The dynamics of three-dimensional turbulence under the influence of density stratification can be classified in different regimes that differ fundamentally; see Brethouwer et al. (2007) for a good review. Up to now, strongly stratified turbulent flows were mainly studied by direct numerical simulations (DNS). The available computer resources, however, limit the application of DNS to Reynolds numbers that are too small for studying the regime of real scale atmospheric problems. Large Reynolds number flows in general can be simulated efficiently by large- eddy simulation (LES). However, most subgrid-scale (SGS) models for LES are not suitable for stratified flows, as local isotropy of the SGS turbulence is assumed, and therefore require ad-hoc modifications. We propose an implicit subgrid-scale model that handles anisotropic turbulence in a straight forward way without any limiting assumptions.
We solve the non-linear Boussinesq equations for a fluid with a constant background stratification using a finite- volume solver. DNS are performed with a 4th order centered scheme. The implicit sub-grid scale model is based on the Adaptive Local Deconvolution Method (ALDM) for the incompressible Navier-Stokes equations (Hickel et al. 2006) and the ALDM for passive scalar transport (Hickel et al. 2007). The turbulence theoretical background of ALDM and the numerical details will be given in the full paper.
Two generic test cases are considered. First, we computed the temporal evolution of a 3D Taylor-Green-vortex (Brachet 1991) under the influence of stratification. We ran several fully resolved simulations with up to 7683 cells and corresponding implicit LES with 643 cells. The LES show good agreement with a fully resolved DNS. The total dissipation rate is predicted correctly and also the proportions of kinetic and potential energy are well estimated. We repeated the LES and DNS at a number of different Froude and Reynolds numbers. In all cases we found good agreement between LES and DNS.
As a second test case, we computed homogeneous stratified turbulence (Brethouwer et al. 2007) at different Froude numbers. The Boussinesq equations are supplemented by a volume force that acts on the large horizontal scales only. Three-dimensional structures with finite vertical length scale develop only due to stratification. To ensure complete resolution of the smallest scales, the DNS domain contained about 900 million cells. We studied the influence of varying stratification on the averaged longitudinal kinetic energy spectra in the vertical and horizontal directions.
We will discuss the energy budget, dissipation rates, spectra of turbulence, turbulence length scales, and anisotropy of the DNS and draw conclusions with respect to SGS modeling. Our computational results support that implicit LES with ALDM can be a suitable tool for the investigation of stratified turbulence. This will enable us to compute and characterize atmospheric turbulence beyond the reach of DNS with reasonable accuracy at low computational costs.

In order to reduce the computational costs of numerical studies of gravity wave breaking in the a... more In order to reduce the computational costs of numerical studies of gravity wave breaking in the atmosphere, the grid resolution has to be reduced as much as possible. Insufficient resolution of small-scale turbulence demands a proper turbulence parametrisation in the framework of large-eddy simulation (LES). We validate three different LES methods - the Adaptive Local Deconvolution Method (ALDM), the dynamic Smagorinsky method (DSM) and a naïve central discretisation without turbulence parametrisation (CDS4) - for three different cases of the breaking of well defined monochromatic gravity waves. For ALDM we developed a modification of the numerical flux functions that significantly improves the simulation results in case of a temporarily very smooth velocity field. The test cases include an unstable and a stable inertia-gravity wave as well as an unstable high-frequency gravity wave. All simulations are carried out both in three-dimensional domains and in two-dimensional domains in which the velocity and vorticity fields are three dimensional (so-called 2.5-D simulations). We find that results obtained with ALDM and DSM are generally in good agreement with the reference direct numerical simulations as long as the resolution in the direction of the wave vector is sufficiently high. The resolution in the other directions has a weaker influence on the results. The simulations without turbulence parametrisation are only successful if the resolution is high and the level of turbulence comparatively low.

We have performed fully resolved three-dimensional numerical simulations of a statically unstable... more We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence... more Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.

Density stratification has a strong impact on turbulence in geophysical flows. Stratification change... more Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate
simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with
direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.

Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence... more Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence modeling. We propose an implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method. To validate this turbulence model, we performed direct numerical simulations of the transition of the three-dimensional Taylor--Green vortex and homogeneous stratified turbulence. Our analysis proves that the implicit turbulence model correctly predicts the turbulence energy budget and the spectral structure of stratified turbulence.

Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyanc... more Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyancy forces make the energy spectra anisotropic and change the way in which energy
is converted and transported within the spectrum. Based on results of direct numerical simulations of homogeneous stratified turbulence, we show two–dimensional energy spectra at different intensities of stratification. Additionally, we analyze the spectral contribution of the different terms in the energy transport equations to the overall energy budget and trace the flow energy through all its conversions and transport in spectral
space from the injection at large scales to the molecular dissipation on small scales.

