arXiv subjects

Navid C. Constantinou

Publications and source records attributed to Navid C. Constantinou.

At least 19 recordsLinked to original sources

arXiv2025

High-level, high-resolution ocean modeling at all scales with Oceananigans

We describe the user interface, governing equations, and numerical methods underpinning the community ocean modeling software called "Oceananigans". Oceananigans development has been lead by the Climate Modeling Alliance to build a trainable climate model with quantifiable uncertainty. Oceananigans is written in the Julia programming language, which, like similar recent efforts based on modern programming languages, distinguishes it from usual software based on Fortran. Oceananigans can efficiently simulate all scales of ocean motion, ranging from millimeter-scale turbulence in a small box to planetary-scale ocean circulation. Oceananigans design combines (i) a basic structured finite volume algorithm (ii) optimized for high-resolution simulations on GPUs which is (iii) exposed behind a high-level, programmable user interface. This design negotiates a dual mandate for highest-possible performance (to support state-of-the-art applications) and enhanced accessibility (to facilitate adoption and development). The dual mandate aims ultimately to accelerate the progress of Earth system science. Achieving this aim, however, requires a substantial and sustained increase in the collective effort of Oceananigans development.

physics.ao-ph↗

arXiv2025

Evaluating and improving wave and non-wave stress parametrisations for oceanic flows

Whenever oceanic currents flow over rough topography, there is an associated stress that acts to modify the flow. In the deep ocean, this stress is predominantly a form drag due to pressure differentials across topography, caused by the formation of internal waves and other baroclinic motions: processes that act on such small scales most global ocean models cannot resolve. Despite the need to incorporate this stress into ocean models, existing parametrisations are limited in their applicability. For instance, most parametrisations are only suitable for small-scale topography and are either for periodic or steady flows, but rarely a combination thereof. Here we summarise some of the most widely used parametrisations and evaluate the accuracy of a carefully selected subset using hundreds of idealised two-dimensional and three-dimensional simulations spanning a wide parameter space. We focus on the case of an isolated Gaussian hill as an idealised representation of a seamount. In cases where the parametrisations prove to be inaccurate, we use our data to suggest improved formulations. Our results thus provide a starting point for a comprehensive parameterisation of topographic stresses in ocean models where fine scale topography is unresolved.

physics.ao-ph↗

arXiv2025

Phenomenology of decaying turbulence beneath surface waves

This paper explores decaying turbulence beneath surface waves that is initially isotropic and shear-free. We start by presenting phenomenology revealed by wave-averaged numerical simulations: an accumulation of angular momentum in coherent vortices perpendicular to the direction of wave propagation, suppression of kinetic energy dissipation, and the development of depth-alternating jets. We interpret these features through an analogy with rotating turbulence (Holm 1996), wherein the curl of the Stokes drift, $\boldsymbol{\nabla}\times\boldsymbol{u}^S$, takes on the role of the background vorticity (for example, $(f_0 + βy) \hat{\boldsymbol{z}}$ on the beta plane). We pursue this thread further by showing that a two-equation model proposed by Bardina et al. (1985) for rotating turbulence reproduces the simulated evolution of volume-integrated kinetic energy. This success of the two-equation model -- which explicitly parametrizes wave-driven suppression of kinetic energy dissipation -- carries implications for modeling turbulent mixing in the ocean surface boundary layer. We conclude with a discussion about a wave-averaged analogue of the Rossby number appearing in the two-equation model, which we term the "pseudovorticity number" after the pseudovorticity $\boldsymbol{\nabla}\times\boldsymbol{u}^S$. The pseudovorticity number is related to the Langmuir number in an integral sense.

physics.flu-dyn↗

arXiv2025

Asymmetric response of the North Atlantic gyres to the North Atlantic Oscillation

The North Atlantic Oscillation (NAO) is a leading mode of atmospheric variability, affecting the North Atlantic Ocean on sub-seasonal to multi-decadal timescales. The NAO changes the atmospheric forcing at the ocean's surface, including winds and surface buoyancy fluxes, both of which are known to impact large-scale gyre circulation. However, the relative role of other physical processes (such as mesoscale eddies and topography) in influencing gyre circulation under NAO variability is not fully understood. Here, we analyze a series of ocean--sea ice simulations using a barotropic vorticity budget to understand the long-term response of the North Atlantic gyre circulation to NAO forcing. We find that for each standard deviation increase in the NAO index, the subtropical and subpolar gyres intensify by 0.90 Sv and 3.41 Sv (1 Sv = 10$^6$ m$^3$ s$^{-1}$) respectively. The NAO-induced wind stress anomalies drive approximately 90\% of the change in the subtropical gyre's interior flow. However, in the subpolar gyre's interior, in addition to wind stress, flow-topography interactions, stratification (influenced by surface heat fluxes), and non-linear advection significantly influence the circulation. Along the western boundary the bottom pressure torque plays a key role in steering the flow, and the vorticity input by the bottom pressure torque is partly redistributed by non-linear advection. Our study highlights the importance of both atmospheric forcing and oceanic dynamical processes in driving long-term gyre circulation responses to the NAO.

