Search Results (14)

Wave-induced radiation stress (RS), as a primary driver of ocean currents influenced by waves, plays an important role in the response of upper ocean temperatures under typhoons. Previous studies have mainly focused on wave-generated currents and coastal currents in nearshore areas. This paper incorporates the geostrophic effect into the wave-induced radiation stress of wave-current interaction, and the effect of waves on the changes in upper ocean temperature (including sea surface temperature (SST) and mixed layer temperature) under typhoon Nanmadol (2022) is studied. The FVCOM-SWAVE model is used to conduct a preliminary numerical study in the western Pacific Ocean. The RS with the geostrophic effect increased the horizontal and vertical components, leading to an enhancement in turbulent mixing and a decrease in SST by up to 1.0 °C to 1.4 °C, which is closer to the SST obtained by OISST remote sensing fusion observation data. In the strong divergence domain, the direction of the vortex flow exhibits a more pronounced turn to the right, accompanied by an increase in water velocity. The vertical temperature profile of the ocean shows that the water below is perturbed by the RS component of the geostrophic effect, and the depth of the mixed layer increases by about 2 m, which is closer to the depth of the mixed layer observed by the Argo floats, indirectly enhancing the vertical mass transport of the ocean. In general, this shows that RS, which takes into account geostrophic effects, enhances the effect of waves on the water below, indirectly leading to lower temperatures in the upper ocean, and the simulated results align more closely with the observed data, offering valuable insights for enhancing marine numerical forecasting accuracy. Full article

The development and breakdown of Kelvin–Helmholtz (KH) waves (billows) in the stable atmospheric boundary layer (SABL) and their impact on vertical transport of momentum and scalars have been examined utilizing large eddy simulations. These simulations are initialized with a vertically uniform geostrophic wind and a constant potential temperature lapse rate. An Ekman type of boundary layer develops, and an inflection point forms in the SABL, which triggers the KH instability (KHI). KHI develops with the kinetic energy (KE) in the KH billows growing exponentially with time. The subsequent onset of secondary shear instability along S-shaped braids leads to the turbulent breakdown of the KH billow cores and braids. The frictional ground surface tends to slow down the growth of KE near the surface, reduce the KH billow core depth, and likely suppress other types of secondary instability. KH billows induce substantial down-gradient transport of momentum and sensible heat, which can be further enhanced by the onset of secondary shear instability. Although the KHI-induced strong transport only lasts for around 10–20 min, it reduces vertical shear and stratification in the SABL, enhances surface winds, and results in a 2–3-fold increase in the SABL depth. Full article

Many issues pioneered by Jackson Herring deal with how nonlinear interactions shape atmospheric dynamics. In this context, we analyze new direct numerical simulations of rotating stratified flows with a large-scale forcing, which is either random or quasi-geostrophic (QG). Runs were performed at a moderate Reynolds number $Re$ and up to 1646 turn-over times in one case. We found intermittent fluctuations of the vertical velocity w and temperature $\theta$ in a narrow domain of parameters as for decaying flows. Preliminary results indicate that parabolic relations between normalized third- and fourth-order moments of the buoyancy flux $\propto ⟨w\theta ⟩$ and of the energy dissipation emerge in this domain, including for passive and active scalars, with or without rotation. These are reminiscent of (but not identical to) previous findings for other variables and systems such as oceanic and atmospheric flows, climate re-analysis data, fusion plasmas, the Solar Wind, or galaxies. For QG forcing, sharp scaling transitions take place once the Ozmidov length scale ${\ell }_{Oz}$ is resolved—${\ell }_{Oz}$ being the scale after which a turbulent Kolmogorov energy spectrum likely recovers at high $Re$. Full article