AIAA journal, Jan 1, 2010

A method is proposed to calculate the trailing-edge broadband noise emitted from an airfoil, base... more A method is proposed to calculate the trailing-edge broadband noise emitted from an airfoil, based on a steady Reynolds-averaged Navier-Stokes solution of the flowfield. For this purpose, the pressure spectrum on the airfoil surface near the trailing edge is calculated using a statistical model from the Reynolds-averaged Navier-Stokes mean velocity and turbulence data in the airfoil boundary layer. The obtained wall-pressure spectrum is used to compute the radiated sound by means of an aeroacoustic analogy, namely, Amiet's theory of airfoil sound. The statistical model for wall-pressure fluctuations is validated with two test cases from the literature, a boundary layer with an adverse pressure gradient, and a flat plate boundary layer without a pressure gradient. The influence of specific model assumptions is studied, such as the convection velocity of pressure-producing structures and the scale anisotropy of boundary-layer turbulence. Furthermore, the influence of the Reynolds-averaged Navier-Stokes simulation on the calculated spectra is investigated using three different turbulence models. The method is finally applied to the case of a Valeo controlled-diffusion airfoil placed in a jet wind tunnel in the anechoic facility of École Centrale de Lyon. Reynolds-averaged Navier-Stokes solutions for this test case are computed with different turbulence models, the wall-pressure spectrum near the trailing edge is calculated using the statistical model, and the radiated noise is computed with Amiet's theory. All intermediate results of the method are compared with experimental data.

High Performance Computing in Science and Engineering ‘14, 2014

As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and cor... more As inertia-gravity waves we refer to gravity waves that have a sufficiently low frequency and correspondingly large horizontal wavelength to be strongly influenced by the Coriolis force. Inertia-gravity waves are very active in the middle atmosphere and their breaking is potentially an important influence on the circulation in this region. The parametrization of this process requires a good theoretical understanding, which we want to enhance with the present study.

The differentially heated rotating annulus is a classical experiment for the investigation of bar... more The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure. Both models employ an implicit parameterization of the subgrid-scale turbulence by the Adaptive Local Deconvolution Method (ALDM). One part of the laboratory procedure, which is commonly neglected in simulations, is the annulus spin-up. During this phase the annulus is accelerated from a state of rest to a desired angular velocity. We use a simple modelling approach of the spin-up to investigate whether it increases the agreement between experiment and simulation. The model validation compares the azimuthal mode numbers of the baroclinic waves and does a principal component analysis of time series of the temperature field. The Eady model of baroclinic instability provides a guideline for the qualitative understanding of the observations.

Fluid Mechanics and Its Applications, 1994

ABSTRACT

Dynamics of Atmospheres and Oceans, 1996

... Sci., 41: 2202-2216. Nieuwstadt, FTM, Mason, PJ, Moeng, C.-H. and Schumann, U., 1993. ... Lar... more ... Sci., 41: 2202-2216. Nieuwstadt, FTM, Mason, PJ, Moeng, C.-H. and Schumann, U., 1993. ... Large-eddy simulation of turbulent convection over flat and wavy terrain. In: B. Galperin and SA Orszag (Editors), Large Eddy Simulation of Complex Engineering and Geophysi-cal Flows. ...

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric iner... more A systematic approach to the direct numerical simulation (DNS) of breaking upper
mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is
presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase
velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and
structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional
velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is
then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to
three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the
computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to
breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day
computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave,
a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity
wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of
the wave and generation of turbulence is faster in three dimensions, but the results are otherwise
qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the
domain and initial condition are chosen properly.

The dynamics of three-dimensional turbulence under the influence of density stratification can be... more The dynamics of three-dimensional turbulence under the influence of density stratification can be classified in different regimes that differ fundamentally; see Brethouwer et al. (2007) for a good review. Up to now, strongly stratified turbulent flows were mainly studied by direct numerical simulations (DNS). The available computer resources, however, limit the application of DNS to Reynolds numbers that are too small for studying the regime of real scale atmospheric problems. Large Reynolds number flows in general can be simulated efficiently by large- eddy simulation (LES). However, most subgrid-scale (SGS) models for LES are not suitable for stratified flows, as local isotropy of the SGS turbulence is assumed, and therefore require ad-hoc modifications. We propose an implicit subgrid-scale model that handles anisotropic turbulence in a straight forward way without any limiting assumptions.
We solve the non-linear Boussinesq equations for a fluid with a constant background stratification using a finite- volume solver. DNS are performed with a 4th order centered scheme. The implicit sub-grid scale model is based on the Adaptive Local Deconvolution Method (ALDM) for the incompressible Navier-Stokes equations (Hickel et al. 2006) and the ALDM for passive scalar transport (Hickel et al. 2007). The turbulence theoretical background of ALDM and the numerical details will be given in the full paper.
Two generic test cases are considered. First, we computed the temporal evolution of a 3D Taylor-Green-vortex (Brachet 1991) under the influence of stratification. We ran several fully resolved simulations with up to 7683 cells and corresponding implicit LES with 643 cells. The LES show good agreement with a fully resolved DNS. The total dissipation rate is predicted correctly and also the proportions of kinetic and potential energy are well estimated. We repeated the LES and DNS at a number of different Froude and Reynolds numbers. In all cases we found good agreement between LES and DNS.
As a second test case, we computed homogeneous stratified turbulence (Brethouwer et al. 2007) at different Froude numbers. The Boussinesq equations are supplemented by a volume force that acts on the large horizontal scales only. Three-dimensional structures with finite vertical length scale develop only due to stratification. To ensure complete resolution of the smallest scales, the DNS domain contained about 900 million cells. We studied the influence of varying stratification on the averaged longitudinal kinetic energy spectra in the vertical and horizontal directions.
We will discuss the energy budget, dissipation rates, spectra of turbulence, turbulence length scales, and anisotropy of the DNS and draw conclusions with respect to SGS modeling. Our computational results support that implicit LES with ALDM can be a suitable tool for the investigation of stratified turbulence. This will enable us to compute and characterize atmospheric turbulence beyond the reach of DNS with reasonable accuracy at low computational costs.

