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15 pages, 3495 KiB

Open AccessArticle

Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

by Leonid M. Ivanov, Collins A. Collins and Tetyana Margolina

Fluids 2021, 6(3), 111; https://doi.org/10.3390/fluids6030111 - 9 Mar 2021

Cited by 3 | Viewed by 1745

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (< [...] Read more.

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X²>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X²> =

\lim_{T \to \infty} τ_{X}^{2} (T, s)

, where

τ_{X}^{2}

(T, s) = 1/(T − s)

\int_{0}^{T - s} (X (t + Δ t)

− X(t))² dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X²> =

\lim_{T \to \infty} ≪ τ_{X}^{2} (T, s) ≫

, where

≪ \dots ≫

is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 10⁵ to 10⁶ cm²/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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24 pages, 12043 KiB

Open AccessArticle

Spectral Early-Warning Signals for Sudden Changes in Time-Dependent Flow Patterns

by Moussa Ndour, Kathrin Padberg-Gehle and Martin Rasmussen

Fluids 2021, 6(2), 49; https://doi.org/10.3390/fluids6020049 - 22 Jan 2021

Cited by 4 | Viewed by 2163

Abstract

Lagrangian coherent sets are known to crucially determine transport and mixing processes in non-autonomous flows. Prominent examples include vortices and jets in geophysical fluid flows. Coherent sets can be identified computationally by a probabilistic transfer-operator-based approach within a set-oriented numerical framework. Here, we [...] Read more.

Lagrangian coherent sets are known to crucially determine transport and mixing processes in non-autonomous flows. Prominent examples include vortices and jets in geophysical fluid flows. Coherent sets can be identified computationally by a probabilistic transfer-operator-based approach within a set-oriented numerical framework. Here, we study sudden changes in flow patterns that correspond to bifurcations of coherent sets. Significant changes in the spectral properties of a numerical transfer operator are heuristically related to critical events in the phase space of a time-dependent system. The transfer operator approach is applied to different example systems of increasing complexity. In particular, we study the 2002 splitting event of the Antarctic polar vortex. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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34 pages, 11340 KiB

Open AccessEditor’s ChoiceArticle

An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows

by Margaux Filippi, Irina I. Rypina, Alireza Hadjighasem and Thomas Peacock

Fluids 2021, 6(1), 39; https://doi.org/10.3390/fluids6010039 - 12 Jan 2021

Cited by 14 | Viewed by 4187

Abstract

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building [...] Read more.

In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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34 pages, 2521 KiB

Open AccessArticle

Separating Mesoscale and Submesoscale Flows from Clustered Drifter Trajectories

by Sarah Oscroft, Adam M. Sykulski and Jeffrey J. Early

Fluids 2021, 6(1), 14; https://doi.org/10.3390/fluids6010014 - 31 Dec 2020

Cited by 4 | Viewed by 2672

Abstract

Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to a local Taylor expansion of the velocity [...] Read more.

Drifters deployed in close proximity collectively provide a unique observational data set with which to separate mesoscale and submesoscale flows. In this paper we provide a principled approach for doing so by fitting observed velocities to a local Taylor expansion of the velocity flow field. We demonstrate how to estimate mesoscale and submesoscale quantities that evolve slowly over time, as well as their associated statistical uncertainty. We show that in practice the mesoscale component of our model can explain much first and second-moment variability in drifter velocities, especially at low frequencies. This results in much lower and more meaningful measures of submesoscale diffusivity, which would otherwise be contaminated by unresolved mesoscale flow. We quantify these effects theoretically via computing Lagrangian frequency spectra, and demonstrate the usefulness of our methodology through simulations as well as with real observations from the LatMix deployment of drifters. The outcome of this method is a full Lagrangian decomposition of each drifter trajectory into three components that represent the background, mesoscale, and submesoscale flow. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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24 pages, 11619 KiB

Open AccessArticle

Eulerian and Lagrangian Comparison of Wind Jets in the Tokar Gap Region

by Larry J. Pratt, E. Jason Albright, Irina Rypina and Houshuo Jiang

Fluids 2020, 5(4), 193; https://doi.org/10.3390/fluids5040193 - 29 Oct 2020

Cited by 3 | Viewed by 2177

Abstract

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a Weather Research and Forecasting (WRF) model hindcast for 2008. Winds in the Tokar Gap reach 25 m s⁻¹ and remain coherent [...] Read more.

