arXiv subjects

Clara Marika Velte

Publications and source records attributed to Clara Marika Velte.

7 recordsLinked to original sources

arXiv2025

Generative Super-Resolution of Turbulent Flows via Stochastic Interpolants

Capturing the intricate multiscale features of turbulent flows remains a fundamental challenge due to the limited resolution of experimental data and the computational cost of high-fidelity simulations. In many practical scenarios only coarse representations of the flows are feasible, leaving crucial fine-scale dynamics unresolved. This study addresses that limitation by leveraging generative models to perform super-resolution of velocity fields and reconstruct the unresolved scales from low-resolution conditionals. In particular, the recently formalized stochastic interpolants are employed to super-resolve a case study of two-dimensional turbulence. Key to our approach is the iterative application of stochastic interpolants over local patches of the flow field, that enables efficient reconstruction without the need to process the full domain simultaneously. The patch-wise strategy is shown to yield physically consistent super-resolved flow snapshots, and key statistical quantities -- such as the kinetic energy spectrum and the spatially averaged dissipation rate -- are accurately recovered. Moreover, compared with full-field reconstruction, the patch-wise approach produces higher-quality super-resolutions, and, in general, stochastic interpolants are observed to outperform contesting generative models across a range of metrics. These results establish stochastic interpolants as a viable tool for super-resolving turbulent flows and highlight their potential for future applications.

physics.flu-dyn↗

arXiv2025

The role of symmetries in the axisymmetric jet mean velocity profile development

The fact that physical conservation laws can be derived from symmetry properties of space and time, as shown by Emily Nöther, has been utilized in predicting the development of the round turbulent jet from the jet exit to the far field. In particular, the developing region has been described using an analytical approach in combination with using a numerical recursive program. Both approaches assume that the only forces acting on the flow are internal shear forces in a Newtonian constant density fluid. The analytical and numerical predictions both display excellent agreement with carefully conducted measurements. The jet spreading angle is observed to be directly coupled to the turbulent momentum diffusion, hence the spreading rate depends on the upstream, or initial, conditions. The jet entrainment and momentum rate are both observed to be constant, even across the developing jet. Since the solution of the jet development depends on the initial conditions, the total (molecular and turbulent) viscosity and the initial velocity profile must be input into the analytical or numerical solver to obtain the correct solution. The Reynolds number is observed to not enter into the analytical or numerical solution and experiments confirm that the jet spreading is independent of the Reynolds number in the tested range, $Re = 3\,200 - 32\,000$. We emphasize that our results do not rely on any assumptions of self-similarity or prior knowledge about the jet from experiments, only the Galilei symmetry properties, and that the results are valid throughout the jet.

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arXiv2023

Dissipation-based proper orthogonal decomposition of turbulent Rayleigh-Bénard convection flow

We present a formulation of proper orthogonal decomposition (POD) producing a velocity-temperature basis optimized with respect to an $H^1$ dissipation norm. This decomposition is applied, along with a conventional POD optimized with respect to an $L^2$ energy norm, to a data set generated from a direct numerical simulation of Rayleigh-Bénard convection in a cubic cell ($\mathrm{Ra}=10^7$, $\mathrm{Pr}=0.707$). The data set is enriched using symmetries of the cell, and we formally link symmetrization to degeneracies and to the separation of the POD bases into subspaces with distinct symmetries. We compare the two decompositions, demonstrating that each of the 20 lowest dissipation modes is analogous to one of the 20 lowest energy modes. Reordering of modes between the decompositions is limited, although a corner mode known to be crucial for reorientations of the large-scale circulation is promoted in the dissipation decomposition, indicating suitability of the dissipation decomposition for capturing dynamically important structures. Dissipation modes are shown to exhibit enhanced activity in boundary layers. Reconstructing kinetic and thermal energy, viscous and thermal dissipation, and convective heat flux, we show that the dissipation decomposition improves overall convergence of each quantity in the boundary layer. Asymptotic convergence rates are nearly constant among the quantities reconstructed globally using the dissipation decomposition, indicating that a range of dynamically relevant scales are efficiently captured. We discuss the implications of the findings for using the dissipation decomposition in modeling, and argue that the $H^1$ norm allows for a better modal representation of the flow dynamics.

