arXiv subjects

Alberto Scotti

Publications and source records attributed to Alberto Scotti.

9 recordsLinked to original sources

arXiv2026

A Versatile Laboratory Approach to Reproduce and Analyze Internal Ocean Wave Dynamics

Internal waves, or waves that propagate within a stratified fluid, may break and cause mixing. While each individual mixing event may be small, collectively, internal wave breaking drive processes in the ocean that are critical to understanding the maritime climate and biosphere. In this paper we show how to set up an experiment, suitable for an undergraduate-level lab, that illustrates a common generation and breaking mechanism in the ocean. In particular, we show how the process changes in response to a non dimensional parameter, the buoyancy Reynolds number, that can be easily varied. This parameter highlights the role of viscous vs. inertial/buoyancy forces. We outline our methods of creating a linear stratification, injecting energy with a forced topography, and analyzing the resulting dynamics with Background Oriented Schlieren and energy spectra from a conductivity probe. By altering our forcing to accommodate three values of the buoyancy Reynolds, three distinct internal wave regimes can be observed: no turbulence, slight turbulence, and extreme turbulence. Our methods aim to increase the accessibility to studying these internal waves in future experimental work, ocean modeling, and math and physics undergraduate learning.

physics.flu-dyn↗

arXiv2024

Experimental Investigation of Tidally-Forced Internal Wave Turbulence at High Reynolds Number

Through basin-scale circulations, the ocean regulates global distributions of heat, nutrients, and greenhouse gases. To properly predict the future of the ocean under climate change, we need to develop a thorough understanding of the underlying mechanisms that drive global circulations. An estimated 2 TW of power is required to support interior mixing. Roughly half of this power is believed to come from tidal flow over topography, producing internal gravity waves (IGW's), which can radiate energy throughout the ocean interior. But it is difficult to track the subsequent journey from tidal injection to dissipation, as the energy cascade spans an enormous range of spatio-temporal scales and multiple different nonlinear transfer mechanisms. To investigate the full energy pathway from topographic forcing to irreversible mixing, we built a model ocean in a large-scale laboratory wavetank (9 m x 2.9 m x 0.75 m) allowing Reynolds numbers up to O(10$^5$). We replicate the tidal forcing by oscillating an idealized ocean ridge. We track energy transfer across the first cascade, driven by wave turbulence, using Background Oriented Schlieren (BOS) over the full tank. Through the BOS we observe the formation of various sets of subharmonics, driven by Triadic Resonant Instabilities (TRI). At later times, the subharmonics born from TRI engage in different interactions, which ultimately develop a continuum of waves at frequencies up to $N$. We validate the three-wave resonant conditions through a Fourier decomposition and confirm a backward cascade in frequency but a forward cascade in vertical wavenumber. Through our spatial analysis, we identify relevant three-wave interactions and show the significance of elastic scattering, a nonlocal interaction, in our fully evolved system. We note however that the majority of our triads are local, which have been historically overlooked.

physics.flu-dyn↗

arXiv2024

A fully observer-covariant formulation of the fluid dynamics of simple fluids: derivation, simple examples and a generalized Orr-Sommerfeld equation

We present a formalism to describe the motion of a fluid that is fully covariant with respect to arbitrary observers. To achieve full covariance, we write prognostic equations for quantities that belong to the graded exterior algebra of the cotangent bundle of the manifold occupied by the fluid. In particular, equations are that are fully covariant can be written for a purely Lagrangian observer, for which the fluid velocity (qua section of the tangent bundle) is not a meaningful concept. With the new formalism, we consider problems of stability, and we derive a generalization of the Orr-Sommerfeld equation that describes the evolution of perturbations relative to an arbitrary observer. The latter is applied to cases where the observer is the Lagrangian observer comoving with the background flow.

physics.flu-dyn↗

arXiv2020

Limiting regimes of turbulent horizontal convection. Part I: Intermediate and low Prandtl numbers

We report the existence of two new limiting turbulent regimes in horizontal convection (HC) using direct numerical simulations at intermediate to low Prandtl numbers. The flow driven by a horizontal gradient along a horizontal surface, perpendicular to the acceleration of gravity is shown to transition to turbulence in the plume and the core, modifying the rate of heat and momentum transport. These transitions set a sequence of scaling laws blending the theoretical arguments from both the Shishkina, Grossmann & Lohse (SGL) theory with the Hughes, Griffiths & Mullarney (HGM) regime. These results embed the HGM model in the SGL theory, agree, and extend the known regime diagram of horizontal convection at high Rayleigh numbers. In particular, we show that HC and Rayleigh-B\'enard share similar turbulent characteristics at low-Prandtl numbers, where HC is shown for the first time to be ruled by its core dynamics and turbulent boundary layers. This new scenario confirms that fully turbulent HC enhances the transport of heat and momentum with respect to previously reported regimes at high Rayleigh numbers. This work provides new insights on the applicability of horizontal convection for geophysical flows such as overturning circulations found in the atmosphere, the oceans, and flows near the earth's inner core.