physics.ao-ph↗

arXiv2025

Unravelling how winds and surface heat fluxes control the Atlantic Ocean's meridional heat transport

The North Atlantic Ocean circulation, fuelled by winds and surface buoyancy fluxes, carries 1.25 PettaWatts of heat poleward in the subtropics, and helps in regulating global weather and climate patterns. Here, we assess the relative impacts of changes in winds and surface heat fluxes on the Atlantic Ocean circulation and heat transport on short timescales (<10 years) and long timescales (>50 years) using ocean simulations. We decompose the circulation and heat transport into warm and cold cells (resembling a subtropical gyre and the dense overturning circulation respectively), and a mixed cell capturing waters transitioning between warm and cold regions. Warm and mixed cells transport more heat poleward as wind stress increases; however, these anomalies are compensated by reductions in the cold cell's heat transport. Warm and cold cells transport more heat poleward when we increase meridional heat flux gradients. Our findings underscore the distinct roles of winds and surface heat fluxes in controlling the Atlantic Ocean's meridional heat transport.

physics.ao-ph↗

arXiv2025

Rapid topographic scatter of near-inertial waves generated by storms

Internal waves propagate on the ocean's stratification, carrying energy and redistributing momentum through the ocean. When internal waves break, they contribute to diapycnal mixing in the ocean interior, but this breaking behaviour depends upon the scale of the waves. Low-mode internal waves have larger horizontal and vertical scales, and thus break less readily than higher-mode waves. The scattering of internal waves by topography is an important mechanism in transferring internal wave energy to smaller scales that are more conducive to wave breaking and mixing processes. In this study, we propose and investigate a mechanism in which storm-generated low-mode internal waves scatter at topography. We hypothesise that horizontally propagating internal wave modes generated by strong winds (i.e., due to a storm) can rapidly dephase; these dephased waves can then be scattered from topography, resulting in higher-mode upward-propagating waves within hours of the passage of a storm. We investigate this phenomenon in an idealised numerical model of a storm passing over a prominent ridge. Bottom-scattered near-inertial internal waves propagate away from the ridge rapidly in the wake of the storm. We perform several perturbation experiments varying the properties of the ocean, the winds and the topography. The bottom-scattered waves exhibit spatial downscaling, and have an energy flux equivalent to 10% the magnitude of the energy flux from surface-generated near-inertial waves in our domain. Although small in a globally averaged sense, we argue that the topographic scatter of storm-generated near-inertial waves could account for the unexplained near-inertial wave signals found in ocean observations and numerical studies.

physics.ao-ph↗

arXiv2024

Oceananigans.jl: A Julia library that achieves breakthrough resolution, memory and energy efficiency in global ocean simulations

Climate models must simulate hundreds of future scenarios for hundreds of years at coarse resolutions, and a handful of high-resolution decadal simulations to resolve localized extreme events. Using Oceananigans.jl, written from scratch in Julia, we report several achievements: First, a global ocean simulation with breakthrough horizontal resolution -- 488m -- reaching 15 simulated days per day (0.04 simulated years per day; SYPD). Second, Oceananigans simulates the global ocean at 488m with breakthrough memory efficiency on just 768 Nvidia A100 GPUs, a fraction of the resources available on current and upcoming exascale supercomputers. Third, and arguably most significant for climate modeling, Oceananigans achieves breakthrough energy efficiency reaching 0.95 SYPD at 1.7 km on 576 A100s and 9.9 SYPD at 10 km on 68 A100s -- the latter representing the highest horizontal resolutions employed by current IPCC-class ocean models. Routine climate simulations with 10 km ocean components are within reach.

physics.ao-ph↗

arXiv2024

Formulation and calibration of CATKE, a one-equation parameterization for microscale ocean mixing

