Horizontal Kinetic Energy Research Articles

Global Observations of Deep Ocean Kinetic Energy Transfers

Abstract Observations of deep Argo displacements (located between 950 and 1150 dbar) and their associated integrated Lagrangian velocities allow for the first time to compute worldwide deep horizontal transfers of kinetic energy (KE) between the 3° × 3° mean and eddy reservoirs [mean kinetic energy (MKE) and eddy kinetic energy (EKE), respectively]. This diagnostic reveals that the transfers are mainly localized along western boundaries and in the Southern Ocean. Overall, the MKE-to-EKE transfers appear dominant globally and in all specifically tested regions (i.e., Gulf Stream, Kuroshio, Agulhas Current, and Antarctic Circumpolar Current). However, an important exception is the Zapiola Gyre where EKE-to-MKE transfers dominate. Beyond that, we find that horizontal KE transfers are better described by the horizontal properties of the mean flow deformation (divergence and strain) than by the horizontal properties of the turbulent velocities. Our theoretical analysis also demonstrates that the mean flow vorticity does not contribute to KE transfers. We show the existence of two consistent transfer modes: one from MKE to EKE and one from EKE to MKE, which are based on the eigendirections of the mean flow deformation tensor. The alignment of the turbulence along these directions selects the transfer modes, and it is the competition between these two transfer modes that leads to the actual transfers. We compute these transfer modes globally, regionally, and locally. We explain the distinctive situation of the Zapiola Gyre by the favored alignment of the turbulence with the EKE-to-MKE transfer mode. Overall, the dominance of the large-scale flow properties on the structure of the MKE-to-EKE transfers suggests the potential for large-scale parameterization.

Energy Partition between Submesoscale Internal Waves and Quasigeostrophic Vortical Motion in the Pycnocline

Abstract Shipboard ADCP velocity and towed CTD chain density measurements from the eastern North Pacific pycnocline are used to segregate energy between linear internal waves (IW) and linear vortical motion [quasigeostrophy (QG)] in 2D wavenumber space spanning submesoscale horizontal wavelengths λx ∼ 1–50 km and finescale vertical wavelengths λz ∼ 7–100 m. Helmholtz decomposition and a new Burger number (Bu) decomposition yield similar results despite different methodologies. While these wavelengths are conventionally attributed to internal waves, both QG and IW contribute significantly at all measured scales. Partition between IW and QG total energies depends on Bu. For Bu < 0.01, available potential energy EP exceeds horizontal kinetic energy EK and is contributed mostly by QG. In contrast, energy is nearly equipartitioned between QG and IW for Bu ≫ 1. For Bu < 2, EK is contributed mainly by IW, and EP by QG, while, for Bu > 2, contributions are reversed. Finescale near-inertial IW dominate vertical shear variance, implying negligible QG contribution to vertical shear instability. In contrast, both QG and IW at the smallest λx ∼ 1 km contribute large horizontal shear variance, so that both may lead to horizontal shear instability, while QG, with its longer time scales, likely dominates isopycnal stirring. Both QG and IW contribute to vortex stretching at small vertical scales. For QG, the relative vorticity contribution to linear potential vorticity anomaly increases with decreasing horizontal and increasing vertical scales.

Surface and Sub‐Surface Kinetic Energy Wavenumber‐Frequency Spectra in Global Ocean Models and Observations