physics.flu-dyn↗

arXiv2020

Limiting regimes of turbulent horizontal convection. Part II : Large Prandtl numbers

Horizontal Convection (HC) at large Rayleigh and Prandtl numbers, is studied experimentally in a regime up to seven orders of magnitude larger in terms of Rayleigh numbers than previously achieved. To reach Rayleigh up to $10^{17}$, the horizontal density gradient is generated using differential solutal convection by a differential input of salt and fresh water controlled by diffusion in a novel experiment where the zero-net mass flux of water is ensured through permeable membranes. This setup allows for measuring accurately the Nusselt number in solutal convection by carefully controlling the amount of salt water exchanged through the membranes. Combined measurements of density and velocity across more than five orders of magnitude in Rayleigh numbers show that the flow transitions from the Beardsley & Festa regime to the Chiu-Webster et al. regime and frames the present results within the scope of Shishkina et al., and the companion paper theory. In particular, we show that even for large Prandtl numbers, the circulation eventually clusters underneath the forcing horizontal boundary leaving a stratified core without motion. Finally, previous regime diagrams are extended combining the present results at high Prandtl numbers, the results at low Prandtl numbers of the companion paper, together with previous results from the literature. This work sets a new picture of the transition landscape of horizontal convection across six orders of magnitude in Prandtl number and sixteen orders of magnitude in Rayleigh numbers.

physics.flu-dyn↗

arXiv2018

Heat and momentum transport in turbulent horizontal convection at low Prandtl numbers

The transition to a new turbulent regime in horizontal convection in the case of low Prandtl numbers is analyzed using the Shishkina, Grossmann & Lohse (SGL) theory. The flow driven by the horizontal gradient along a horizontal surface, perpendicular to the acceleration of gravity is shown to transition to turbulence in the plume and the core. This transition to turbulence sets a sequence of heat transfer and momentum transport scalings which are found to follow the SGL prediction for the scaling factors and the prediction of Hughes, Griffith & Mullarney (HGM) for larger forcing amplitudes. These results embed the HGM model in the SGL theory, agreed and extends the known regime diagram of horizontal convection, and provide the first evidence of both regimes at low and intermediate Prandtl numbers and sheds new insights on the role of HC in the earth's inner core dynamics.

physics.flu-dyn↗

arXiv2017

A local diagnostic energy to study diabatic effects on a class of degenerate Hamiltonian systems with application to mixing in stratified flows

In Hamiltonian systems characterized by a degenerate Poisson algebra, we show how to construct a local energy-like quantity that can be used to study diabatic effects on the evolution of the Available Energy of the system, the latter concept formalizing the original idea of Margules'. We calculate the local diagnostic energy for geophysically relevant flows. For the particular case of stratified Boussinesq flows, we show that under moderately general conditions, in inertial frames where the initial distribution of potential vorticity is even around the origin, our framework recovers the Available Potential Energy introduced by Holliday and McIntyre \cite{HollidayM81}, and as such depends only on the mass distribution of the flow. In non-inertial frames, we show that the local diagnostic energy of flows which are, in an appropriate sense, characterized by a low-Rossby number ${\rm Ro}$ ground state, has to lowest order in ${\rm Ro}$, a universal character.

physics.flu-dyn↗

arXiv2016

Fluid dynamics in the spirit of Cartan: A coordinate-free formulation of fluid dynamics for an inviscid fluid in inertial and non-inertial frames

Using Cartan's exterior calculus, we derive a coordinate-free formulation of the Euler equations. These equations are invariant under Galileian transformations, which constitute a global symmetry. With the introduction of an appropriate generalized Coriolis force, these equations become symmetric under general coordinate transformations. We show how exterior calculus simplifies dramatically the derivation of conservation laws. We also discuss the advantage of an exterior calculus formulation with respect to symmetry-preserving discretizations of the equations.

physics.flu-dyn↗

arXiv2011

An Efficient Method For Solving Highly Anisotropic Elliptic Equations

Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterised by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest derivative in one direction is much larger than the terms in the remaining directions, the discretized elliptic operator often has a very large condition number - taking the solution even further out of reach using traditional methods. This paper will demonstrate a solution method for such ill-behaved problems. The high condition number of the D-dimensional discretized elliptic operator will be exploited to split the problem into a series of well-behaved one and (D-1)-dimensional elliptic problems. This solution technique can be used alone on sufficiently coarse grids, or in conjunction with standard iterative methods, such as Conjugate Gradient, to substantially reduce the number of iterations needed to solve the problem to a specified accuracy. The solution is formulated analytically for a generic anisotropic problem using arbitrary coordinates, hopefully bringing this method into the scope of a wide variety of applications.

physics.comp-ph↗