We describe CATKE, a parameterization for fluxes associated with small-scale or "microscale" ocean turbulent mixing on scales between 1 and 100 meters. CATKE uses a downgradient formulation that depends on a prognostic turbulent kinetic energy (TKE) variable and a diagnostic mixing length scale that includes a dynamic convective adjustment (CA) component. With its dynamic convective mixing length, CATKE predicts not just the depth spanned by convective plumes but also the characteristic convective mixing timescale, an important aspect of turbulent convection not captured by simpler static convective adjustment schemes. As a result, CATKE can describe the competition between convection and other processes such as shear-driven mixing and baroclinic restratification. To calibrate CATKE, we use Ensemble Kalman Inversion to minimize the error between 21 large eddy simulations (LES) and predictions of the LES data by CATKE-parameterized single column simulations at three different vertical resolutions. We find that CATKE makes accurate predictions of both idealized and realistic LES compared to microscale turbulence parameterizations commonly used in climate models.

physics.ao-ph↗

arXiv2024

Intrinsically episodic Antarctic shelf intrusions of circumpolar deep water via canyons

The structure of the Antarctic Slope Current at the continental shelf is crucial in governing the poleward transport of warm water. Canyons on the continental slope may provide a pathway for warm water to cross the slope current and intrude onto the continental shelf underneath ice shelves, which can increase rates of ice shelf melting, leading to reduced buttressing of ice shelves, accelerating glacial flow and hence increased sea level rise. Observations and modelling studies of the Antarctic Slope Current and cross-shelf warm water intrusions are limited, particularly in the East Antarctica region. To explore this topic, an idealised configuration of the Antarctic Slope Current is developed, using an eddy-resolving isopycnal model that emulates the dynamics and topography of the East Antarctic sector. Warm water intrusions via canyons are found to occur in discrete episodes of large onshore flow induced by eddies, even in the absence of any temporal variability in external forcings, demonstrating the intrinsic nature of these intrusions to the slope current system. Canyon width is found to play a key role in modulating cross-shelf exchanges; warm water transport through narrower canyons is more irregular than transport through wider canyons. The intrinsically episodic cross-shelf transport is found to be driven by feedbacks between wind energy input and eddy generation in the Antarctic Slope Current. Improved understanding of the intrinsic variability of warm water intrusions can help guide future observational and modelling studies in the analysis of eddy impacts on Antarctic shelf circulation.

physics.ao-ph↗

arXiv2023

Nusselt number scaling in horizontal convection

We report a numerical study of horizontal convection (HC) at Prandtl number $Pr = 1$, with both no-slip and free-slip boundary conditions. We obtain 2D and 3D solutions and determine the relation between the Rayleigh number $Ra$ and the Nusselt number $Nu$. In 2D we vary $Ra$ between $0$ and $10^{14}$. In the range $10^6 \le Ra \le 10^{10}$ the $Nu$-$Ra$ relation is $Nu \sim Ra^{1/5}$. With $Ra$ greater than about $10^{11}$ we find a 2D regime with $Nu \sim Ra^{1/4}$ over three decades, up to the highest 2D $Ra$. In 3D, with maximum $Ra = 10^{11.5}$, we find only $Nu \sim Ra^{1/5}$. These results apply to both free slip and no slip boundary conditions. The $Nu \sim Ra^{1/4}$ regime has a double boundary layer (BL): there is a thin BL with thickness $\sim Ra^{-1/4}$ nested inside a thicker BL with thickness $\sim Ra^{-1/5}$. The $Ra^{-1/4}$ BL thickness, which determines $Nu$, coincides with the Kolmogorov and Batchelor scales of HC. Numerical and theoretical results indicate that 3D HC is qualitatively and quantitatively similar to 2D HC. At the same $Ra$, the 3D $Nu$ exceeds the 2D $Nu$ by less than $20$%, i.e., there is very little 3D enhancement of heat transport. Boundary conditions are more important than dimensionality: the 2D free-slip solutions have larger $Nu$ than 3D no-slip solutions. Using the mechanical energy power integral of HC we show that the mean square vorticity of 3D HC is nearly equal to that of 2D HC at the same $Ra$. Thus vorticity amplification by strain-mediated vortex stretching does not operate in 3D HC.