AbstractThis paper examines spectra of horizontal kinetic energy (HKE) in the surface and sub‐surface ocean, with an emphasis on internal gravity wave (IGW) motions, in global high‐resolution ocean simulations. Horizontal wavenumber‐frequency spectra of surface HKE are computed over seven oceanic regions from two global simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three global simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). In regions with high IGW activity, high surface HKE variance in the horizontal wavenumber‐frequency spectra is aligned along IGW linear dispersion curves. For both HYCOM and MITgcm, and in almost all regions, finer horizontal resolution yields more energetic supertidal IGW continuum spectra. The ratio of high‐horizontal‐wavenumber variance in semi‐diurnal and supertidal motions relative to lower‐frequency motions, a quantity of great interest for swath altimetry, depends on the model employed and the horizontal resolution within the model, implying that quantitative predictions of the partition between low‐ and high‐frequency motions taken from particular simulations should be treated with care. The frequency‐vertical wavenumber spectra, frequency spectra, and vertical wavenumber spectra from the models are compared to spectra computed from McLane profilers at nine locations. In general, MITgcm spectra match the McLane profiler spectra more closely at high frequencies (|ω| > 4.5 cpd). In both models, vertical wavenumber spectra roll off more steeply than observations at high vertical wavenumbers (m > 10−2 cpm). The vertical wavenumber spectra in such models is an important target for improvement, due to turbulence production and dissipation that takes place at high vertical wavenumbers.

The Rotational and Divergent Kinetic Energy Spectra of Geostrophic Vortices and Inertia‐Gravity Waves

AbstractThe rotational and divergent kinetic energy (RKE and DKE) spectra of geostrophic vortices (Rossby waves; RWs) and inertia‐gravity waves (IGWs) in the global atmosphere are investigated with ERA5 reanalysis. The separation of RWs and IGWs in physical space is based on the normal‐mode decomposition, and the Helmholtz decomposition produces their RKE and DKE spectra at different layers, with a focus on spherical wavenumbers 10 ≤ l ≤ 100. In the upper troposphere and the middle and lower stratosphere, the RKE spectra of the total mode closely resemble the horizontal kinetic energy (HKE) spectra of RWs over most wavenumbers; the DKE spectra of the total mode are more comparable to the DKE spectra rather than the HKE spectra of IGWs, although their slopes are similar. The HKE of RWs is dominated by its rotational component, accounting for more than 80% of the HKE in most ranges of concern. Although the HKE of IGWs is dominated by its divergent component, its rotation component is also significant, with an average percentage exceeding 25% in all three vertical layers analyzed. Care must be taken when employing divergence as a proxy of IGWs, as the DKE may underestimate the HKE of IGWs. With the increase of altitude and the decrease of scale, the contribution of the divergent component increases in the horizontal circulation of both RWs and IGWs.

Energy budget characteristics of the subseasonal Scandinavian pattern

Based on daily Japanese 55-year reanalysis data, this study analysed the daily energy budget characteristics of 94 Scandinavian (SCA) events in the positive phase during 62 winters from 1958 to 2020. Low-frequency circulation anomalies characterize the SCA events. The maintenance of low-frequency anomalies mainly comes from the extraction of both available potential energy (APE) and kinetic energy (KE) from the background field during both the developing stage and the decaying stage. This energy conversion characteristic is related to the “locking” effect of the background field. During the developing stage, the interactions among the low-frequency circulation anomalies continuously generate KE, which is the main source for initiating the primary circulation anomalies around western Europe and the Scandinavian Peninsula. Meanwhile, the horizontal KE advection maintains the KE of the circulation anomalies around Lake Baikal. The decay process of the SCA events is mainly related to the damping effect on the APE due to diabatic heating and the interactions among the low-frequency circulation anomalies. The SCA event is a type of atmospheric internal dynamic pattern.

Exploring the Differences in Kinetic Energy Spectra between the NCEP FNL and ERA5 Datasets

