A Review of Rapid Distortion Theory

With the depleting non-renewable fuel sources like coal and an ever-increasing demand for energy, we need to start looking into renewable energy sources. These are of paramount importance for a sustainable and green future. Wind Energy is one of the most important sources of renewable energy. But, setting up a wind farm requires considerable land area and land acquisitions are often faced with legal hurdles. This necessitates setting up offshore wind turbines. But, when we talk about offshore wind farms, we need to address the age-old phenomenon: “Turbulence”. Presently, we are trying to develop enhanced controllers for wind farms which will increase the efficiency of the wind farms. The effects of rapidly changing wake aerodynamics i.e. breakdown of strong tip and hub vortices mixed up with low intensity turbulence in the inflow of the rotor and counter-rotation of the wake i.e. determinate velocity component in wake turbulence field will affect the overall performance of the wind farm. This paper provides a brief review on Rapid Distortion Theory (RDT) to model the turbulence.

Experimental study of Wave-turbulence interaction

<p>Turbulence is ubiquitous in the topmost skin of the ocean, where it interacts with surface waves. Rapid distortion theory predicts that wave motion will increase turbulent energy, leading to a dissipation of waves [1]. Waves are believed to contribute significantly to the turbulence in the ocean mixed layer, yet field measurements are unable to validate or distinguish between models and theories [2].</p><p>In this work we study the modification of turbulence by surface waves using experimental measurements of turbulent flows in the presence of waves, in a laboratory set-up acting as a small-scale model of the water side of the ocean surface layer. Turbulent Langmuir numbers comparable to those in the ocean are achieved, ensuring scalability. Particle image velocimetry (PIV) measurements were performed in a large water channel wherein mechanically generated waves may propagate on a current. An active grid at the inlet allowed the turbulence intensity and mean flow to be tailored independently. The flow field was measured in the streamwise-vertical plane for various flow cases and waves of varying steepness and frequency. The turbulence characteristics are compared to cases without waves to study the impact of the waves on the turbulence and the results are discussed considering predictions from rapid distortion theory.</p><p> </p><p>[1] Teixeira M. and S. Belcher 2002 “On the distortion of turbulence by a progressive surface wave” Journal of Fluid Mechanics  <strong>458 </strong>229-267.</p><p>[2] D’Asaro E.A. 2014 “Turbulence in the upper-ocean mixed layer” Annual Reivew of Marine Sciences <strong>6 </strong>101-115.</p>

Theoretical Foundation of Rapid Distortion Theory on Transversely Sheared Mean Flows

The focus of this paper is on Rapid Distortion Theory on transversely sheared mean flows, which is often used to investigate turbulence-solid surface interactions. The main purpose of the paper is to bring together and present in a consistent fashion a general theory that has been developed in several different papers that have been published in the Journal of Fluid Mechanics. The equations for the unsteady pressure and velocity flections (which decouple from the entropy fluctuations) are rewritten in terms of a gauge function in order to obtain expressions that involve two arbitrarily convected quantities. A pair of very general conservation laws are used to derive upstream boundary conditions that relate these quantities to the actual physical variables. The entropy fluctuations can be determined after the fact once the solutions for the pressure and velocity fluctuations are known. The result involves a third arbitrary convected quantity that is equal to the entropy fluctuations at upstream infinity and can, therefore, be specified as an additional upstream boundary condition. A secondary purpose of the paper is to summarize a number of applications of the theory that have also appeared in the literature and show how they compare with an experiment.

Rapid distortion theory for homogeneous shear-driven MHD turbulence

<p><span><span>In this report we study statistical properties of astrophysical turbulent plasma flows </span></span><span><span>subjected to large scale velocity shear and an external magnetic field</span></span><span><span> using Rapid Distortion Theory (RDT). </span></span><span><span>The problem of shear-driven turbulence arises in several important physical systems, such as</span></span> <span><span>the </span></span><span><span>solar wind </span></span><span><span>and ionized atmospheres of exoplanets</span></span><span><span>.</span></span> <span><span>Rapid distortion theory is a linearization method for Reynolds-averaged Navier-Stockes equations. Its</span></span> <span><span>main</span></span><span><span> assumption is that the turbulence responds to the external distortion </span></span><span><span>by velocity shear</span></span><span><span> so fast, that inertial </span></span><span><span>forces </span></span><span><span>result in a negligible change in velocity </span></span><span><span>field statistics at small time scales</span></span><span><span>. This allows to linearize equations and to derive equations for second moments of turbulence. We apply RDT </span></span><span><span>approach</span></span><span><span> to incompressible </span></span><span><span>homogeneous </span></span><span><span>MHD </span></span><span><span>turbulence</span></span><span><span> distorted with </span></span><span><span>an </span></span><span><span>external magnetic field and </span></span><span><span>a </span></span><span><span>linear velocity shear in cases of rotating and non-rotating plasma. It is shown that even with a strong nonlinearity many properties of turbulence can be qualitatively studied using a linear theory. A closed system of linear equations </span></span><span><span>is derived</span></span><span><span> for </span></span><span><span>e</span></span><span><span>nergy, helicity and polarization </span></span><span><span>of velocity and magnetic field correlations</span></span><span><span>. </span></span><span><span>Structural analysis is conducted showing the change of energy distribution between components of spectral tensor of turbulence. </span></span><span><span>Development of initially isotropic turbulence and transition to anisotropy are studied. </span></span><span><span>Model e</span></span><span><span>quations for fluid, current and cross helicity are derived. Differences in cases of rotating and non-rotating flows are discussed. This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</span></span></p>

Rapid distortion theory on transversely sheared mean flows of arbitrary cross-section

This paper is concerned with rapid distortion theory on transversely sheared mean flows that (among other things) can be used to analyse the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It expands on a previous analysis of Goldstein et al. (J. Fluid Mech., vol. 824, 2017, pp. 477–512) that uses a pair of conservation laws to derive upstream boundary conditions for planar mean flows and extends these findings to transversely sheared flows of arbitrary cross-section. The results, which turn out to be quite general, are applied to the specific case of a round jet interacting with the trailing edge of a flat plate and are used to calculate the radiated sound field, which is then compared with experimental data taken at the NASA Glenn Research Center.

Sound generation due to the interaction of turbulence with surfaces embedded in transversely sheared flow

This paper reviews the application of Rapid Distortion Theory (RDT) on transversely shear mean flows to the prediction of sound generated from solid surfaces imbedded in turbulent shear flows. This phenomenon is relevant to the so-called installation noise problem which has received considerable attention in recent years. A few representative results from applications that have appeared in the literature are also presented. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.