An official website of the United States government
Abstract By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier–Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler (Drivas and Eyink in Commun Math Phys 359(2):733–763, 2018.https://doi.org/10.1007/s00220-017-3078-4; Majda in Am Math Soc 43(281):93, 1983.https://doi.org/10.1090/memo/0281) and by recent constructions of dissipative incompressible Euler solutions (Brue and De Lellis in Commun Math Phys 400(3):1507–1533, 2023.https://doi.org/10.1007/s00220-022-04626-0 624; Brue et al. in Commun Pure App Anal, 2023), as well as passive scalars (Colombo et al. in Ann PDE 9(2):21–48, 2023.https://doi.org/10.1007/s40818-023-00162-9; Drivas et al. in Arch Ration Mech Anal 243(3):1151–1180, 2022.https://doi.org/10.1007/s00205-021-01736-2). For$$L^q_tL^r_x$$ suitable Leray–Hopf solutions of the$$d-$$ dimensional Navier–Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure$$\mathcal {P}^{s}$$ , which gives$$s=d-2$$ as soon as the solution lies in the Prodi–Serrin class. In the three-dimensional case, this matches with the Caffarelli–Kohn–Nirenberg partial regularity.
more »
« less
Assessment of the Precision of Spectral Model Turbulence Analysis Techniques Using Direct Numerical Simulation Data
Abstract The spectral model turbulence analysis technique is widely used to derive kinetic energy dissipation rates of turbulent structures (ɛ) from different in situ measurements in the Earth's atmosphere. The essence of this method is to fit a model spectrum to measured spectra of velocity or scalar quantity fluctuations and thereby to deriveɛonly from wavenumber dependence of turbulence spectra. Owing to the simplicity of spectral model of Heisenberg (1948),https://doi.org/10.1007/bf01668899its application dominates in the literature. Making use of direct numerical simulations which are able to resolve turbulence spectra down to the smallest scales in dissipation range, we advance the spectral model technique by quantifying uncertainties for two spectral models, the Heisenberg (1948),https://doi.org/10.1007/bf01668899and the Tatarskii (1971) model, depending on (a) resolution of measurements, (b) stage of turbulence evolution, (c) model used. We show that the model of Tatarskii (1971) can yield more accurate results and reveals higher sensitivity to the lowestɛ‐values. This study shows that the spectral model technique can reliably deriveɛif measured spectra only resolve half‐decade of power change within the viscous (viscous‐convective) subrange. In summary, we give some practical recommendations on how to derive the most precise and detailed turbulence dissipation field from in situ measurements depending on their quality. We also supply program code of the spectral models used in this study in Python, IDL, and Matlab.
more »
« less
- Award ID(s):
- 2032678
- PAR ID:
- 10378475
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Atmospheres
- Volume:
- 127
- Issue:
- 4
- ISSN:
- 2169-897X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Recent field studies have shown that the presence of ash in the atmosphere can produce measurable attenuation of Global Positioning System (GPS) signals (Aranzulla et al., 2013,https://doi.org/10.1007/s10291-012-0294-4; Larson, 2013,https://doi.org/10.1002/grl.50556; Larson et al., 2017,https://doi.org/10.1016/j.jvolgeores.2017.04.005). The ability to detect plumes using GPS is appealing because many active volcanoes are already instrumented with high‐quality receivers. However, analyses using a Ralyeigh approximation have shown that the large attenuations cannot be explained by the scattering and absorption associated with ash or hydrometeors alone. Here, we show that the extinction of GPS signals, which fall into the L‐band of the electromagnetic spectrum, may be exacerbated significantly by excess surface charge on pyroclasts. Indeed, volcanic eruptions are often accompanied by a range of electrostatic processes, leading, in some cases, to spectacular lightning storms. We use a modified Mie scattering model to demonstrate that electrostatic effects can increase the extinction of L‐band radiation by up to an order of magnitude, producing attenuations consistent with those observed in the field. Thus, future work involving GPS as a tool to remotely probe plumes must take into account the electrification of ash in radiative transfer models. Additionally, we propose that the sensitivity of GPS to particle charging may catalyze the development of new techniques to explore electrostatic processes in plumes, especially if GPS measurements are complemented with millimeter‐wave RADAR measurements.more » « less