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a Weather Research and Forecasting (WRF) model hindcast for 2008. Winds in the Tokar Gap reach 25 m s⁻¹ and remain coherent as a jet far out over the Red Sea, whereas equally strong wind jets occurring in neighboring gaps are attenuated abruptly by jump-like hydraulic transitions that occur just offshore of the Sudan coast. The transition is made possible by the supercritical nature of the jets, which are fed by air that spills down from passes at relatively high elevation. By contrast, the spilling flow in the ravine-like Tokar Gap does not become substantially supercritical and therefore does not undergo a jump, and also carries more total horizontal momentum. The Tokar Wind Jet carries some air parcels across the Red Sea and into Saudi Arabia, whereas air parcel trajectories in the neighboring jets ascend as they cross through the jumps, then veer sharply to the southeast and do not cross the Red Sea. The mountain parameter Nh/U is estimated to lie in the range of 1.0–4.0 for the general region, a result roughly consistent with a gap jet having a long extension, and supercritical flows spilling down from higher elevation passes. The strong event is marked by the formation of a feature with a vertical cellular structure in the upstream entrance region of the Tokar Gap, a feature absent from the more moderate events that occur throughout the summer. The cell contains descending air parcels that are fed into the Tokar Gap and one of the neighboring gaps. An analysis of the Bernoulli function along air parcel trajectories reveals an approximate balance between the loss of potential energy and gain of internal energy and pressure, with surprisingly little contribution from kinetic energy, along the path of the descending flow. The winds in all gaps attain the critical wind speed nominally required to loft dust into the atmosphere, though only the Tokar Gap has a broad, silty delta region capable of supplying particulate matter for dust storms. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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10 pages, 7196 KiB

Open AccessArticle

Uncovering Fine-Scale Wave-Driven Transport Features in a Fringing Coral Reef System via Lagrangian Coherent Structures

by Matthieu Leclair, Ryan Lowe, Zhenlin Zhang, Greg Ivey and Thomas Peacock

Fluids 2020, 5(4), 190; https://doi.org/10.3390/fluids5040190 - 24 Oct 2020

Cited by 2 | Viewed by 2282

Abstract

Understanding the transport and exchange of water masses both within a reef and between a reef and the surrounding ocean is needed to describe a wide-range of ecosystem processes that are shaped by the movement of material and heat. We show how novel [...] Read more.

Understanding the transport and exchange of water masses both within a reef and between a reef and the surrounding ocean is needed to describe a wide-range of ecosystem processes that are shaped by the movement of material and heat. We show how novel Lagrangian data processing methods, specifically developed to reveal key and often hidden transport structures, can help visualize flow transport patterns within and around morphologically complex reef systems. As an example case study, we consider the wave-driven flow transport within the Ningaloo Reef in Western Australia. We show that a network of attracting, repelling, and trapping flow transport structures organizes the flow transport into, around, and out of the reef. This approach is broadly applicable to coral reef systems, since the combination of well-defined bathymetry and persistent flow-forcing mechanisms (e.g., by wave breaking or tides) is conducive to the existence of persistent Lagrangian transport structures that organize material transport. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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25 pages, 35320 KiB

Open AccessArticle

Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents

by Xuping Xie, Peter J. Nolan, Shane D. Ross , Changhong Mou and Traian Iliescu

Fluids 2020, 5(4), 189; https://doi.org/10.3390/fluids5040189 - 23 Oct 2020

Cited by 6 | Viewed by 3452

Abstract

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In [...] Read more.

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote

α

-ROM and

λ

-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the

α

-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs’ accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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23 pages, 15945 KiB

Open AccessEditor’s ChoiceArticle

Uncertainty Quantification of Trajectory Clustering Applied to Ocean Ensemble Forecasts

by Guilherme S. Vieira, Irina I. Rypina and Michael R. Allshouse

Fluids 2020, 5(4), 184; https://doi.org/10.3390/fluids5040184 - 17 Oct 2020

Cited by 8 | Viewed by 2967

Abstract

Partitioning ocean flows into regions dynamically distinct from their surroundings based on material transport can assist search-and-rescue planning by reducing the search domain. The spectral clustering method partitions the domain by identifying fluid particle trajectories that are similar. The partitioning validity depends on [...] Read more.

Partitioning ocean flows into regions dynamically distinct from their surroundings based on material transport can assist search-and-rescue planning by reducing the search domain. The spectral clustering method partitions the domain by identifying fluid particle trajectories that are similar. The partitioning validity depends on the accuracy of the ocean forecasting, which is subject to several sources of uncertainty: model initialization, limited knowledge of the physical processes, boundary conditions, and forcing terms. Instead of a single model output, multiple realizations are produced spanning a range of potential outcomes, and trajectory clustering is used to identify robust features and quantify the uncertainty of the ensemble-averaged results. First, ensemble statistics are used to investigate the cluster sensitivity to the spectral clustering method free-parameters and the forecast parameters for the analytic Bickley jet, a geostrophic flow model. Then, we analyze an operational coastal ocean ensemble forecast and compare the clustering results to drifter trajectories south of Martha’s Vineyard. This approach identifies regions of low uncertainty where drifters released within a cluster predominantly remain there throughout the window of analysis. Drifters released in regions of high uncertainty tend to either enter neighboring clusters or deviate from all predicted outcomes. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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19 pages, 3594 KiB

Open AccessArticle

Cross-Shelf Transport Through the Interaction among a Coastal Jet, a Topographic Wave, and Tides

by Helga S. Huntley, Charles W. McMahon, Joseph J. Kuehl and A. D. Kirwan, Jr.