Abstract Two global atmospheric circulation datasets (ERA5 and NCEP FNL) with horizontal resolutions of 0.25° × 0.25° are investigated in terms of kinetic energy (KE) spectra at 200 hPa (roughly between 11 and 12 km). The horizontal KE (HKE) in NCEP FNL is larger and flatter than that in ERA5 at subsynoptic scales and mesoscales. Restoring the energy of this wavenumber range to the physical space shows that the HKE in NCEP FNL is larger than that in ERA5 over most areas but smaller mainly in the Indo-Pacific warm pool. The spectral budgets show that at these scales, the positive contribution from net vertical flux in ERA5 is stronger than that in NCEP FNL, while the negative contribution from available potential energy (APE) conversion is smaller; assuming that the atmosphere is in a quasi-stationary state, more dissipation is found in ERA5 than in NCEP FNL, which should be responsible for the HKE spectrum in ERA5 to be steeper and weaker than that in NCEP FNL. Our formulation shows that the APE conversion and net vertical flux are related to the pressure vertical velocity (PVV). The APE conversion and net vertical flux differences between the two datasets, like the PVV difference, are mainly from the tropical region. At large scales, the vertical motion in ERA5 is larger than that in NCEP FNL. The amplitude differences of the PVV spectra between two datasets are consistent with those of the large-scale precipitation spectra associated with microphysics parameterizations. These results support that vertical motion is a key dynamical factor explaining energy discrepancies at mesoscales. Significance Statement The atmospheric kinetic energy spectrum reflects energy distribution characteristics in atmospheric motion at different scales. According to the Helmholtz decomposition, the horizontal wind field can be decomposed into two parts: rotational wind field and divergent wind field. We explore the dynamical causes of the atmospheric energy spectra differences among different datasets from the perspective of rotational and divergent components of motion. Our results reveal that the differences in energy spectra and their energy budget at scales below a few hundred kilometers are relatively significant in tropical regions and are closely related to vertical motion. A better understanding of the differences in kinetic energy spectra will contribute to the improvement of atmospheric models.

Characterization of physical properties of a coastal upwelling filament with evidence of enhanced submesoscale activity and transition from balanced to unbalanced motions in the Benguela upwelling region

Abstract. We combine high-resolution in situ data (acoustic Doppler current profiler (ADCP), Scanfish, and surface drifters) and remote sensing to investigate the physical characteristics of a major filament observed in the Benguela upwelling region. The 30–50 km wide and about 400 km long filament persisted for at least 40 d. Mixed-layer depths were less than 40 m in the filament and over 60 m outside of it. Observations of the Rossby number Ro from the various platforms provide the spatial distribution of Ro for different resolutions. Remote sensing focuses on geostrophic motions of the region related to the mesoscale eddies that drive the filament formation and thereby reveals |Ro|<0.1. Ship-based measurements in the surface mixed layer reveal 0.5<|Ro|<1, indicating the presence of unbalanced, ageostrophic motions. Time series of Ro from triplets of surface drifters trapped within the filament confirm these relatively large Ro values and show a high variability along the filament. A scale-dependent analysis of Ro, which relies on the second-order velocity structure function, was applied to the latter drifter group and to another drifter group released in the upwelling zone. The two releases explored the area nearly distinctly and simultaneously and reveal that at small scales (<15 km) Ro values are twice as large in the filament in comparison to its environment with Ro>1 for scales smaller than ∼500 m. This suggests that filaments are hotspots of ageostrophic dynamics, pointing to the presence of a forward energy cascade. The different dynamics indicated by our Ro analysis are confirmed by horizontal kinetic energy wavenumber spectra, which exhibit a power law k−α with α∼5/3 for wavelengths 2π/k smaller than a transition scale of 15 km, supporting significant submesoscale energy at scales smaller than the first baroclinic Rossby radius (Ro1∼30 km). The detected transition scale is smaller than those found in regions with less mesoscale eddy energy, consistent with previous studies. We found evidence for the processes which drive the energy transfer to turbulent scales. Positive Rossby numbers 𝒪(1) associated with cyclonic motion inhibit the occurrence of positive Ertel potential vorticity (EPV) and stabilize the water column. However, where the baroclinic component of EPV dominates, submesoscale instability analysis suggests that mostly gravitational instabilities occur and that symmetric instabilities may be important at the filament edges.