In order to reduce the computational costs of numerical studies of gravity wave breaking in the a... more In order to reduce the computational costs of numerical studies of gravity wave breaking in the atmosphere, the grid resolution has to be reduced as much as possible. Insufficient resolution of small-scale turbulence demands a proper turbulence parametrisation in the framework of large-eddy simulation (LES). We validate three different LES methods - the Adaptive Local Deconvolution Method (ALDM), the dynamic Smagorinsky method (DSM) and a naïve central discretisation without turbulence parametrisation (CDS4) - for three different cases of the breaking of well defined monochromatic gravity waves. For ALDM we developed a modification of the numerical flux functions that significantly improves the simulation results in case of a temporarily very smooth velocity field. The test cases include an unstable and a stable inertia-gravity wave as well as an unstable high-frequency gravity wave. All simulations are carried out both in three-dimensional domains and in two-dimensional domains in which the velocity and vorticity fields are three dimensional (so-called 2.5-D simulations). We find that results obtained with ALDM and DSM are generally in good agreement with the reference direct numerical simulations as long as the resolution in the direction of the wave vector is sufficiently high. The resolution in the other directions has a weaker influence on the results. The simulations without turbulence parametrisation are only successful if the resolution is high and the level of turbulence comparatively low.

We have performed fully resolved three-dimensional numerical simulations of a statically unstable... more We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence... more Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.

Density stratification has a strong impact on turbulence in geophysical flows. Stratification change... more Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate
simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with
direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.

Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence... more Simulation of geophysical turbulent flows requires a robust and accurate subgrid-scale turbulence modeling. We propose an implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method. To validate this turbulence model, we performed direct numerical simulations of the transition of the three-dimensional Taylor--Green vortex and homogeneous stratified turbulence. Our analysis proves that the implicit turbulence model correctly predicts the turbulence energy budget and the spectral structure of stratified turbulence.

Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyanc... more Stable density stratification has a strong effect on the properties of turbulence in fluids. Buoyancy forces make the energy spectra anisotropic and change the way in which energy
is converted and transported within the spectrum. Based on results of direct numerical simulations of homogeneous stratified turbulence, we show two–dimensional energy spectra at different intensities of stratification. Additionally, we analyze the spectral contribution of the different terms in the energy transport equations to the overall energy budget and trace the flow energy through all its conversions and transport in spectral
space from the injection at large scales to the molecular dissipation on small scales.

AIAA journal, Jan 1, 2010

A method is proposed to calculate the trailing-edge broadband noise emitted from an airfoil, base... more A method is proposed to calculate the trailing-edge broadband noise emitted from an airfoil, based on a steady Reynolds-averaged Navier-Stokes solution of the flowfield. For this purpose, the pressure spectrum on the airfoil surface near the trailing edge is calculated using a statistical model from the Reynolds-averaged Navier-Stokes mean velocity and turbulence data in the airfoil boundary layer. The obtained wall-pressure spectrum is used to compute the radiated sound by means of an aeroacoustic analogy, namely, Amiet's theory of airfoil sound. The statistical model for wall-pressure fluctuations is validated with two test cases from the literature, a boundary layer with an adverse pressure gradient, and a flat plate boundary layer without a pressure gradient. The influence of specific model assumptions is studied, such as the convection velocity of pressure-producing structures and the scale anisotropy of boundary-layer turbulence. Furthermore, the influence of the Reynolds-averaged Navier-Stokes simulation on the calculated spectra is investigated using three different turbulence models. The method is finally applied to the case of a Valeo controlled-diffusion airfoil placed in a jet wind tunnel in the anechoic facility of École Centrale de Lyon. Reynolds-averaged Navier-Stokes solutions for this test case are computed with different turbulence models, the wall-pressure spectrum near the trailing edge is calculated using the statistical model, and the radiated noise is computed with Amiet's theory. All intermediate results of the method are compared with experimental data.