Bottom changes in coastal areas with complex shorelines

A model for the sea-bottom change simulations in coastal areas with complex shorelines is proposed. In deep and intermediate water depths, the hydrodynamic quantities are calculated by numerically integrating the contravariant Boussinesq equations, devoid of Christoffel symbols. In the surf zone, the propagation of the breaking waves is simulated by the nonlinear shallow water equations. The momentum equation is solved inside the turbulent boundary layer in order to calculate intrawave hydrodynamic quantities. An integral formulation for the contravariant suspended sediment advection-diffusion equation is proposed and used for the sea-bottom dynamic simulations. The proposed model is applied to the real case study of Pescara harbor (in Italy)

Large time behavior in perfect incompressible flows

3rd cycl

Thermodynamical Equilibrium of Vortices in the Isotropic Bidimensional Kac Rotator

We consider here the problem of extrema for the Kac functional with long range, ferromagnetic interaction, and vorticity conditions at infinity which make it not weakly closed. Using a gradient-flow dynamics, we investigate local minima, showing strong analogies with the Ginzburg-Landau functional in infinite volume.Comment: 48page

Analysis and approximation of a vorticity-velocity-pressure formulation for the Oseen equations

We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous problem is addressed by invoking a global inf-sup property in an adequate abstract setting for non-symmetric systems. The proposed finite element schemes, which produce exactly divergence-free discrete velocities, are shown to be well-defined and optimal convergence rates are derived in suitable norms. In addition, we establish optimal rates of convergence for a class of discontinuous Galerkin schemes, which employ stabilisation. A set of numerical examples serves to illustrate salient features of these methods

Structure-preserving discretization of Maxwell’s equations as a port-Hamiltonian system

This work demonstrates the discretization of the boundary-controlled Maxwell equations, recast as a port-Hamiltonian system (pHs). After a reminder on the Stokes-Dirac structure associated with the Maxwell system, we introduce different partitioned weak formulations that preserve the pHs structure, and its associated power balance, at the semi- discrete level. These weak formulations are compared through numerical applications to closed non-perfectly conducting cavities and open waveguides under transverse approximation

Cascades and transitions in turbulent flows

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal 3D/2D isotropic cases characterized by the presence of a strictly direct/inverse energy cascade, respectively. We review recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse cascades, the different scenarios include: split cascades to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a condensate is formed. We classify all transitions as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, MHD and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We discuss the presence of anomalous scaling laws in connection with the intermittent nature of the energy dissipation in configuration space. An overview is also provided concerning cascades in other applications such as bounded flows, quantum, relativistic and compressible turbulence, and active matter, together with implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201

Coherent structures in a baroclinic atmosphere

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric and Planetary Sciences, 1985.Microfiche copy available in Archives and Science.Bibliography: leaves 127-130.by Piero Malguzzi.Ph.D

Study: Simulation of planetary atmospheres

This thesis analyzes different ways of simulating planetary atmospheres to reproduce the observed phenomena and further understand its dynamics. To do so, a two dimensional Shallow Water model in ellipsoidal coordinates will be used in order to start capturing part of the dynamics that occur at large scales in the atmospheres of gas giant planets. Then, some additions will be done in order to control the instabilities that appear in the model, the possibility of simulating the poles will be presented and a new way of perturbing the system to achieve accurate steady-state vortices will be assessed. Then, a three dimensional Boussinesq model will be implemented to capture the convective movement of atmospheres in the radial direction. The results prove that the Shallow Water with the additions here presented is a very good option to reproduce with good accuracy the horizontal dynamics of planetary atmospheres, while the three dimensional model, at a smaller scale, is capable of reproducing the upwards movement of uid that the Shallow Water lacks. Both codes are capable of running in parallel computers improving the resolutions of the simulations carried out. Then, these codes might be used to further understand the dynamics of planetary atmospheres and complement the observational data availabl