Observations of near-inertial internal wave amplification and enhanced mixing after surface reflection

The overreflection process of near-inertial internal waves (NIWs) has been theoretically predicted for several decades; however, to the best of our knowledge, this phenomenon has never been comprehensively investigated in real ocean scenarios. Based on the buoy observations collected several days after the passage of Typhoon Lekima in the Yellow Sea, a NIW surface overreflection event is clearly captured. The observed NIWs undergo nearly total reflection meridionally but are amplified zonally after reflection by approximately 20% in amplitude and 56% in vertically integrated horizontal kinetic energy. Ray tracing analysis indicates that the NIW was generated in the wake of Typhoon Lekima in the area north of the Shandong Peninsula and may propagated to the buoy station as coastal-trapped internal Kelvin waves. A simulation using a slab mixed layer model suggests that local wind work was insufficient to generate the amplified NIWs. The temporal evolution of near-inertial energy also implies that the intensified near-inertial waves cannot be attributed to the spontaneous generation resulting from unbalanced flows or the parametric subharmonic instability of M2 internal tides during the reflection period. We found a high temporal correlation between the zonal NIW enhancement and the duration of a meridional lens-type shear flow after reflection, which is consistent with the Stern’s overreflection theory (Stern, 1977) that perpendicular background shear flow can feed energy to the incident NIWs. This indicates that the enhanced NIW may be stimulated by the near-surface reflection and the rotation effect plays a crucial role in the NIWs overreflection process in the real ocean. Furthermore, enhanced instability are found between the ocean surface and the upper thermocline after reflection. This study provides observational evidence that the background field could inject energy into the near-inertial band through NIW overreflection process, and may shed some light on understanding upper ocean mixing caused by NIW reflection.

Numerical Simulations of Internal Tide Dynamics in a Steep Submarine Canyon

Abstract This study investigates three-dimensional semidiurnal internal tide (IT) energetics in the vicinity of La Jolla Canyon, a steep shelf submarine canyon off the Southern California coast, with the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) numerical simulator. Numerical simulations show vertical structure and temporal phasing consistent with detailed field observations. ITs induce large (approximately 34 m from peak to peak) isotherm displacements and net onshore IT energy flux up to 200 W m−1. Although the net IT energy flux is onshore, the steep supercritical slope around the canyon results in strong reflection. The model provides the full life span of internal tides around the canyon, including internal tide generation, propagation, and dissipation. ITs propagate into the canyon from the south and are reflected back toward offshore from the canyon’s north side. In the inner part of the canyon, elevated mixing occurs in the middle layer due to an interaction between incident mode-1 ITs and reflected higher-mode ITs. The magnitude of IT flux, generation, and dissipation on the south side of the canyon are higher than those on the north side. An interference pattern in horizontal kinetic energy and available potential energy with a scale of approximately 20–50 km arises due to low-mode wave reflections. Our results provide new insight into IT dynamics associated with a small-scale canyon topography. Significance Statement Internal waves play an important role in ocean circulations and ecosystems. In particular, internal waves with frequencies of tides, known as internal tides, strongly enhance energy, heat, and mass transport in coastal oceans. This study presents internal tide dynamics in La Jolla Canyon, California, using a high-resolution numerical model. Model results show energy convergence in the canyon leading to internal tide energy dissipation and mixing. Some parts of internal tide energy reflect back offshore resulting in standing internal waves off California. This study provides new insights into internal tide dynamics and energy budgets in submarine canyons.

Horizontal kinetic energy analysis of tropical transition simulations with the WRF and HARMONIE‐AROME models