physics.flu-dyn↗

arXiv2023

Surface heating steers planetary-scale ocean circulation

Gyres are central features of large-scale ocean circulation and are involved in transporting tracers such as heat, nutrients, and carbon-dioxide within and across ocean basins. Traditionally, the gyre circulation is thought to be driven by surface winds and quantified via Sverdrup balance, but it has been proposed that surface buoyancy fluxes may also contribute to gyre forcing. Through a series of eddy-permitting global ocean model simulations with perturbed surface forcing, the relative contribution of wind stress and surface heat flux forcing to the large-scale ocean circulation is investigated, focusing on the subtropical gyres. In addition to gyre strength being linearly proportional to wind stress, it is shown that the gyre circulation is strongly impacted by variations in the surface heat flux (specifically, its meridional gradient) through a rearrangement of the ocean's buoyancy structure. On shorter timescales ($\sim$ decade), the gyre circulation anomalies are proportional to the magnitude of the surface heat flux gradient perturbation, with up to $\sim 0.15\,\mathrm{Sv}$ anomaly induced per $\mathrm{W}\,\mathrm{m}^{-2}$ change in the surface heat flux. On timescales longer than a decade, the gyre response to surface buoyancy flux gradient perturbations becomes non-linear as ocean circulation anomalies feed back onto the buoyancy structure induced by the surface buoyancy fluxes. These interactions complicate the development of a buoyancy-driven theory for the gyres to complement the Sverdrup relation. The flux-forced simulations underscore the importance of surface buoyancy forcing in steering the large-scale ocean circulation.

physics.ao-ph↗

arXiv2023

Stokes drift should not be added to ocean general circulation model velocities

Studies of ocean surface transport often invoke the "Eulerian-mean hypothesis": that wave-agnostic general circulation models neglecting explicit surface waves effects simulate the Eulerian-mean ocean velocity time-averaged over surface wave oscillations. Acceptance of the Eulerian-mean hypothesis motivates reconstructing the total, Lagrangian-mean surface velocity by adding Stokes drift to model output. Here, we show that the Eulerian-mean hypothesis is inconsistent, because wave-agnostic models cannot accurately simulate the Eulerian-mean velocity if Stokes drift is significant compared to the Eulerian-mean or Lagrangian-mean velocity. We conclude that Stokes drift should not be added to ocean general circulation model velocities. We additionally show the viability of the alternative "Lagrangian-mean hypothesis" using a theoretical argument and by comparing a wave-agnostic global ocean simulation with an explicitly wave-averaged simulation. We find that our wave-agnostic model accurately simulates the Lagrangian-mean velocity even though the Stokes drift is significant.

physics.ao-ph↗

arXiv2022

Eigenvalue initialisation and regularisation for Koopman autoencoders

Regularising the parameter matrices of neural networks is ubiquitous in training deep models. Typical regularisation approaches suggest initialising weights using small random values, and to penalise weights to promote sparsity. However, these widely used techniques may be less effective in certain scenarios. Here, we study the Koopman autoencoder model which includes an encoder, a Koopman operator layer, and a decoder. These models have been designed and dedicated to tackle physics-related problems with interpretable dynamics and an ability to incorporate physics-related constraints. However, the majority of existing work employs standard regularisation practices. In our work, we take a step toward augmenting Koopman autoencoders with initialisation and penalty schemes tailored for physics-related settings. Specifically, we propose the "eigeninit" initialisation scheme that samples initial Koopman operators from specific eigenvalue distributions. In addition, we suggest the "eigenloss" penalty scheme that penalises the eigenvalues of the Koopman operator during training. We demonstrate the utility of these schemes on two synthetic data sets: a driven pendulum and flow past a cylinder; and two real-world problems: ocean surface temperatures and cyclone wind fields. We find on these datasets that eigenloss and eigeninit improves the convergence rate by up to a factor of 5, and that they reduce the cumulative long-term prediction error by up to a factor of 3. Such a finding points to the utility of incorporating similar schemes as an inductive bias in other physics-related deep learning approaches.

cs.LG↗

arXiv2022

How winds and ocean currents influence the drift of floating objects

Arctic icebergs, unconstrained sea ice floes, oil slicks, mangrove drifters, lost cargo containers, and other flotsam are known to move at 2-4% of the prevailing wind velocity relative to the water, despite vast differences in the material properties, shapes, and sizes of objects. Here, we revisit the roles of density, aspect ratio, and skin and form drag in determining how an object is driven by winds and water currents. Idealized theoretical considerations show that although substantial differences exist for end members of the parameter space (either very thin or thick and very light or dense objects), most realistic cases of floating objects drift at $\approx$3% of the free-stream wind velocity (measured outside an object's surface boundary layer). This relationship, known as a long-standing rule of thumb for the drift of various types of floating objects, arises from the square root of the ratio of the density of air to that of water. We support our theoretical findings with flume experiments using floating objects with a range of densities and shapes.

