Fluid Dynamics Commons^™

Generating Live Heatmaps Of Edr Data Through A Spatiotemporal Weighting, Joel T. Williams, C. Sean Bohun, Alberto Fornaci, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

This paper introduces a novel method for generating live heatmaps of eddy dissipation rate (EDR) data through a spatiotemporal weighting designed to enhance turbulence visualization in aviation. As more flight data become available, approaches relying solely on in-flight EDR measurements have the potential to accurately nowcast and visualize turbulence with low computational cost. The proposed method significantly improves the turbulence visualization capabilities of common commercial aircraft. This is particularly valuable for pilot decision-making and trip planning, enhancing flight safety and operational efficiency. This approach also incorporates an innovative uncertainty threshold, which refrains from predicting when there are insufficient data, thereby …

Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev

Honors Scholar Theses

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …

Robust Spacecraft Autonomy For Deep Space Exploration In Special Euclidean Group Se(3), Matthew Wittal

Doctoral Dissertations and Master's Theses

Over the past half-century, humanity has gained extensive experience conducting manned spaceflight near Earth. Arguably, "near Earth" could even include the Moon — the most distant destination humans have reached. However, "near" in this work primarily refers low Earth orbit (LEO). One could argue that we have not truly left Earth since the Apollo, as spacecraft in some LEOs remain subject to atmospheric drag thus emphasizing their continued connection to Earth's immediate environment. Reflecting on this, it becomes clear that humanity has largely remained bound to Earth’s immediate vicinity since the Apollo missions reached the Moon. However, that is set …

Progress In Physics: Twentieth Year Of Publication, Florentin Smarandache, Andreas Ries, Pierre Millette, Ebenezer Chifu

Branch Mathematics and Statistics Faculty and Staff Publications

The journal Progress in Physics was created in January 2005 on behalf of many influential scientists with whom we were in correspondence. The main reason was that publications in other journals were allowed only if the submitter was affiliated with a scientific institution or research organization. Given this situation, many working scientists finding themselves partially employed or unemployed, such as in between research grants, find themselves unable to publish their research results. Even e-print archives such as Cornell’s arXiv required scientific affiliation and still follow this policy.

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

LSU New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov

Articles

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …

The Computational Model Of Nanofluid Considering Heat Transfer And Entropy Generation Across A Curved And Fat Surface, Sayer Obaid Alharbi, Florentin Smarandache, Awatif M.A. Elsiddieg, Aisha M. Alqahtani, M. Riaz Khan, V. Puneeth, Nidhal Becheikh

Branch Mathematics and Statistics Faculty and Staff Publications

The entropy generation analysis for the nanofluid flowing over a stretching/shrinking curved region is performed in the existence of the cross-diffusion effect. The surface is also subjected to second-order velocity slip under the effect of mixed convection. The Joule heating that contributes significantly to the heat transfer properties of nanofluid is incorporated along with the heat source/sink. Furthermore, the flow is assumed to be governed by an exterior magnetic field that aids in gaining control over the flow speed. With these frameworks, the mathematical model that describes the flow with such characteristics and assumptions is framed using partial differential equations …

The Fluid Margin Between Physical Causal Closure And Non-Physical Causal Closure, Extended To The Neutrosophic Causal Closure Principle, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

(R1978) Heated Laminar Vertical Jet Of Psudoplastic Fluids-Against Gravity, Manisha Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

A heated laminar jet of Pseudo-plastic fluid flowing vertically upwards from a long narrow slit into a region of the same fluid which is at a rest and at a uniform temperature is considered. The governing non-linear Partial differential equations (PDEs) for the defined flow problem are transformed into non-linear ordinary differential equations using the effective similarity technique-one parameter deductive group theory method. The obtained non-linear coupled Ordinary differential equations are solved and the results are presented by graphs. The effect of the Prandtl number and Grashof number on the velocity and temperature of the jet flow is discussed. Also, …

Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden

Rose-Hulman Undergraduate Mathematics Journal

The Navier-Stokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the Navier-Stokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares …

A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov

Dissertations

Currently, all forecasts of currents, waves, and seafloor evolution are limited by a lack of fundamental knowledge and the parameterization of small-scale processes at the seafloor-ocean interface. Commonly used Euler-Lagrange models for sediment transport require parameterizations of the drag and lift forces acting on the particles. However, current parameterizations for these forces only work for spherical particles. In this dissertation we propose a new method for predicting the drag and lift forces on arbitrarily shaped objects at arbitrary orientations with respect to the direction of flow that will ultimately provide models for predicting the sediment sorting processes that lead to …

Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu

Mathematics & Statistics Faculty Publications

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and Q-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the Q-tensor theory in dynamic configurations.

Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov

Publications

A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow …

Euler, Father Of Haemodynamics, Sylvio R. Bistafa

Euleriana

This article is being published in conjunction with the translation and synopsis of E855. Principia pro motu sanguinis per arterias determinando of 1775 - view the translation and synopsis by clicking here.

Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante

Articles

In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K₁ + K₂ = K₃ (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …

Numerical Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Method, Charles Armstrong, Yan Peng

Mathematics & Statistics Faculty Publications

In this work a quasisteady, dual time-stepping lattice Boltzmann method is proposed for simulation of capsule deformation. At each time step the steady-state lattice Boltzmann equation is solved using the full approximation storage multigrid scheme for nonlinear equations. The capsule membrane is modeled as an infinitely thin shell suspended in an ambient fluid domain with the fluid structure interaction computed using the immersed boundary method. A finite element method is used to compute the elastic forces exerted by the capsule membrane. Results for a wide range of parameters and initial configurations are presented. The proposed method is found to reduce …

Modeling Residence Time Distribution Of Chromatographic Perfusion Resin For Large Biopharmaceutical Molecules: A Computational Fluid Dynamic Study, Kevin Vehar

KGI Theses and Dissertations

The need for production processes of large biotherapeutic particles, such as virus-based particles and extracellular vesicles, has risen due to increased demand in the development of vaccinations, gene therapies, and cancer treatments. Liquid chromatography plays a significant role in the purification process and is routinely used with therapeutic protein production. However, performance with larger macromolecules is often inconsistent, and parameter estimation for process development can be extremely time- and resource-intensive. This thesis aimed to utilize advances in computational fluid dynamic (CFD) modeling to generate a first-principle model of the chromatographic process while minimizing model parameter estimation's physical resource demand. Specifically, …

Numerical Simulations Of Nonlinear Waves And Their Stability: Stokes Waves And Nonlinear Schroedinger Equation, Anastassiya Semenova

Mathematics & Statistics ETDs

The present work offers an investigation of dynamics and stability of nonlinear waves in Hamiltonian systems. The first part of the manuscript discusses the classical problem of water waves on the surface of an ideal fluid in 2D. We demonstrate how to construct the Stokes waves, and how to apply a continuation method to find waves in close vicinity to the limiting Stokes wave. We provide new insight into the stability of the Stokes waves by identifying previously inaccessible branches of instability in the equations of motion for the fluid. We provide numerical evidence that pairs of unstable eigenvalues of …

A Study Of The Design Of Adaptive Camber Winglets, Justin J. Rosescu

Master's Theses

A numerical study was conducted to determine the effect of changing the camber of a winglet on the efficiency of a wing in two distinct flight conditions. Camber was altered via a simple plain flap deflection in the winglet, which produced a constant camber change over the winglet span. Hinge points were located at 20%, 50% and 80% of the chord and the trailing edge was deflected between -5° and +5°. Analysis was performed using a combination of three-dimensional vortex lattice method and two-dimensional panel method to obtain aerodynamic forces for the entire wing, based on different winglet camber configurations. …

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …

Remark On Lehnert’S Revised Quantum Electrodynamics (Rqed) As An Alternative To Francesco Celani’S Et Al. Maxwell-Clifford Equations: With An Outline Of Chiral Cosmology Model And Its Role To Cmns, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper published in JCMNS in 2017, Francesco Celani, Di Tommaso & Vassalo argued that Maxwell equations rewritten in Clifford algebra are sufficient to describe the electron and also ultra-dense deuterium reaction process proposed by Homlid et al. Apparently, Celani et al. believed that their Maxwell-Clifford equations are an excellent candidate to surpass both Classical Electromagnetic and Zitterbewegung QM. Meanwhile, in a series of papers, Bo Lehnert proposed a novel and revised version of Quantum Electrodynamics (RQED) based on Proca equations. Therefore, in this paper, we gave an outline of Lehnert’s RQED, as an alternative framework to Celani …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda

Theses and Dissertations

High-speed Schlieren photography was utilized to visualize flow in the Air Force Research Laboratory Mach 6 Ludwieg tube facility. A 7° half-angle cone/flare model with variable nosetip radius and flare angle options was used in the study. Testing was performed at two driver tube pressures, generating freestream Reynolds numbers of 10.0x10⁶ and 19.8x10⁶ per meter. The variable-angle flare portion of the model provided a method for adjusting the intensity of the adverse pressure gradient at the cone/flare junction. As expected from existing literature, boundary layer separation along the cone frustum occurred further upstream as the magnitude of the …

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …

A Study Of Several Applications Of Parallel Computing In The Sciences Using Petsc, Nicholas Stegmeier

Electronic Theses and Dissertations

The importance of computing in the natural sciences continues to grow as scientists strive to analyze complex phenomena. The dynamics of turbulence, astrophysics simulations, and climate change are just a few examples where computing is critical. These problems are computationally intractable on all computing platforms except supercomputers, necessitating the continued development of efficient algorithms and methodologies in parallel computing. This thesis investigates the use of parallel computing and mathematical modeling in the natural sciences through several applications, namely computational fluid dynamics for impinging jets in mechanical engineering, simulation of biofilms in an aqueous environment in mathematical biology, and the solution …

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …