arXiv subjects

Gerardo Hernández-Dueñas

Publications and source records attributed to Gerardo Hernández-Dueñas.

6 recordsLinked to original sources

arXiv2026

A new model for two-layer liquid-gas stratified flows in pipes with general cross sections

In this work, we derive a new model for immiscible two-layer gas-liquid stratified flows in pipes with general cross sections. The bottom layer is occupied by an incompressible fluid in liquid phase with hydrodynamics based on a hydrostatic pressure, following a shallow water approximation. The top layer is occupied by a compressible gas, following an ideal gas law leading to conservation of mass, momentum and energy. The two subsystems are linked through non-conservative products, representing momentum and energy exchanges between layers. The hyperbolic properties of the resulting model are analyzed, including the derivation of entropy inequalities, and the approximations of eigenvalues of the corresponding coefficient matrix. Numerical tests are included to demonstrate the merits of the model and the numerical approximations, including well-balancedness, Riemann problems, and perturbations and convergence toward steady states at rest. Besides simulations of water and air where the density difference between layers is significant, a case where such difference is not so pronounced (like gas and liquid hydrogen) is also shown.

physics.comp-ph↗

arXiv2025

Measuring fluxes between wave and geostrophic features in rotating non-hydrostatic flows with variable stratification

A challenge in physical oceanography is quantifying the energy content of waves and balanced flows and the fluxes that connect these reservoirs with their sources and sinks. Methodological limitations have prevented decompositions for realistic flows with non-hydrostatic motions and variable stratification. We present a framework that separates the flow into wave and geostrophic components using the principle that waves have no Eulerian available potential vorticity signature. Starting from new expressions for available energy and potential vorticity conservation, we construct a basis of wave and geostrophic modes, complete and orthogonal with respect to quadratic approximations of the conserved quantities. Using the resulting non-hydrostatic projection operators, the nonlinear equations of motion are expressed as coupled wave and geostrophic equations, quantifying cascade and transfer fluxes of wave and geostrophic energy. We apply the method to non-hydrostatic mid-ocean simulations with geostrophic mean-flow, near-inertial, and tidal forcing. From these experiments, we construct source-sink-reservoir diagrams for exact and quadratic fluxes, quantifying the fluxes between geostrophic and wave components. Because the cascade fluxes obey total energy conservation, we construct energy flow diagrams within the wave and geostrophic reservoirs and diagnose nonlocal transfers. The simulations show a geostrophic inverse cascade, a forward wave cascade, and a direct transfer of geostrophic to wave energy, with no indication of a forward geostrophic cascade. The mean-flow-only simulation shows weak spontaneous wave emission during spin-up, which diminishes to zero. Finally, we evaluate the decomposition by comparing linearized and fully conserved available potential vorticity, finding that errors become significant at scales below 15\,km.

physics.flu-dyn↗

arXiv2024

Available potential vorticity and the wave-vortex decomposition for arbitrary stratification

We consider a rotating non-hydrostatic flow with arbitrary stratification and argue that 1) the appropriate form of potential vorticity (PV) for this system is in terms of isopycnal deviation and 2) the decomposition into energetically orthogonal solutions is fundamentally a PV-inversion. The new closed-form expression for available potential vorticity (APV) is expressed in terms of isopycnal deviation, following the ideas in Wagner & Young (2015). This form of APV linearizes to quasigeostrophic PV (QGPV) after discarding the nonlinear stretching term and a height nonlinearity, the latter of which is not present in constant stratification. This formulation leads to positive definite definitions of potential enstrophy and total energy expressed in terms of isopycnal deviation, from which the quadratic versions emerge at lowest order. It is exactly these quantities diagonalized by the linear eigenmodes. Internal-gravity waves, geostrophic motions, inertial oscillations, and a mean density anomaly form the energetically and enstrophically orthogonal constituents of flow. The complete state of the fluid can be represented in terms of these physically realizeable modes and determined from the derived projection operators using the horizontal velocity and density anomaly. The projection of the fluid state onto the non-hydrostatic wave modes, reveals that one must first account for the PV portion of the flow before recovering the wave solutions. We apply the physical insights of the decomposition to a mesoscale eddy showing how strict adherence to adiabatic rearrangement places strong constraints on the vertical structure of such eddies, including a skew towards stronger cyclonic eddies in the upper water-column. Finally, the expression for APV is shown to reproduce the height nonlinearity of shallow-water PV, a well know feature that breaks the cyclone-anticyclone symmetry in QGPV.

physics.ao-ph↗

arXiv2023

A patch in time saves nine: Methods for the identification of localised dynamical behaviour and lifespans of coherent structures

We develop a transfer operator-based method for the detection of coherent structures and their associated lifespans. Characterising the lifespan of coherent structures allows us to identify dynamically meaningful time windows, which may be associated with transient coherent structures in the localised phase space, as well as with time intervals within which these structures experience fundamental changes, such as merging or separation events. The localised transfer operator approach we pursue allows one to explore the fundamental properties of a dynamical system without full knowledge of the dynamics. The algorithms we develop prove useful not only in the simple case of a periodically driven double well potential model, but also in more complex cases generated using the rotating Boussinesq equations.

math.DS↗

arXiv2022

Exact expressions for available potential energy and available potential vorticity

Exact analytical expressions for available potential energy density (APE) and available potential vorticity (APV) are derived from first principles. These APE and APV expressions align with previously known quantities found using perturbation expansions in Holliday & McIntyre (1981) and Wagner & Young (2015), respectively. The key is to recast the equations of motion and their conservation laws in terms of the coordinate label $z-η$, where z is a fluid parcels height at the current time, and $η$ is the isopycnal deviation from the parcels current height after adiabatic rearrangement of all parcels into the no-motion state. In addition to their intuitive appeal and simplicity, the new APE and APV expressions are easily implemented in numerical computations of Boussinesq dynamics with non-constant stratification.

physics.ao-ph↗

arXiv2011

Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles

We are consider domains in cotangent bundles with the property that the null foliation of their boundary is fibrating and the leaves satisfy a Bohr-Sommerfeld condition (for example, the unit disk bundle of a Zoll metric). Given such a domain, we construct an algebra of associated semiclassical pseudodifferential operators with singular symbols. The Schwartz kernels of the operators have frequency set contained in the union of the diagonal and the flow-out of the null foliation of the boundary of the domain. We develop a symbolic calculus, prove the existence of projectors (under a mild additional assumption) whose range can be thought of as quantizing the domain, give a symbolic proof of a Szegö limit theorem, and study associated propagators.

math.FA↗