Research Interests

Fluid Dynamics

Understanding transition to turbulence in shear flows, even for rather simple fluid systems, is a major challenge that has attracted the attention of the scientific community for over a century. Its technological implications are far-reaching, very especially in the case of aeronautics, for which shear flows are of outstanding importance. Computational fluid mechanics, dynamical systems analysis and bifurcation theory must be used in combination to try and shed some light on the unsolved problem of subcritical transition in wall-bounded shear flows.

Most technological problems involving fluids in motion have, at some point, to deal with turbulence. In some applications, such as those requiring mixing, turbulence is a very useful phenomenon, but, more often than not, it is a nuisance.

A variety of flows exists exhibiting instabilities that eventually lead to turbulence. In the nonlinear fluid dynamics group, we set the focus on centrifugal instability of rotating fluids as well as on shear instabilities appearing in wall-bounded shear flows. Shear flows are those for which the velocity gradients have a strong component in a direction normal (or quasi normal) to the main orientation of the flow. Some examples are pipe and channel flows, boundary layers, jets and wakes. These flows often experience transition to turbulence for values of the Reynolds number (Re) well below that for which they become linearly unstable, some of them being even believed to remain linearly stable for all values of Re. This transition not stemming from linear instability is usually called bypass (or subcritical) transition.

Pipe Flow

In pipe or Hagen-Poiseuille flow, a fluid of kinematic viscosity ν is axially driven through a circular pipe of diameter D by means of a uniform axial pressure gradient that keeps the mean axial velocity U and the massflow Q constant. The basic solution of the Navier-Stokes equations is a parabolic, streamwise-independent, axisymmetric and steady purely axial flow. The basic flow Reynolds number is defined as Re=U D/ν and the parabolic solution is linearly stable for all values of Re.

Notwithstanding its linear stability, beyond a certain critical value of Re ~ 2000 pipe flow undergoes transition to turbulence in the presence of large enough finite amplitude perturbations. The parabolic profile ceases to be a global attractor and its basin of attraction is no longer the full phase space. Furthermore, experimental evidence shows that pipe flow becomes more sensitive to perturbations when increasing the Reynolds number. Since the flow is linearly stable, finite (yet small) amplitude perturbations must be responsible for the transition to turbulence.

Transition to turbulence in Hagen-Poiseuille flow has been object of analysis for over a century. Since the seminal work of Osborne Reynolds published in 1883, many physicists and applied mathematicians have devoted enormous efforts to provide a theoretical explanation of the phenomenon of subcritical transition to turbulence in shear flows such as plane Couette or pipe flow.

The numerical computation of finite-amplitude solutions in the form of equilibria and relative equilibria (travelling waves), whose existence relies on a mechanism called the self-sustained process, initially advanced to account for turbulent regeneration, has brought renewed interest to the problem of subcritical shear flow transition within the dynamical systems community.

Taylor-Couette

A comprehensive understanding of turbulent phenomena necessarily requires a previous explanation of the mechanisms that mediate between laminar and fully disordered fluid motion. One of the most challenging shear flow problems is the understanding of laminar-turbulent coexistence phenomena or intermittency, i.e., spatiotemporal coexistence of laminar and turbulent regions in a fluid flow.

While transition in open shear flows is typically subcritical, i.e., bypassing linear stability, Taylor-Couette flow exhibits a huge variety of secondary supercritical steady, time periodic, or almost periodic laminar flows before an eventual transition to chaotic regimes. This allows the study of transition in a supercritical setting, along with its degeneration into subcriticality.

Nonlinear Dynamics

Dynamical systems (contiuous and discrete time), center manifold, normal form and symmetry group theory, play a central role in the study of hydrodynamical stability. The fact that very low-dimensional analysis can provide insight into the subject of stability of solutions of infinite-dimensional systems such as those governed by partial differential equations (e.g. fluid flows), makes of dynamical systems theory an extremely powerful tool that has revolutionised the way instability problems are faced. Concepts such as phase space, state, invariant manifold, orbit and bifurcation provide the basic tools for a deep understanding of the physics underlying fluid flow instability, transition and turbulence.

Numerical Methods

Spectral methods have been extensively applied for the approximation of solutions of the Navier–Stokes equations in simple geometries. Collocation or pseudospectral methods have been more popular than Galerkin spectral methods because they are easier to formulate and implement. One of the arguments that have been frequently given to encourage the use of Galerkin instead of collocation methods is that sometimes the former provide banded matrices in the spatial discretization of linear operators, which improves the efficiency of the linear solvers in the time integrations. The main drawback of Galerkin methods lies on their mathematical formulation, which can become very complex.

Fisheries Research

Trawl Fishing

Trawling is of paramount importance to both economics and food supply, since well over 50% of fish and shellfish production comes from trawl fishing. Pelagic trawl doors are hydrofoils that fly underwater producing the forces required for appropriate opening of fishing nets. Efficient and sustainable trawling requires tight control of net opening and fishing depth. This can be achieved through the development of efficient control strategies that must necessarily rely on a deep understanding and a careful modelling of how trawl doors interact with water flow to produce the forces and moments required.

Bone Fracture Mechanics

Bone Quality Estimates via Micro-Indentation

Bone densitometry is the most extended technique for bone fracture risk assessment. Its main limitation derives from the fact that only Calcium density is reported, overlooking many other risk factors such as both macro and microscopic bone structure, accumulated microscopic damage, quality of collagen, mineral crystal size or bone turnover. A new technique based on bone response to micro-indentation has been developed in recent years. Micro-indentation consist in measuring how deep a needle penetrates cortical bone for a given sudden release of energy. This allows for a low-cost, hardly invasive technique that is ideal for extensive use in a clinical environment. Preliminary correlation studies suggest that micro-indentation results constitute a far better estimate of bone quality than traditional bone density, but relating indentation depth with bone fracture mechanics is a challenging task that has opened up a wide new field of research.