arXiv subjects

Hossein A. Kafiabad

Publications and source records attributed to Hossein A. Kafiabad.

10 recordsLinked to original sources

arXiv2026

Two-way coupling of gravity waves and wind farm wakes: a reduced-order boundary-layer model

This paper develops a reduced-order numerical framework for modelling the two-way coupling between gravity waves and turbulent wakes in large-scale wind farms. Starting with the non-hydrostatic Boussinesq equations and introducing simplifications appropriate to the boundary layer and the overlying stratified free atmosphere yield separate governing equations for the two regions. These are coupled through a dynamic boundary condition at the capping inversion, which directly captures the feedback of gravity waves on the boundary-layer flow. A mixed pseudo-spectral finite-difference discretisation yields a computationally efficient model while retaining vertical boundary-layer structure. For the semi-infinite wind farm considered here, a complete solution is obtained in a matter of seconds on a standard laptop. Comparisons with large-eddy simulations (LES) confirm the model successfully reproduces both internal wind-farm flow and large-scale gravity-wave effects. It captures the upstream blockage induced by adverse pressure gradients, as well as the accelerated wake recovery within and downwind of the farm, driven by favourable pressure gradients.

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arXiv2026

Modelling Farm-to-Farm Interaction Using a Fast Linearised Numerical Approach

This paper presents a computationally efficient, linearised numerical method for modelling aerodynamic interactions between wind farms. The linearised two-dimensional incompressible equations are solved using Fourier transforms in the horizontal direction and finite-difference discretisation in the vertical. Model predictions are validated against large-eddy simulation (LES) data, focusing on a tandem wind farm configuration where a downstream wind farm operates within the wake of an upstream array. A parametric study is then conducted to examine the impact of this wake on the performance of the downstream farm across a range of inter-farm distances and hub-height ratios. We demonstrate that the upward vertical displacement of these wakes is driven by asymmetric turbulent entrainment caused by the farm's proximity to the ground, which restricts downward wake expansion. Consequently, the results suggest that, due to this upward wake displacement, downstream wind farms with higher hub heights may be more strongly affected by upstream farms than those with lower hub heights.

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arXiv2025

Lagrangian filtering for wave-mean flow decomposition

Geophysical flows are typically composed of wave and mean motions with a wide range of overlapping temporal scales, making separation between the two types of motion in wave-resolving numerical simulations challenging. Lagrangian filtering - whereby a temporal filter is applied in the frame of the flow - is an effective way to overcome this challenge, allowing clean separation of waves from mean flow based on frequency separation in a Lagrangian frame. Previous implementations of Lagrangian filtering have used particle tracking approaches, which are subject to large memory requirements or difficulties with particle clustering. Kafiabad and Vanneste (2023, KV23) recently proposed a novel method for finding Lagrangian means without particle tracking by solving a set of partial differential equations alongside the governing equations of the flow. In this work, we adapt the approach of KV23 to develop a flexible, on-the-fly, PDE-based method for Lagrangian filtering using arbitrary convolutional filters. We present several different wave-mean decompositions, demonstrating that our Lagrangian methods are capable of recovering a clean wave-field from a nonlinear simulation of geostrophic turbulence interacting with Poincaré waves.

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arXiv2024

Efficient Lagrangian averaging with exponential filters

Lagrangian averaging is a valuable tool for the analysis and modelling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by tracking a large number of particles or, following a recent approach, by solving a dedicated set of partial differential equations (PDEs). Both approaches are computationally demanding because they require an entirely new computation for each time at which the Lagrangian mean fields are desired. We overcome this drawback by developing a PDE-based method that delivers Lagrangian mean fields for all times through the single solution of evolutionary PDEs. This allows for an on-the-fly implementation, in which Lagrangian averages are computed along with the dynamical variables. This is made possible by the use of a special class of temporal filters whose kernels are sums of exponential functions. We focus on two specific kernels involving one and two exponential functions. We implement these in the rotating shallow-water model and demonstrate their effectiveness at filtering out large-amplitude Poincaré waves while retaining the salient features of an underlying slowly evolving turbulent flow.

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arXiv2024

Inhomogeneity-induced wavenumber diffusion

Inertia-gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the WKB regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities the waves encounter, such as density variations, also cause scattering and spectral diffusion. We generalise the spectral diffusion equation to account for these inhomogeneities. We apply the result to the rotating shallow water system, for which height inhomogeneities arise from velocity inhomogeneities through geostrophy, and to the Boussinesq system for which buoyancy inhomogeneities arise similarly. We compare the contributions that height and buoyancy variations make to the spectral diffusion with the contribution of the Doppler shift. In both systems, we find regimes where all contributions are significant. We support our findings with exact solutions of the diffusion equation and with ray tracing simulations in the shallow water case.