-
Abstract We show that atmospheric gravity waves can generate plasma ducts and irregularities in the plasmasphere using the coupled SAMI3/WACCM‐X model. We find the equatorial electron density is irregular as a function of longitude which is consistent with CRRES measurements (Clilverd et al., 2007,https://doi.org/10.1029/2007ja012416). We also find that plasma ducts can be generated forL‐shells in the range 1.5–3.0 with lifetimes of ∼ 0.5 hr; this is in line with observations of ducted VLF wave propagation with lifetimes of 0.5–2.0 hr (Clilverd et al., 2008,https://doi.org/10.1029/2007ja012602; Singh et al., 1998,https://doi.org/10.1016/s1364-6826(98)00001-7).more » « less
-
Abstract We present modeling results of tube and knot (T&K) dynamics accompanying thermospheric Kelvin Helmholtz Instabilities (KHI) in an event captured by the 2018 Super Soaker campaign (R. L. Mesquita et al., 2020,https://doi.org/10.1029/2020JA027972). Chemical tracers released by a rocketsonde on 26 January 2018 showed coherent KHI in the lower thermosphere that rapidly deteriorated within 45–90 s. Using wind and temperature data from the event, we conducted high resolution direct numerical simulations (DNS) employing both wide and narrow spanwise domains to facilitate (wide domain case) and prohibit (narrow domain case) the axial deformation of KH billows that allows tubes and knots to form. KHI T&K dynamics are shown to produce accelerated instability evolution consistent with the observations, achieving peak dissipation rates nearly two times larger and 1.8 buoyancy periods faster than axially uniform KHI generated by the same initial conditions. Rapidly evolving twist waves are revealed to drive the transition to turbulence; their evolution precludes the formation of secondary convective instabilities and secondary KHI seen to dominate the turbulence evolution in artificially constrained laboratory and simulation environments. T&K dynamics extract more kinetic energy from the background environment and yield greater irreversible energy exchange and entropy production, yet they do so with weaker mixing efficiency due to greater energy dissipation. The results suggest that enhanced mixing from thermospheric KHI T&K events could account for the discrepancy between modeled and observed mixing in the lower thermosphere (Garcia et al., 2014,https://doi.org/10.1002/2013JD021208; Liu, 2021,https://doi.org/10.1029/2020GL091474) and merits further study.more » « less
-
Abstract Wave breaking induced bubbles contribute a significant part of air‐sea gas fluxes. Recent modeling of the sea state dependent CO2flux found that bubbles contribute up to ∼40% of the total CO2air‐sea fluxes (Reichl & Deike, 2020,https://doi.org/10.1029/2020gl087267). In this study, we implement the sea state dependent bubble gas transfer formulation of Deike and Melville (2018,https://doi.org/10.1029/2018gl078758) into a spectral wave model (WAVEWATCH III) incorporating the spectral modeling of the wave breaking distribution from Romero (2019,https://doi.org/10.1029/2019gl083408). We evaluate the accuracy of the sea state dependent gas transfer parameterization against available measurements of CO2gas transfer velocity from 9 data sets (11 research cruises, see Yang et al. (2022,https://doi.org/10.3389/fmars.2022.826421)). The sea state dependent parameterization for CO2gas transfer velocity is consistent with observations, while the traditional wind‐only parameterization used in most global models slightly underestimates the observations of gas transfer velocity. We produce a climatology of the sea state dependent gas transfer velocity using reanalysis wind and wave data spanning 1980–2017. The climatology shows that the enhanced gas transfer velocity occurs frequently in regions with developed sea states (with strong wave breaking and high significant wave height). The present study provides a general sea state dependent parameterization for gas transfer, which can be implemented in global coupled models.more » « less