Chaos in stochastic 2d Galerkin-Navier-Stokes

We prove that all Galerkin truncations of the 2d stochastic Navier-Stokes equations in vorticity form on any rectangular torus subjected to hypoelliptic, additive stochastic forcing are chaotic at sufficiently small viscosity, provided the frequency truncation satisfies $N\geq 392$. By ``chaotic'' we mean having a strictly positive Lyapunov exponent, i.e. almost-sure asymptotic exponential growth of the derivative with respect to generic initial conditions. A sufficient condition for such results was derived in previous joint work with Alex Blumenthal which reduces the question to the non-degeneracy of a matrix Lie algebra implying H\"ormander's condition for the Markov process lifted to the sphere bundle (projective hypoellipticity). The purpose of this work is to reformulate this condition to be more amenable for Galerkin truncations of PDEs and then to verify this condition using a) a reduction to genericity properties of a diagonal sub-algebra inspired by the root space decomposition of semi-simple Lie algebras and b) computational algebraic geometry executed by Maple in exact rational arithmetic. Note that even though we use a computer assisted proof, the result is valid for all aspect ratios and all sufficiently high dimensional truncations; in fact, certain steps simplify in the formal infinite dimensional limit.Comment: 40 pages, 3 figure

Three-dimensional numerical simulation of fluid flow and heat transfer in fin-and-tube heat exchangers at different flow regimes