Fluids 2020, 5(4), 181; https://doi.org/10.3390/fluids5040181 - 16 Oct 2020

Cited by 1 | Viewed by 2428

Abstract

Shelf break flows are often characterized by along-isobath jets with cross-shelf currents associated with tides and waves guided by variable topography. Here, we address the question: Can a superposition of such flows produce significant aperiodic cross-shelf transport? To answer this question, we use [...] Read more.

Shelf break flows are often characterized by along-isobath jets with cross-shelf currents associated with tides and waves guided by variable topography. Here, we address the question: Can a superposition of such flows produce significant aperiodic cross-shelf transport? To answer this question, we use a barotropic analytic model for the jet based on a similarity solution of the shallow water equations over variable topography, a wave disturbance determined by the topography, and a diurnal tidal disturbance. We use standard Lagrangian methods to assess the cross-shelf transport, presenting the results, however, in a Eulerian frame, so as to be amenable to oceanographic observations. The relative roles of the different flow components in cross-shelf transport are assessed through an extensive parameter study. We find that a superposition of all three flow components can indeed produce consequential background aperiodic transport. An application of the model using recent observations from the Texas Shelf demonstrates that a combination of these background mechanisms can produce significant transport under realistic conditions. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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38 pages, 7825 KiB

Open AccessArticle

Investigating the Formation of Submesoscale Structures along Mesoscale Fronts and Estimating Kinematic Quantities Using Lagrangian Drifters

by John Lodise, Tamay Özgökmen, Rafael C. Gonçalves, Mohamed Iskandarani, Björn Lund, Jochen Horstmann, Pierre-Marie Poulain, Jody Klymak, Edward H. Ryan and Cedric Guigand

Fluids 2020, 5(3), 159; https://doi.org/10.3390/fluids5030159 - 14 Sep 2020

Cited by 14 | Viewed by 3957

Abstract

Much of the vertical transport near the surface of the ocean, which plays a critical role in the transport of dissolved nutrients and gases, is thought to be associated with ageostrophic submesoscale phenomena. Vertical velocities are challenging not only to model accurately, but [...] Read more.

Much of the vertical transport near the surface of the ocean, which plays a critical role in the transport of dissolved nutrients and gases, is thought to be associated with ageostrophic submesoscale phenomena. Vertical velocities are challenging not only to model accurately, but also to measure because of how difficult they are to locate in the surface waters of the ocean. Using unique massive drifter releases during the Lagrangian Submesoscale Experiment (LASER) campaign in the Gulf of Mexico and the Coherent Lagrangian Pathways from the Surface Ocean to the Interior (CALYPSO) experiment in the Mediterranean Sea, we investigate the generation of submesoscale structures along two different mesoscale fronts. We use a novel method to project Lagrangian trajectories to Eulerian velocity fields, in order to calculate horizontal velocity gradients at the surface, which are used as a proxy for vertical transport. The velocity reconstruction uses a squared-exponential covariance function, which characterizes velocity correlations in horizontal space and time, and determines the scales of variation using the data itself. SST and towed CTD measurements support the findings revealed by the drifter data. Due to the production of a submesoscale instability eddy in the Gulf of Mexico, convergence magnitudes of up to ∼20 times the planetary vorticity, f, are observed, the value of which is almost 3 times larger than that found in the mesoscale dominated Western Mediterranean Sea. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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18 pages, 4502 KiB

Open AccessArticle

Lagrangian Statistics of Heat Transfer in Homogeneous Turbulence Driven by Boussinesq Convection

by Jane Pratt, Angela Busse and Wolf-Christian Müller

Fluids 2020, 5(3), 127; https://doi.org/10.3390/fluids5030127 - 3 Aug 2020

Cited by 1 | Viewed by 3169

Abstract

The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, [...] Read more.

The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, both because of local spatial variations due to plumes and because of intermittency in time. We develop a statistical approach to more completely describe the structure of heat transfer, using an exit-distance extracted from Lagrangian tracer particles, which we call the Lagrangian heat structure. In a comparison between simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as a clear trend with Prandtl number and Rayleigh number. This has encouraging implications for simulations performed with the goal of understanding turbulent convection in natural settings such as Earth’s atmosphere and oceans, as well as planetary and stellar dynamos. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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25 pages, 5479 KiB

Open AccessArticle

Role of Surface-Layer Coherent Eddies in Potential Vorticity Transport in Quasigeostrophic Turbulence Driven by Eastward Shear

by Wenda Zhang, Christopher L. P. Wolfe and Ryan Abernathey

Fluids 2020, 5(1), 2; https://doi.org/10.3390/fluids5010002 - 22 Dec 2019

Cited by 10 | Viewed by 3841

Abstract

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted [...] Read more.

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10–20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence. Full article

(This article belongs to the Special Issue Lagrangian Transport in Geophysical Fluid Flows)

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