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Abstract Separating the effects of waves and turbulence in oceanographic time series is an ongoing challenge because surface wave motion and turbulence fluctuations can occur at overlapping frequencies. Therefore, simple bandpass filters cannot effectively separate their dynamics. While more advanced decomposition techniques have been developed, they often entail restrictive assumptions about the wave and turbulence interactions, require synchronized measurements, and/or only decompose the signal spectrally without a time series reconstruction. We present our new wave–turbulence decomposition technique which uses dynamic mode decomposition (DMD). The technique is signal agnostic so it can be applied to any time series, and our only assumptions are that the waves and turbulence can be separated and that the waves are the most coherent features in the signal. Our approach requires minimal tuning, where the main user input is the wave frequency range of interest. To demonstrate the method, we apply it to synthetic, field, and laboratory data and compare the results to other modal decomposition methods. A sensitivity analysis on the synthetic data shows that the most sensitive parameter to the accuracy is the rank truncation in the DMD, and that the decomposition performs the best when the wave energy in the signal is of equal or greater magnitude than that of the turbulence. Given the accuracy of our decomposition, we are able to analyze the velocity autocorrelation of the separated turbulence time series with minimal wave contamination. Overall, our decomposition method outperforms the other decomposition methods and provides for robust separation of the waves and turbulence, demonstrating wide applicability to ocean signal processing. Significance StatementWhen measuring physical, chemical, and biological quantities in the ocean, the measurements are often influenced by both waves and turbulence. Isolating the individual effects of waves and turbulence on those variables is important to a wide range of analyses, such as estimating how momentum, heat, and nutrients are mixed throughout the water column. In this work, we propose a new method to separate the wave and turbulence components in ocean-data time series. When tested on laboratory, field, and synthetic data, our method was able to separate the wave and turbulence components of a signal more effectively than previously proposed algorithms.
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Extracting Spatial–Temporal Coherent Patterns in Geomagnetic Secular Variation Using Dynamic Mode Decomposition
Key Points Dynamic mode decomposition (DMD) is applied to the geomagnetic radial field and its time variation Waves with 20‐year and 60‐year periods are identified from the DMD decomposition The 60‐year waves are compatible with fluid stratification at the top of the core
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- Award ID(s):
- 2214244
- PAR ID:
- 10447704
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 50
- Issue:
- 5
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The decomposition of oceanic flow into its geostrophically balanced and unbalanced motions carries theoretical and practical significance for the oceanographic community. These two motions have distinct dynamical characteristics and affect the transport of tracers differently from one another. The launch of the Surface Water and Ocean Topography (SWOT) satellite provides a prime opportunity to diagnose the surface balanced and unbalanced motions on a global scale at an unprecedented spatial resolution. Here, we apply dynamic‐mode decomposition (DMD), a linear‐algebraic data‐driven method, to tidally‐forced idealized and realistic numerical simulations at submesoscale‐permitting resolution and one‐day‐repeat SWOT observations of sea‐surface height (SSH) in the Gulf Stream downstream of Cape Hatteras, a region commonly referred to as the separated Gulf Stream. DMD is able to separate out the spatial modes associated with sub‐inertial periods from super‐inertial periods. The sub‐inertial modes of DMD can be used to extract geostrophically balanced motions from SSH fields, which have an imprint of internal gravity waves, so long as the data extends long enough in time. We utilize the statistical relation between relative vorticity and strain rate as the metric to gauge the extraction of geostrophy.more » « less
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We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath’s vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.more » « less
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null (Ed.)Using the newly introduced ``occupation kernels,'' the present manuscript develops an approach to dynamic mode decomposition (DMD) that treats continuous time dynamics, without discretization, through the Liouville operator. The technical and theoretical differences between Koopman based DMD for discrete time systems and Liouville based DMD for continuous time systems are highlighted, which includes an examination of these operators over several reproducing kernel Hilbert spaces.more » « less
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The turbulent wake flow past a sphere at ReD= 3700 is investigated via Direct Numerical Simulation (DNS). The characteristic motions in the wake flow, such as vortex shedding and bubble pumping are identified by the probes placed in the near wake with a dominating frequency of St= fu∞/D= 0.22 and 0.004, respectively. The modal analysis is conducted in the wake area using Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The vortex shedding and bubble pumping motions are also captured by the modal analysis. The results from POD and DMD show comparable patterns of both characteristic motions. For the bubble pumping motion, the dominating frequency of the corresponding POD mode is St= 0.004, while the DMD mode that is directly related to the separation bubble has the frequency of St= 0.009.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1029/2022GL101288