physics.ao-ph↗

arXiv2021

Intrinsic oceanic decadal variability of upper-ocean heat content

Atmosphere and ocean are coupled via air-sea interactions. The atmospheric conditions fuel the ocean circulation and its variability, but the extent to which ocean processes can affect the atmosphere at decadal time scales remains unclear. In particular, such low-frequency variability is difficult to extract from the short observational record, meaning that climate models are the primary tools deployed to resolve this question. Here, we assess how the ocean's intrinsic variability leads to patterns of upper-ocean heat content that vary at decadal time scales. These patterns have the potential to feed back on the atmosphere and thereby affect climate modes of variability, such as El Niño or the Interdecadal Pacific Oscillation. We use the output from a global ocean-sea ice circulation model at three different horizontal resolutions, each driven by the same atmospheric reanalysis. To disentangle the variability of the ocean's direct response to atmospheric forcing from the variability due to intrinsic ocean dynamics, we compare model runs driven with inter-annually varying forcing (1958-2018) and model runs driven with repeat-year forcing. Models with coarse resolution that rely on eddy parameterizations, show (i) significantly reduced variance of the upper-ocean heat content at decadal time scales and (ii) differences in the spatial patterns of low-frequency variability compared with higher resolution models. Climate projections are typically done with general circulation models with coarse-resolution ocean components. Therefore, these biases affect our ability to predict decadal climate modes of variability and, in turn, hinder climate projections. Our results suggest that for improving climate projections, the community should move towards coupled climate models with higher oceanic resolution.

physics.ao-ph↗

arXiv2020

Cause-and-effect of linear mechanisms sustaining wall turbulence

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in theoretical and conceptual arguments. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean-flow ($\bf U$) to the fluctuating velocities ($\bf u'$). We use cause-and-effect analysis based on interventions. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from $\bf U$ to $\bf u'$ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes, and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow. Finally, we demonstrate that an ensemble of simulations with various frozen-in-time $\bf U$ arranged so that only transient growth is active, can faithfully represent the energy transfer from $\bf U$ to $\bf u'$ as in realistic turbulence. Our approach provides direct cause-and-effect evaluation of the linear energy-injection mechanisms from $\bf U$ to $\bf u'$ in the fully nonlinear system and simplifies the conceptual model of self-sustaining wall turbulence.

physics.flu-dyn↗

arXiv2020

The Nusselt numbers of horizontal convection

We consider the problem of horizontal convection in which non-uniform buoyancy, $b_{\rm s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\mathbf{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\mathbf{J}\cdot\mathbf{\nabla}b_{\rm s}}=-κ\langle|\boldsymbol{\nabla}b|^2\rangle$; overbar denotes a space-time average over the top surface, angle brackets denote a volume-time average and $κ$ is the molecular diffusivity of buoyancy $b$. This connection between $\mathbf{J}$ and $κ\langle|\boldsymbol{\nabla}b|^2\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $κ\langle|\boldsymbol{\nabla}b|^2\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number currently in use. We investigate transient effects and show that $κ\langle|\boldsymbol{\nabla}b|^2\rangle$ equilibrates more rapidly than other global averages, such as the domain averaged kinetic energy and bottom buoyancy. We show that $κ\langle|\boldsymbol{\nabla} b|^2\rangle$ is essentially the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux of entropy through the top surface. This leads to an equivalent "surface Nusselt number", defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{\rm s}(x,y)$. In experiments it is likely easier to evaluate the surface entropy flux, rather than the volume integral of $|\mathbf{\nabla}b|^2$ demanded by $κ\langle|\mathbf{\nabla}b|^2\rangle$.

physics.flu-dyn↗

arXiv2019

Alternative physics to understand wall turbulence: Navier-Stokes equations with modified linear dynamics

Despite the nonlinear nature of wall turbulence, there is evidence that the energy-injection mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities from mean-flow inflection points, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified theories and conceptual arguments. Whether the flow follows any or a combination of them remains unclear. In the present study, we devise a collection of numerical experiments in which the Navier-Stokes equations are sensibly modified to quantify the role of the different linear mechanisms. This is achieved by direct numerical simulation of turbulent channel flows with constrained energy extraction from the streamwise-averaged mean-flow. We demonstrate that (i) transient growth alone is not sufficient to sustain wall turbulence and (ii) the flow remains turbulent when the exponential instabilities are suppressed. On the other hand, we show that (iii) transient growth combined with the parametric instability of the time-varying mean-flow is able to sustain turbulence.

physics.flu-dyn↗