Macroscale turbulence in the atmosphere is observed to be self-organized into large-scale structures such as zonal jets and robust waves and vortices. A simple model containing the relevant dynamics of turbulence self-organization is quasi-geostrophic turbulence in a stably stratified atmosphere approximated with a single-layer fluid on a beta-plane. Numerical simulations of this model have shown the dominance of Rossby waves, zonal jets and robust vortices in different regions of the parameter space. In this work, we perform numerical integrations of this model and focus on the regime in which robust large-scale vortices dominate the flow. The goal is to identify the Lagrangian coherent vortices that trap the same air masses in their core throughout their life cycle and to obtain their characteristics. The vortices are identified using an objective algorithm based on the Lagrangian-averaged vorticity deviation calculated using the advection of Lagrangian particles by the flow. Long-lived vortices with scales comparable to the deformation scale are found with a symmetry between cyclones and anti-cyclones as expected from the simplified dynamics of the model. The scale as well as the life span of the vortices are also found to increase alongside an increase in the strength of turbulence. Full article

The connection between the heat transfer and characteristic flow velocities of planetary core-style convection remains poorly understood. To address this, we present novel laboratory models of rotating Rayleigh–Bénard convection in which heat and momentum transfer are simultaneously measured. Using water (Prandtl number, $Pr\simeq 6$) and cylindrical containers of diameter-to-height aspect ratios of $\Gamma \simeq 3,1.5,0.75$, the non-dimensional rotation period (Ekman number, E) is varied between ${10}^{-7}\lesssim E\lesssim 3\times {10}^{-5}$ and the non-dimensional convective forcing (Rayleigh number, $Ra$) ranges from ${10}^7\lesssim Ra\lesssim {10}^{12}$. Our heat transfer data agree with those of previous studies and are largely controlled by boundary layer dynamics. We utilize laser Doppler velocimetry (LDV) to obtain experimental point measurements of bulk axial velocities, resulting in estimates of the non-dimensional momentum transfer (Reynolds number, $Re$) with values between $4\times {10}^2\lesssim Re\lesssim 5\times {10}^4$. Behavioral transitions in the velocity data do not exist where transitions in heat transfer behaviors occur, indicating that bulk dynamics are not controlled by the boundary layers of the system. Instead, the LDV data agree well with the diffusion-free Coriolis–Inertia–Archimedian (CIA) scaling over the range of $Ra$ explored. Furthermore, the CIA scaling approximately co-scales with the Viscous–Archimedian–Coriolis (VAC) scaling over the parameter space studied. We explain this observation by demonstrating that the VAC and CIA relations will co-scale when the local Reynolds number in the fluid bulk is of order unity. We conclude that in our experiments and similar laboratory and numerical investigations with $E\gtrsim {10}^{-7}$, $Ra\lesssim {10}^{12}$, $Pr\simeq 7$, heat transfer is controlled by boundary layer physics while quasi-geostrophically turbulent dynamics relevant to core flows robustly exist in the fluid bulk. Full article

Topography-induced turbulence poses a potential hazard for aviation safety, in particular during the final approach and landing. In this context, it is essential to assure that the impact of topography-induced turbulence on the flight paths during take-off and landing is minimized already during the design and planning phase. As an example of the siting and planning of a potential new airport in complex terrain, this study investigates the distribution of terrain-induced boundary layer turbulence in the vicinity of the current Lofoten airport at Leknes (LKN). For that purpose, large-eddy simulations (LES) have been performed with the PAralellized Large-eddy Simulation Model (PALM) on a $40\times 45\times 4{\mathrm{km}}^3$ computational domain around LKN. An initial parametric sensitivity study resulted in a grid spacing of 50 m and an overall simulation time of 12 h for our individual model runs. A suite of 32 model simulations for 16 different wind directions and two geostrophic wind speeds of 10 ms${}^{-1}$ and 20 ms${}^{-1}$, was then performed and analysed. A turbulence risk analysis along idealized flight trajectories shows that the high-risk conditions are substantially determined by the wind conditions and their interaction with the topography. With respect to wind speed, the results indicate that for a geostrophic flow below 10 ms${}^{-1}$, the risk of aviation critical, terrain-induced boundary layer turbulence (BLT), is rather low in the vicinity of LKN. At 20 ms${}^{-1}$ the situation has completely changed, as for 14 out of 16 investigated wind directions the 9 m${}^2$s${}^{-2}$ aviation critical threshold of turbulent kinetic energy per unit air mass (TKE) is exceeded. In the northwesterly wind scenarios, the largest areas with critical turbulence in the vicinity of LKN are observed. Full article