AbstractFour tropical transition (TT) events in the North Atlantic basin are simulated with the Weather Research and Forecasting (WRF) and the HARMONIE‐AROME (HAR) models to study the main features of the horizontal kinetic energy (HKE) spectra of these kinds of high‐energetic atmospheric system. Though most of the times similar results are obtained with both models, HAR shows a more intense filtering and numerical dissipation, whereas WRF tends to represent overenergized spectra in the synoptic scale and especially at smaller wavelengths. Predictability is dissimilar for the four TTs studied due to the different spectral curve slope obtained for each case, ranging from unlimited to very poor predictability at synoptic scale. Additionally, an increased HKE is presented in the middle–upper troposphere spectra. A deep analysis of the different terms involved in the equation of the spectral energy budget is presented through a detailed study of one of these TTs. The role of all of them is studied, connecting the energy spectra and the meteorological processes involved. The energy budget terms related to the nonlinear spectral transfer, the three‐dimensional divergence, and diabatic process tendencies are identified as the key ones, whereas the potential and kinetic conversion terms and the vertical flux HKE and pressure divergence terms play a secondary role on modulating the spectrum behaviour. The major energetic contributions are found at the synoptic scale, but results show that a two‐dimensional energy cascade does not fully capture the whole spectrum of a TT. The role of convection, latent heat release, and moist convection outbursts is sketched and a link within different vertical levels is found. Results show that a high‐energetic system, such as a TT, can effectively alter the atmospheric energy behaviour.

On energy conservation for the hydrostatic Euler equations: an Onsager conjecture

Onsager’s conjecture, which relates the conservation of energy to the regularity of weak solutions of the Euler equations, was completely resolved in recent years. In this work, we pursue an analogue of Onsager’s conjecture in the context of the hydrostatic Euler equations (also known as the inviscid primitive equations of oceanic and atmospheric dynamics). In this case the relevant conserved quantity is the horizontal kinetic energy. We first consider the standard notion of weak solution which is commonly used in the literature. We show that if the horizontal velocity (u, v) is sufficiently regular then the horizontal kinetic energy is conserved. Interestingly, the spatial Hölder regularity exponent which is sufficient for energy conservation in the context of the hydrostatic Euler equations is frac{1}{2} and hence larger than the corresponding regularity exponent for the Euler equations (which is frac{1}{3}). This is due to the anisotropic regularity of the velocity field: Unlike the Euler equations, in the case of the hydrostatic Euler equations the vertical velocity w is one degree spatially less regular with respect to the horizontal variables, compared to the horizontal velocity (u, v). Since the standard notion of weak solution is not able to deal with this anisotropy properly, we introduce two new notions of weak solutions for which the vertical part of the nonlinearity is interpreted as a paraproduct. We finally prove several sufficient conditions for such weak solutions to conserve energy.

Kinetic Energy Spectra and Spectral Budget of Radiative–Convective Equilibrium

Abstract The atmospheric kinetic energy spectrum and energy cascade are investigated in idealized simulations of radiative–convective equilibrium (RCE). WRF is employed to perform cloud-resolving simulations of an idealized radiative–convective equilibrium with and without aggregation with Δx = 4 km. The horizontal kinetic energy (HKE) spectrum for the aggregated simulation in the upper troposphere is steeper than the nonaggregated case and closer to −5/3. The HKE spectra for the nonaggregated simulation in the upper troposphere and the lower stratosphere are much shallower than the −5/3 spectrum. In the upper troposphere, the divergent kinetic energy has a similar magnitude to the rotational kinetic energy in both the nonaggregated simulation and aggregated simulation. Energy is mainly gained from the buoyancy flux and mainly lost from the vertical energy flux for scales larger than 20 km. Downscale energy transfer is found in the upper troposphere. Numerical dissipation is the main source of energy loss at small scales. In the lower stratosphere, the divergent kinetic energy dominates the kinetic energy spectrum in both simulations. Energy is mainly gained from the vertical energy flux and is balanced by the loss from the buoyancy flux term, transfer term, and dissipation. An Eliassen–Palm flux analysis suggests that wave–mean-flow interaction may be responsible for the upscale energy transfer found in the lower stratosphere. The magnitudes of our kinetic energy spectra are similar to spectra calculated from aircraft data. Rotation is found to promote aggregation and steepen the energy spectrum.

Observed Oceanic Surface Modes in the Northern South China Sea

Abstract Using observations and theoretical models, a substantial topographic modulation on the quasigeostrophic (QG) dynamics, which results in a primary surface mode distinct from the classic first baroclinic (BC1) mode with a flat bottom, is revealed in the northern South China Sea (NSCS). In contrast to open oceans, the surface-intensified modes decay downward more rapidly over the continental slope of the NSCS, with a mean e-folding scale of approximately 1/5 of water depth. The subinertial flow variability appears to be vertically incoherent, with planetary and topographic Rossby waves dominating in the upper and deep layers, respectively. With a larger deformation radius (Rd), the surface-mode Rossby waves propagate at a phase speed ∼1.5 times of that of the BC1 mode. Moreover, the modal structures can be substantially modified by seasonal NSCS circulation, which is significantly enhanced over continental slopes. Analysis of the triad interactions further implies that the short waves tend to transfer energy to larger scales via the inverse cascade and only those with wavelengths larger than Rd ≈ 70 km in the NSCS can persist because of a slower unstable growth rate but a higher fraction of upscale energy transfer. The present theory excludes the bottom-trapped mode, which is closely associated with topographic Rossby waves and is observed to be significant in the abyssal NSCS. Hence, a complete normal-mode basis for any QG state is required for a study that focuses on flow variability throughout the water column. Our findings provide an insight into the vertical partition of horizontal kinetic energy for QG motions, as well as the relevant oceanic variation in marginal seas.

Material point method‐based simulation of dynamic process of soil landslides considering pore fluid pressure

AbstractIn this study, the dynamic process of soil landslides is investigated using the material point method (MPM). A basal friction algorithm is developed based on the MPM, and the pore water pressure is considered for calculating the basal friction. A large‐scale debris flow experiment is performed to validate the effectiveness of the MPM in simulating the dynamic process of soil landslides. The calculated depths of the debris flow using the MPM are consistent with the experimental results. The effects of the basal friction angle and internal friction angle on the debris flow depths are discussed. Moreover, a landslide case is simulated using the MPM, and the calculation results are consistent with the measured results. The horizontal velocity, vertical velocity, velocity direction, and kinetic energy of the landslide are analyzed. Finally, a case involving a different slope near a landslide is evaluated using the MPM. The distributions of velocity in different directions and changes in the average velocity, kinetic energy, and sliding distance are analyzed. By setting a retaining wall, the accumulation height of a landslide accumulated at the retaining wall and the normal force on the retaining wall can be estimated.

Analysis of mooring-observed bottom current on the northern continental shelf of the South China Sea

The bottom current is an important component of the three-dimensional ocean circulation, which is of significance for the safeties of ocean bottom engineering and facilities, the research on sediment and pollutant transports, and the ecological environment. Due to the lack of observation data, research on the bottom current in the South China Sea (SCS) has been limited. This study systematically analyzes bottom currents from 0.5 to 5 m above the seafloor based on 20-month-long mooring observations on the shelf slope west of the Dongsha Atoll. The spectral analysis results indicate that currents induced by the internal tides and the internal solitary waves (ISWs) comprise dominant constituents of bottom currents with velocity amplitudes up to O(50–90) cm/s. Dominant internal tide-induced bottom currents of the velocity amplitude of O(50) cm/s occupy 53% of the total horizontal kinetic energy. The pulsating ISW-induced bottom currents reach a maximum amplitude of 93 cm/s, which has intrinsic relation to the amplitude of the ISWs, according to the soliton propagation speed solutions of the Korteweg–De Vries (KdV) equation. The background bottom current is strongest in winter, followed by spring, and weak in summer and autumn, which is closely correlated with the behavior of mesoscale eddies. These results are of significance for understanding the dynamics of the bottom boundary layer.