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arXiv2023

Triad interactions investigated by dual vortex shedding

The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been carried out by Direct Numerical Simulations or by power spectral measurements. Due to the complexity of the problem and the great range of velocity scales in high Reynolds number developed turbulence, direct measurements of the interaction between the individual wave components have been rare. In the present work, we therefore present measurements and related computer simulations of triad interactions between controlled wave components injected into an approximately laminar and uniform flow from an open wind tunnel by vortex shedding from two rods suspended into the flow. This well-defined vortex shedding approximates well a two-dimensional flow, which makes the analysis of the triadic interactions considerably less complex to analyze than in a fully developed spatially three-dimensional flow. With the information obtained from the simulations, we are hereby able to isolate and display the individual triad interactions taking place as the flow develops downstream as well as the strengths of these interactions. The experiments provide the time constants governing the development of higher order frequency components. The combination of these experiments and simulations provide unique insight into the inner workings of turbulence and shows how the nonlinear term in the Navier-Stokes equation on average forces the energy towards higher frequencies, which is the reason for the so-called energy cascade.

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arXiv2022

Understanding developing turbulence by a study of the nonlinear energy transfer in the Navier-Stokes equation

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear term are presented and discussed. The calculations take the full 4D flow as its starting point and continuously projects the forces acting on the fluid at a fixed Eulerian point in a stationary coordinate system onto the direction of the instantaneous velocity. Pressure is included through modeling. Adhering to the requirement that time must in general be considered an independent variable, the time development of the time records and power spectra of the velocity fluctuations are studied. It is found that the actions of the nonlinear term in the Navier-Stokes equation manifests itself by generating sharp pulses in the time traces, where the sharpness is bounded by the finite viscosity. In the spectral domain, the sharp gradients in the pulses generate energy contributions at high frequencies that yields a $-2$ slope across the inertial range. The $-2$ (or $-6/3$) slope is explained through a simple example and the classically expected $-5/3$ slope in the inertial range can be recovered from the pressure fluctuations from the full flow field that can be considered a noise contribution at the point considered. We also observe that the spectrum can in principle keep spreading to higher frequencies or wavenumbers without upper bound, as the viscosity is approaching the zero limit.

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arXiv2021

A novel laser Doppler anemometer (LDA) for high-accuracy turbulence measurements

High accuracy and dynamic range have been some of the most prominent challenges when it comes to fine-scale turbulence measurements. The current commercial LDA processors, which perform the signal processing of Doppler bursts directly using hardware components, are essentially black boxes and in particular are renown for suffering from practical limitations that reduce the measurement reliability and accuracy. A transparently functioning novel LDA, utilizing advanced technologies and up-to-date hardware and software has therefore been developed to enhance the measurement quality and the dynamic range. In addition, the self-developed software comes with a highly flexible functionality for the signal processing and data interpretation. The LDA setup and the combined forward/side scattering optical alignment (to minimize the effective measuring volume) are described first, followed by a description of the signal processing aspects. The round turbulent jet has been used as the test bed since it presents a wide range of degree of difficulty for the LDA processor (accuracy, dynamic range etc.) across the different radial distances and downstream development. The data are diagnosed for dynamic range in residence and interarrival times, and compared to a typical hardware driven processor. The radial profiles of measured mean streamwise velocity and variance agree well with previous studies of the round jet. The spatial turbulent kinetic energy spectra in the fully developed region perfectly match the expected (and in this region well established) -5/3 power law even for the largest measured distances from the centerline (where shear and turbulence intensity are significant).

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arXiv2020

Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

The current work presents an experimental investigation of the dynamic interactions between flow scales caused by repeated actions of the nonlinear term of the Navier-Stokes equation. Injecting a narrow band oscillation, representing a single Fourier mode, into a round jet flow allows the measurement of the downstream generation and development of higher harmonic spectral components and to measure when these components are eventually absorbed into fully developed turbulence. Furthermore, the dynamic evolution of the measured power spectra observed corresponds well to the measured cascaded delays reported by others. Closely matching spectral development and cascade delays have also been derived directly from a one-dimensional solution of the Navier-Stokes equation described in a companion paper. The results in the current work provide vital information about how initial conditions influence development of the shape of the spectrum and about the extent of the time scales in the triad interaction process, which should be of significance to turbulence modelers.

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