arXiv subjects

Preben Buchhave

Publications and source records attributed to Preben Buchhave.

16 recordsLinked to original sources

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 N\"other, 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.

physics.flu-dyn↗

arXiv2024

Dynamic Triad Interactions and Evolving Turbulence -- Part 2: Implications for Practical Signals

We investigate how momentum and kinetic energy is transferred between Fourier components (the so-called triad interactions) in measured turbulent flow fields, i.e. in practical, discretely sampled signals with limited temporal and spatial domains. We empirically observe that the finite resolution in experimental investigations causes a decoupling between time and space, which broadens the phase match condition to include both spatial and temporal frequencies as predicted in Part 1. It is also empirically observed that the Fourier components may interact with a finite time delay and within a broadened frequency window (finite overlap widths) in both time and space, as compared to the usual integrals over infinite ranges where Fourier components interact by overlapping Dirac delta functions. Furthermore, it is empirically observed how the finite temporal and spatial measurement domains of velocity records can have a significant effect on the efficiency of the triad interactions and thereby on the shape and development of measured velocity power spectra. These finite spatial/temporal domains thus influence the measured spatial and temporal development of turbulence, the possibility for non-local interactions and hence also non-equilibrium turbulence, e.g. fractal grid generated turbulence.

physics.flu-dyn↗

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.

physics.flu-dyn↗

arXiv2022

Similarity scaling of the axisymmetric turbulent jet

In the current work, we find that a free axisymmetric jet in air displays self-similarity in the fully developed part of the jet. We report accurate measurements of first, second and third order, spatially averaged statistical functions of the axial velocity component performed with a laser Doppler anemometer, including in the outer (high intensity) regions of the jet. The measurements are compared to predictions derived from a simple jet model, described in a separate publication, and we discuss the implications for the further study of self-similarity in a free jet. It appears that all statistical functions included in this study can be scaled with a single geometrical scaling factor -- the downstream distance from a common virtual origin.

physics.flu-dyn↗

arXiv2021

A similarity scaling model for the axisymmetric turbulent jet based on first principles

Similarity scaling, when it can be justified, is a powerful tool for predicting properties of fluid flows and reducing the computational load when using mathematical models. Numerous publications describe different applications of this method, using often different scaling laws with one or more scaling parameters. The justification for these laws is often based on some assumptions or references to experimental results. In this paper, we base the scaling law on basic physical principles of classical Newtonian physics (Galilei group) and derive some predictions that we apply to a simple model for the axisymmetric turbulent jet. In a companion paper, we compare these predictions to careful measurements on a free jet in the laboratory and evaluate how far our model predictions are borne out by the experimental results. We have succeeded in obtaining such high measurement quality that we can compute both second and third order statistical functions even far downstream and far-off axis. We can already here reveal that we find very good agreement between a simple one-parameter geometric scaling law derived from the model and numerous first order and higher order statistical results computed from the experimental data.

physics.flu-dyn↗

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.

physics.flu-dyn↗

arXiv2020

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.

physics.flu-dyn↗

arXiv2019

Measurement of turbulent spatial structure and kinetic energy spectrum by exact temporal-to-spatial mapping

We present a method for converting a time record of turbulent velocity measured at a point in a flow to a spatial velocity record consisting of consecutive convection elements. The spatial record allows computation of dynamic statistical moments such as turbulent kinetic wavenumber spectra and spatial structure functions in a way that bypasses the need for Taylor's Hypothesis. The spatial statistics agree with the classical counterparts, such as the total kinetic energy spectrum, at least for spatial extents up to the Taylor microscale. The requirements for applying the method is access to the instantaneous velocity magnitude, in addition to the desired flow quantity, and a high temporal resolution in comparison to the relevant time scales of the flow. We map, without distortion and bias, notoriously difficult developing turbulent high intensity flows using three main aspects that distinguish these measurements from previous work in the field; 1) The measurements are conducted using laser Doppler anemometry and are therefore not contaminated by directional ambiguity (in contrast to, e.g., frequently employed hot-wire anemometers); 2) The measurement data are extracted using a correctly and transparently functioning processor and is analysed using methods derived from first principles to provide unbiased estimates of the velocity statistics; 3) The method is first confirmed to produce the correct statistics using computer simulations and later applied to measurements in some of the most difficult regions of a round turbulent jet -- the non-equilibrium developing region and the outermost parts of the developed jet. The measurements in the developing region reveal interesting features of an incomplete Richardson-Kolmogorov cascade under development.

physics.flu-dyn↗

arXiv2019

Estimation of burst-mode LDA power spectra

The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased towards higher values and the signal is highly intermittent. The signal can be interpreted correctly by applying residence time weighting to all statistics and using the residence-time-weighted discrete Fourier transform to compute the Fourier transform. A new spectral algorithm using the latter is applied to two experiments; a cylinder wake and an axisymmetric turbulent jet. These are compared to corresponding hot-wire spectra as well as to alternative algorithms for LDA signals such as the time slot correlation method, sample-and-hold and common weighting schemes.