The Relationship between Horizontal and Vertical Velocity Wavenumber Spectra in Global Storm-Resolving Simulations

Abstract Several studies have reported vertical kinetic energy spectra almost white in horizontal wavenumber space with evidence of two maxima at synoptic scales and mesoscales, leaving the explanation of these maxima open. Processes known to influence the shape of the horizontal kinetic energy spectra include the superposition of quasi-linear inertia–gravity waves (IGWs), quasigeostrophic turbulence, and moist convection. In contrast, vertical kinetic energy has been discussed much less, as measuring vertical velocity remains challenging. This study compares the horizontal and vertical kinetic energy spectra and their relationships in global storm-resolving simulations from the DYAMOND experiment. The consistency of these relationships with linear IGW theory is tested by diagnosing horizontal wind fluctuations associated with IGW modes. Furthermore, it is shown that hydrostatic IGW polarization relations provide a quantitative prediction of the spectral slopes of vertical kinetic energy at large scales and mesoscales, where the intrinsic frequencies are inferred from the linearized vorticity equation. Our results suggest that IGW modes dominate the vertical kinetic energy spectra at most horizontal scales, whereas an incompressible, isotropic scaling of the continuity equation captures the relationship between horizontal and vertical kinetic energy spectra at small scales.

Do Submesoscales Affect the Large-Scale Structure of the Upper Ocean?

Abstract Submesoscale baroclinic instabilities have been shown to restratify the surface mixed layer and to seasonally energize submesoscale turbulence in the upper ocean. But do these instabilities also affect the large-scale circulation and stratification of the upper thermocline? This question is addressed for the North Atlantic Subtropical Mode Water region with a series of numerical simulations at varying horizontal grid spacings (16, 8, 4, and 2 km). These simulations are realistically forced and integrated long enough for the thermocline to adjust to the presence or absence of submesoscales. Linear stability analysis indicates that a 2-km grid spacing is sufficient to resolve the most unstable mode of the wintertime mixed layer instability. As the resolution is increased, spectral slopes of horizontal kinetic energy flatten and vertical velocities increase in magnitude, consistent with previous regional and short-time simulations. The equilibrium stratification of the thermocline changes drastically as the grid spacing is refined from 16 to 8 km and mesoscale eddies are fully resolved. The thermocline stratification remains largely unchanged, however, between the 8-, 4-, and 2-km runs. This robustness is argued to arise from a mesoscale constraint on the buoyancy variance budget. Once mesoscale processes are resolved, the rate of mesoscale variance production is largely fixed. This constrains the variance destruction by submesoscale vertical buoyancy fluxes, which thus remain invariant across resolutions. The bulk impact of mixed layer instabilities on upper-ocean stratification in the Subtropical Mode Water region through an enhanced vertical buoyancy flux is therefore captured at 8-km grid spacing, even though the instabilities are severely underresolved.

Numerical investigation of the external emergency coolant transportation inside reactor annular down-comer

A numerical investigation of the ECC (Emergency Core Cooling) coolant transportation in the reactor annular down-comer is performed in this paper. The density difference of coolant is paid special concern and is quantificationally analyzed. If the ECC coolant with low density and high velocity is injected into the annular down-comer, the horizontal kinetic energy decays as the azimuthal angle of down-comer increases. As a result, the ECC coolant transports through the annular down-comer along the clockwise direction. If the ECC coolant with high density and low velocity is injected, the coolant falls vertically and arrives the lower plenum as it enters the annular down-comer. As the lower plenum is filled with the ECC coolant, part of the ECC coolant moves upward due to the mass force effect. With the density difference, remarkable velocity oscillation is generated in the lower space of the down-comer. The transportation of ECC coolant insider the down-comer is decided by Froud number. When the Froud number is larger than 1.2, the inertia force dominant mixing is formed and the ECC coolant transports in the clockwise direction. When the Froud number is lower than 0.8, the buoyancy driven mixing is formed and the ECC coolant transports in the anti-clockwise direction.