We investigate the dynamics of meso- and submesoscale features of the northern South Brazil Bight shelf region with a 500-m horizontal resolution regional model. We focus on the Cabo Frio upwelling center, where nutrient-rich, coastal waters are transported into the mid- and outer shelf, because of its importance for local and remote productivity. The Cabo Frio upwelling center undergoes an upwelling phase, from late September to March, and a relaxation phase, from April to early September. During the upwelling phase, an intense front around 200 $\mathrm{km}$ long and 20 $\mathrm{km}$ wide with horizontal temperature gradients as large as 8 ${}^{\circ }\mathrm{C}$ over less than 10 $\mathrm{km}$ develops. A surface-intensified frontal jet of 0.7 ${\mathrm{ms}}^{-1}$ in the upper 20 m and velocities of around 0.3 ${\mathrm{ms}}^{-1}$ reaching down to 65 m depth makes this front a preferential cross-shelf transport pathway. Large vertical mixing and vertical velocities are observed within the frontal region. The front is associated with strong cyclonic vorticity and strong variance in relative vorticity, frequently with $\mathcal{O}$(1) Rossby numbers. The dynamical balance within the front is between the pressure gradient, Coriolis and vertical mixing terms, which are induced both by the winds, during the upwelling season, and by the geostrophic frontal jet. Therefore, the frontal dynamics may be largely described as sum of Ekman and turbulent thermal wind balances. During the upwelling phase, a mix of barotropic and baroclinic instabilities dominates in the upwelling center. However, these instabilities do not lead to the local formation of coherent eddies when the front is strong. In the relaxation phase, the front vanishes, and the water column becomes less stratified. The interaction between eastward coastal currents generated by sea level variability, coastal intrusions of the Brazil Current, and sporadic wind-driven, coastal upwelling events induce the formation of cyclonic eddies with diameters of, approximately, 20 $\mathrm{km}$. They are in gradient-wind balance and propagate along the 100-m isobath on the shelf. During this phase baroclinic instability dominates. Cold filaments with widths of 2 $\mathrm{km}$ are formed due to straining and stretching of cold, coastal temperature anomalies. They last for a few days and are characterized by downwelling as large as 1 ${\mathrm{cms}}^{-1}$. The turbulent thermal wind balance provides a good first order estimate of the dynamical balance within the filament, but vertical and horizontal advection are shown to be important. To our knowledge, this is the first account of these smaller scale features in the region. Because these meso- and submesoscale features on the shelf heavily affect the water properties crucial to productivity of the South Brazil Bight, it is important to take these features into account for a better understanding of the functioning of this ecosystem and its resilience to both direct human activities as well as to climate change. Full article

The decay of the Convective Boundary Layer (CBL) is studied using large-eddy simulations of free and advective CBLs, in which surface heat supply is suddenly cut off. After the cutoff, coherent convective circulations last about one convective time scale and then fade away. In the mixed layer, the decay time scale increases with height, indicating that nonlocal eddies decay slower than near-surface local eddies. The slower decay of turbulence in the middle of CBL than near-surface turbulence is reconfirmed from the analysis of pattern correlations of perturbations of vertical velocity. Perturbations of potential temperature and scalar concentration decay faster and slower than vertical velocity perturbations, respectively. A downward propagation of negative heat flux and its oscillation are found and a quadrant analysis reveals that warmer air sinking events are responsible for the downward propagation. The fourth quadrant events seem to be induced by demixing of air parcels, entrained from above the CBL. The advective CBL simulation with geostrophic wind illustrates that near-surface eddies are mechanically generated and they decelerate flow from the bottom up in the CBL/residual layer. The two-dimensional spectra show the height- and scale-dependent characteristics of decaying convective turbulence again in the free and advective boundary layer simulations. Full article