This thesis aims at unifying two distinct branches of work within the Heat Transfer Technological Center (CTTC). On one side, extensive experimental work has been done during the past years by the researchers of the laboratory. This experimental work has been complemented with numerical models for the calculation of fin and tube heat exchangers thermal and fluid dynamic behavior. Such numerical models can be referred to as fast numerical tool which can be used for industrial rating and design purposes. On the other hand, the scientists working at the research center have successfully developed a general purpose multi-physics Computational Fluid Dynamics (CFD) code (TermoFluids). This high performance CFD solver has been extensively used by the co-workers of the group mainly to predict complex flows of great academic interest. The idea of bringing together this two branches, comes from the necessity of a reliable numerical platform with detailed local data of the flow and heat transfer on diverse heat exchanger applications. Being able to use local heat transfer coefficients as an input on the rating and design tool will lead to affordable and accurate prediction of industrial devices performance, by which the center can propose enhanced alternatives to its industrial partners. To accomplish these goals, several contributions have been made to the existing TermoFluids software which is in continuous evolution in order to meet the competitive requirements. The most significant problematics to adequately attack this problem are analyzed and quite interesting recommendations are given. Some of the challenging arising issues involve the generation of suitable and affordable meshes, the implementation and validation of three dimensional periodic boundary condition and coupling of different domains with important adjustments for the study of cases with different flow physics like time steps and thermal development. Turbulence is present in most of engineering flows, and refrigeration evaporator heat exchangers are not an exception. The presence of many tubes (acting like bluff bodies for the flow) arranged in different configurations and the fact that the flow is also confined by fins, create complex three dimensional flow features that have usually turbulent or transition to turbulent regime. Therefore, three dimensional turbulent forced convection in a matrix of wall-bounded pins is analyzed. Large Eddy Simulations (LES) are performed in order to assess the performance of three different subgrid-scale models, namely WALE, QR and VMS. The Reynolds numbers of the study were set to 3000, 10000 and 30000. Some of the main results included are the pressure coefficient around the cylinders, the averaged Nusselt number at the endwalls and vorticity of the flow. The final part of the thesis is devoted to study the three dimensional fluid flow and conjugated heat transfer parameters encountered in a plate fin and tube heat exchanger used for no-frost refrigeration. The numerical code and post processing tools are validated with a very similar but smaller case of a heat exchanger with two rows of tubes at low Reynolds for which experimental data is available. The next analysis presented is a typical configuration for no-frost evaporators with double fin spacing (for which very few numerical data is reported in the scientific literature). Conjugated convective heat transfer in the flow field and heat conduction in the fins are coupled and considered. The influence of some geometrical and flow regime parameters is analyzed for design purposes. In conclusion, the implementations and general contributions of the present thesis together with the previous existent multi-physics computational code, has proved to be capable to perform successful top edge three dimensional simulations of the flow features and heat transfer mechanisms observed on heat exchanger devices.Esta tesis tiene como objetivo unificar dos ramas de trabajo dentro del Centro Tecnológico de Transferencia de Calor (CTTC). Por un lado, se ha realizado un amplio trabajo experimental durante los últimos años. Este trabajo experimental se ha complementado con modelos numéricos para el estudio de intercambiadores de calor de tipo aleta-tubo. Tales modelos numéricos pueden considerarse una herramienta numérica de bajo coste empleada con propósitos de diseño principalmente. Por otro lado, los científicos que trabajan en el centro han desarrollado con éxito un código de Dinámica de Fluidos Computacionales (TermoFluids). Este código de alto rendimiento ha sido ampliamente utilizado principalmente para predecir flujos complejos de gran interés académico. La idea de unir a estas dos ramas, proviene de la necesidad de una plataforma numérica fiable con datos locales propios del flujo y de la transferencia de calor en diversas aplicaciones de intercambiadores de calor. Ser capaz de generar coeficientes locales de transferencia de calor para abastecer con datos propios los modelos existentes de bajo coste, permitirá la correcta predicción del rendimiento de dichos dispositivos. Para lograr estos objetivos, se han hecho varias contribuciones al código TermoFluids que está en continua evolución. Algunas de las mayores cuestiones que se plantean implican la generación de mallas adecuadas y asequibles, la implementación y validación de la condición de contorno periódica tridimensional y el acoplamiento de los diferentes dominios para el estudio de casos con diferentes comportamientos físicos, como desarrollo transitorio e inercia térmica. La turbulencia está presente en la mayoría de los flujos de ingeniería, y los intercambiadores de calor de evaporadores para refrigeración no son una excepción. La presencia de muchos tubos (que actúan como obstáculos para el fluido) colocados en diferentes configuraciones y el hecho de que el flujo también está confinado por aletas, crean características de flujo tridimensionales complejas que tienen generalmente régimen turbulento o en transición. Por lo tanto, se analiza la convección forzada turbulenta en una matriz de pines delimitados por paredes. simulando las grandes escalas de turbulencia y modelando las pequeñas (LES) con el fin de evaluar el desempeño de los tres modelos seleccionados, a saber WALE, QR y VMS. Los números de Reynolds establecidos para el estudio son 3000, 10000 y 30000. Algunos de los principales resultados que se incluyen son el coeficiente de presión alrededor los cilindros, el número de Nusselt promedio en las paredes y la vorticidad del flujo. La parte final de la tesis se dedica a estudiar el flujo tridimensional y los parámetros de transferencia de calor encontrados en un intercambiador de calor de tipo aleta-tubo utilizado para la refrigeración doméstica en equipos de 'no-escarcha'. Las implementaciones del código y el postproceso numéricos se validan en un caso muy similar para un intercambiador de calor con dos filas de tubos a bajos Reynolds para el cual se dispone de datos experimentales. El siguiente análisis que se presenta es una configuración típica para evaporadores 'no-escarcha' con paso de aleta doble (para el que se tiene muy poca información numérica en la literatura). Se considera el acoplamiento conjugado de la transferencia de calor convectiva entre fluido y sólido y conductiva dentro de la aleta. La influencia de algunos parámetros geométricos y de régimen de flujo se analizan con propósitos de diseño. En conclusión, las contribuciones generales de esta tesis junto con el código computacional ya existente, ha demostrado ser capaz de realizar con éxito simulaciones tridimensionales para predecir las características del flujo y los mecanismos responsables de la transferencia de calor en intercambiadores de calor de tipo aleta-tuboPostprint (published version