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arXiv2023

Computing Lagrangian means

Lagrangian averaging plays an important role in the analysis of wave--mean-flow interactions and other multiscale fluid phenomena. The numerical computation of Lagrangian means, e.g. from simulation data, is however challenging. Typical implementations require tracking a large number of particles to construct Lagrangian time series which are then averaged using a low-pass filter. This has drawbacks that include large memory demands, particle clustering and complications of parallelisation. We develop a novel approach in which the Lagrangian means of various fields (including particle positions) are computed by solving partial differential equations (PDEs) that are integrated over successive averaging time intervals. We propose two strategies, distinguished by their spatial independent variables. The first, which generalises the algorithm of Kafiabad (2022, J. Fluid Mech. 940, A2), uses end-of-interval particle positions; the second directly uses the Lagrangian mean positions. The PDEs can be discretised in a variety of ways, e.g. using the same discretisation as that employed for the governing dynamical equations, and solved on-the-fly to minimise the memory footprint. We illustrate the new approach with a pseudospectral implementation for the rotating shallow-water model. Two applications to flows that combine vortical turbulence and Poincare waves demonstrate the superiority of Lagrangian averaging over Eulerian averaging for wave--vortex separation.

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arXiv2022

Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence

The scattering of three-dimensional inertia-gravity waves by a turbulent geostrophic flow leads to the redistribution of their action through what is approximately a diffusion process in wavevector space. The corresponding diffusivity tensor was obtained by Kafiabad, Savva & Vanneste (2019, J. Fluid Mech., 869, R7) under the assumption of a time-independent geostrophic flow. We relax this assumption to examine how the weak diffusion of wave action across constant-frequency cones that results from the slow time dependence of the geostrophic flow affects the distribution of wave energy. We find that the stationary wave-energy spectrum that arises from a single-frequency wave forcing is localised within a thin boundary layer around the constant-frequency cone, with a thickness controlled by the acceleration spectrum of the geostrophic flow. We obtain an explicit analytic formula for the wave-energy spectrum which shows good agreement with the results of a high-resolution simulation of the Boussinesq equations.

physics.ao-ph↗

arXiv2020

Wave-averaged balance: a simple example

In the presence of inertia-gravity waves, the geostrophic and hydrostatic balance that characterises the slow dynamics of rapidly rotating, strongly stratified flows holds in a time-averaged sense and applies to the Lagrangian-mean velocity and buoyancy. We give an elementary derivation of this wave-averaged balance and illustrate its accuracy in numerical solutions of the three-dimensional Boussinesq equations, using a simple configuration in which vertically planar near-inertial waves interact with a barotropic anticylonic vortex. We further use the conservation of the wave-averaged potential vorticity to predict the change in the barotropic vortex induced by the waves.

physics.ao-ph↗

arXiv2020

Interaction of near-inertial waves with an anticyclonic vortex

Anticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped near-inertial eigenmodes. These vortex eigenmodes are easily excited by an initial wave with horizontal scale much larger than that of the vortex radius. We study this process using a wave-averaged model of near-inertial dynamics and compare its theoretical predictions with numerical solutions of the three-dimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a near-inertial wave energy signature that is characterized by an approximately time-periodic, azimuthally invariant pattern. The wave-averaged model represents the nonlinear feedback of the waves on the vortex via a wave-induced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results.

physics.flu-dyn↗

arXiv2020

Inertia-gravity-wave scattering by geostrophic turbulence

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with a geostrophically balanced turbulent flow. Advection and refraction by this flow lead to wave scattering, redistributing IGW energy in the position--wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, and makes no assumption of spatial scale separation. The kinetic equation describes energy transfers that are restricted to IGWs with the same frequency, as a result of the timescale separation between waves and flow. We formulate the kinetic equation on the constant-frequency surface -- a double cone in wavenumber space -- using polar spherical coordinates, and we examine the form of the two scattering cross sections involved, which quantify energy transfers between IGWs with, respectively, the same and opposite directions of vertical propagation. The kinetic equation captures both the horizontal isotropisation and the cascade of energy across scales that result from scattering. We focus our attention on the latter to assess the predictions of the kinetic equation against direct simulations of the three-dimensional Boussinesq equations, finding good agreement.

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