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

In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved $(G^{\prime }/G)$ -expansion method. Full article

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler equations, as well as the quasi-geostrophic equations for either single-layer or two-layer flows. Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. In the case of point vortex ensembles, the macroscopic variables describe the spatially coarse-grained vorticity. Dynamical closure in terms of those macrostates is obtained by optimizing over paths in the parameter space of the reduced model subject to the constraints imposed by conserved quantities. This optimization minimizes a cost functional that quantifies the rate of information loss due to model reduction, meaning that an optimal path represents a macroscopic evolution that is most compatible with the microscopic dynamics in an information-theoretic sense. A near-equilibrium linearization of this method is used to derive dissipative equations for the low-order spatial moments of ensembles of point vortices in the plane. These severely reduced models describe the late-stage evolution of isolated coherent structures in two-dimensional and geostrophic turbulence. For single-layer dynamics, they approximate the relaxation of initially distorted structures toward axisymmetric equilibrium states. For two-layer dynamics, they predict the rate of energy transfer in baroclinically perturbed structures returning to stable barotropic states. Comparisons against direct numerical simulations of the fully-resolved many-vortex dynamics validate the predictive capacity of these reduced models. Full article

We put forth a robust reduced-order modeling approach for near real-time prediction of mesoscale flows. In our hybrid-modeling framework, we combine physics-based projection methods with neural network closures to account for truncated modes. We introduce a weighting parameter between the Galerkin projection and extreme learning machine models and explore its effectiveness, accuracy and generalizability. To illustrate the success of the proposed modeling paradigm, we predict both the mean flow pattern and the time series response of a single-layer quasi-geostrophic ocean model, which is a simplified prototype for wind-driven general circulation models. We demonstrate that our approach yields significant improvements over both the standard Galerkin projection and fully non-intrusive neural network methods with a negligible computational overhead. Full article

Geostrophic turbulent eddies play a crucial role in the oceans, mixing properties such as heat, salt, and geochemical tracers. A useful reduced model for geostrophic turbulence is barotropic (2D) turbulence. The focus of this study is on 2D $\beta$ -plane turbulence with quadratic drag, which, although arguably the most realistic barotropic model of ocean turbulence, has remained unexplored thus far. We first review and test classical scaling arguments for the eddy diffusivity in three regimes: the strong friction limit, the weak friction/strong $\beta$ limit, and a transition regime. We then develop a generalized theory by parameterizing the nonlinear eddy–eddy interactions as a stochastic process, which leads to an analytical solution for the eddy diffusivity spectrum, whose integral yields a “bulk” diffusivity. The theory successfully predicts the smooth transition of diffusivity across the three regimes, and echoes with the recent argument that eddy phase propagation relative to the mean flow suppresses the eddy diffusivity. Moreover, the generalized theory reduces to the classical scaling arguments in both the strong friction and strong $\beta$ limits, which has not been clear from the previous work on diffusivity suppression by flow-relative phase propagation. Full article

Oceanic and atmospheric dynamics are often interpreted through potential vorticity, as this quantity is conserved along the geostrophic flow. However, in addition to potential vorticity, surface buoyancy is a conserved quantity, and this also affects the dynamics. Buoyancy at the ocean surface or at the atmospheric tropopause plays the same role of an active tracer as potential vorticity does since the velocity field can be deduced from these quantities. The surface quasi-geostrophic model has been proposed to explain the dynamics associated with surface buoyancy conservation and seems appealing for both the ocean and the atmosphere. In this review, we present its main characteristics in terms of coherent structures, instabilities and turbulent cascades. Furthermore, this model is mathematically studied for the possible formation of singularities, as it presents some analogies with three-dimensional Euler equations. Finally, we discuss its relevance for the ocean and the atmosphere. Full article