Spectral Budget of Rotational and Divergent Kinetic Energy in Global Analyses

Abstract To study the multiscale interactions between rotational and divergent components of atmospheric motion, a new formulation of spectral budget of rotational kinetic energy (RKE) and divergent kinetic energy (DKE) based on the primitive equations in the pressure coordinate is derived, with four main characteristics: 1) horizontal kinetic energy (HKE) spectral transfer is exactly divided into spectral transfer of RKE and DKE, 2) the exact spectral conversion term between DKE and RKE is constructed, 3) the Coriolis term is considered, and 4) both the baroclinic conversion from available potential energy (APE) and the vertical flux of HKE act only on DKE. With this new formulation, outputs from ERA5 global reanalysis are investigated. At planetary scales, HKE spectral transfer, mainly attributed to β effect, is dominated by downscale DKE transfer. At synoptic scales, it is dominated by an upscale transfer of RKE energized by conversion of DKE mainly due to the Coriolis effect. The ultimate source of DKE in the upper troposphere is conversion of APE, while in the stratosphere it is the vertical flux. At mesoscales, the spectral transfers of RKE and DKE are both downscale, and conversion from RKE to DKE exists at sub-800-km scales in the upper troposphere, which is mainly attributed to the contribution from relative vorticity. At different heights, the intersection scales of RKE and DKE spectra are affected by the scales of positive peaks of the local spectral conversion from DKE to RKE around total wavenumber 10. Significance Statement The purpose of this study is to explore more physical insights on the dynamics underlying the atmospheric energy spectra from the perspective of rotational and divergent components of motion. We derive a new formulation of the spectral rotational and divergent kinetic energy budget in the pressure coordinate for the global atmosphere, with application to ERA5 global reanalysis. Our results reveal the differences of spectral energy budget between rotational and divergent motions at different heights and scales. This new formulation provides a good tool for revealing the multiscale cascade and interaction between atmospheric rotational and divergent motions. Future work should investigate these dynamical processes with higher-resolution simulations and datasets.

Vertical structural variability of diurnal internal tides inside a mesoscale anticyclonic eddy based on single virtual-moored Slocum glider observations

The vertical structural variability of the diurnal internal tide (DIT) with a mode-1 wavelength of ~420 km inside a mesoscale baroclinic anticyclonic eddy was examined based on observations by a single virtual-moored (VM) Slocum glider. During the glider observational period from 10 to 19 September 2018, the eddy traveled northward at approximately 50 km, allowing the glider to scan a cross section of 50 km wide and 800 m deep inside the eddy. VM observations showed that DIT experienced a noticeable vertical structural variability near the eddy center. In a range of 30 km horizontally from the eddy center (inner center), DIT’s vertical displacements were significantly intensified in the 400–800-m depth below the eddy. In the range of 30–50 km from the eddy center (outer center), DIT was almost uniformly distributed from the surface to 800-m depth. Owing to the spatiotemporally restricted dataset by the glider, the significance of DIT’s modulation observed inside the eddy can be questionable. As a result of comparing DIT’s vertical structural variability in two domains in terms of available potential energy (APE) and horizontal kinetic energy (HKE) using CTDs inside the eddy and ADCPs outside the eddy, DIT’s vertical structure inside the eddy was significantly distinguished from that outside the eddy. The relative vorticity inside the eddy was estimated based on the satellite dataset; it was negatively great in the inner center (approximately 0.35 – 0.25f) and small in the outer center (approximately 0.2 – 0.1f). These observational behaviors indicate a close relationship between them; the vorticity-dependent modulation of the DIT seems to be observationally confirmed inside the eddy. Further, in order to examine the energy transferring behavior in low vertical modes, a wavenumber spectral analysis was performed on the DIT displacements and the lowest four wavenumbers, Kz (1) through Kz (4), showed a similar behavior to those observed in DIT’s vertical structural variability inside of the eddy; the relative power of the sum of Kz (2) ~ Kz (4) with respect to Kz (1) was strong in the inner center and weakened in the outer center. These results seem to support that the wave–eddy interaction is non-uniform inside the eddy and partially depends on the relative vorticity.