physics.flu-dyn↗

arXiv2019

The effect of dead time on randomly sampled power spectral estimates

We investigate power spectra of a randomly sampled stationary stochastic signal, e.g. a spatial component of a turbulent velocity. We extend the methods of previous authors that basically assumed point or delta function sampling by including features characteristic of real measurement systems. We consider both the effect on the measured spectrum of a finite sampling time, i.e., a finite time during which the signal is acquired, and a finite dead time, that is a time in which the signal processor is busy evaluating a data point and therefore unable to measure a subsequent data point arriving within the dead time delay.

physics.flu-dyn↗

arXiv2019

Dead time effects in laser Doppler anemometry measurements

We present velocity power spectra computed by the so-called direct method from burst type laser Doppler anemometer (LDA) data, both measured in a turbulent round jet and generated in a computer. Using today's powerful computers we have been able to study more properties of the computed spectra than was previously possible, and we noted some unexpected features of the spectra that we now attribute to the unavoidable influence of a finite measurement volume (MV). The most prominent effect, which initially triggered these studies, was the appearance of damped oscillations in the higher frequency range, starting around the cut-off frequency due to the size of the MV. Using computer generated data mimicking the LDA data, these effects have previously been shown to appear due to the effect of dead time, i.e., the finite time during which the system is not able to acquire new measurements. These dead times can be traced back to the fact that the burst-mode LDA cannot measure more than one signal burst at a time. Since the dead time is approximately equal to the residence time for a particle traversing a measurement volume, we are dealing with widely varying dead times, which, however, are assumed to be measured for each data point. In addition, the detector and processor used in the current study introduce a certain amount of fixed processing and data transfer times, which further contribute to the distortion of the computed spectrum. However, we show excellent agreement between a measured spectrum and our modeled LDA data thereby confirming the validity of our model for the LDA burst processor.

physics.flu-dyn↗

arXiv2019

Reduction of noise and bias in randomly sampled power spectra

We consider the origin of noise and distortions in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and removing spectral bias, e.g. distortions caused by modifications of the ideal Poisson sample rate caused by dead time effects and correlations between velocity and sample rate. The noise and dead time effects for finite records are shown to tend to previous results for infinite time records and ensemble averages. For finite records we show that the measured sampling function can be used to correct the spectra for noise and dead time effects by a deconvolution process. We also describe a novel version of a power spectral estimator based on a fast slotted autocovariance algorithm.

physics.flu-dyn↗

arXiv2019

Dynamic Triad Interactions and Evolving Turbulence -- Part 1: 4D Modal Interactions

We investigate the effect of a four-dimensional Fourier transform on the formulation of the Navier-Stokes equation in Fourier space and the way the energy is transferred between Fourier components. Since time in a sampled high intensity turbulence must be considered a stochastic variable in the energy exchange between scales, we refer to these dynamic triad interactions as modal interactions, rather than the commonly referred to triad interactions in the classical 3-dimensional analysis. The inclusion of time as a parameter broadens the phase match condition from the classical one, $\Delta \bm{k} \cdot \bm{r} = \left [ \bm{k} - (\bm{k}_1 + \bm{k}_2 ) \right ] \cdot \bm{r}$, to the more general formulation that also includes temporal frequencies: $\Delta \bm{k} \cdot \bm{r} - \Delta \omega t = \left [ \bm{k} - (\bm{k}_1 + \bm{k}_2 ) \right ] \cdot \bm{r} - \left [ \omega - \left (\omega_1 + \omega_2 \right ) \right ] t$. This renders possible the occurrence of `delayed' and `advanced' interactions. The observation that mismatches in the wavevector triadic interactions may be compensated by a corresponding mismatch in the frequencies supports the empirically deduced delayed interactions reported in [Josserand \textit{et al.}, \textit{J. Stat. Phys.} (2017)]. These results explain the occurrence and inherent time development of the so-called Richardson cascade and also how finite temporal overlap of wave components can result in significant non-local interactions and consequently non-equilibrium turbulence, e.g., fractal grid generated turbulence. The consequences of including time as a parameter in practical experiments or simulations in terms of limited resolution, domain size etc. are treated in the companion paper (Part 2) of the present work.

physics.flu-dyn↗

arXiv2019

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).

physics.flu-dyn↗

arXiv2007

Generation of Polarization Squeezing with Periodically Poled KTP at 1064 nm

We report the experimental demonstration of directly produced polarization squeezing at 1064 nm from a type I optical parametric amplifier (OPA) based on a periodically poled KTP crystal (PPKTP). The orthogonal polarization modes of the polarization squeezed state are both defined by the OPA cavity mode, and the birefringence induced by the PPKTP crystal is compensated for by a second, but inactive, PPKTP crystal. Stokes parameter squeezing of 3.6 dB and anti squeezing of 9.4 dB is observed.

physics.optics↗

arXiv2003

Squeezing based on nondegenerate frequency doubling internal to a realistic laser

We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second harmonic generation process occuring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions indepedent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.

quant-ph↗