Effects of Reynolds number on leading-edge vortex formation dynamics and stability in revolving wings

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} <200$ , the LEV stability is mainly driven by viscous diffusion. At $200<\textit {Re} <1000$ , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

Full vorticity budget of the Arabian Sea from a 0.1° ocean model: Sverdrup dynamics, Rossby waves and nonlinear eddy effects

The Arabian Sea, influenced by the Indian monsoon, has many unique features including its basin scale seasonally reversing surface circulation and the Great Whirl, a seasonal anti-cyclonic system appearing during the southwest monsoon close to the western boundary. To establish a comprehensive dynamical picture of the Arabian Sea, we utilize numerical model output and design a full vorticity budget that includes a fully-decomposed nonlinear term. The ocean general circulation model has 0.1° resolution and is mesoscale eddy-resolving in the region. In the western boundary current system, we highlight the role of nonlinear eddies in the life cycle of the Great Whirl. The nonlinear eddy term is of leading order importance in this feature’s vorticity balance. Specifically, it contributes to the Great Whirl’s persistence in boreal fall after the weakening of the southwesterly winds. In the open ocean, Sverdrup dynamics and annual Rossby waves are found to dominate the vorticity balance; the latter is considered as a key factor in the formation of the Great Whirl and the sea-sonal reversal of the western boundary current. In addition, we discuss different forms of vertically-integrated vorticity equations in the model and argue that the bottom pressure torque term can be interpreted analogously as friction in the western boundary and vortex stretching in the open ocean.

Observing and quantifying ocean flow properties using drifters with drogues at different depths

This paper presents analyses of drifters with drogues at different depths – 1, 10, 30, 50 m – that were deployed in the Mediterranean Sea to investigate frontal subduction and upwelling. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs), and to investigate the balance of terms in the vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm/s), increases with depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of, but not the only, significant term in the vorticity balance. 2D FTLEs are 2 × 10−51/s after 1 day, twice larger than in a 400-m-resolution numerical model. 3D FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping suggests uncertainty levels of ~10% of the time-mean absolute values for divergence and vorticity. Analysis of simulated drifters in a model suggests that drifter-based estimates of divergence and vorticity are close to the Eulerian model estimates, except when drifters get aligned into long filaments. Drifter-based vertical velocity is close to the Eulerian model estimates at 1 m but differs at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths, and partially due to only measuring at 4 depths. Overall, this paper demonstrates how drifters, heretofore restricted to 2D near-surface observations, can be used to learn about 3D flow properties throughout the upper layer of the water column.

Observing and quantifying ocean flow properties using drifters with drogues at different depths

&lt;p&gt;We present analyses of drifters with drogues at 1, 10, 30 and 50 m, which were deployed in the Mediterranean Sea to investigate subduction and upwelling processes. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs), and to investigate the magnitudes of terms in the vertical vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm/s), is larger at depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of, but not the only, significant term in the vertical vorticity balance. 2D FTLEs are 2x10^(-5) 1/s after 1 day, about twice larger than in a 400-m-resolution numerical model. 3D FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping-based uncertainty for both divergence and vorticity is ~10% of the time-mean absolute values. Simulated drifters in a model suggest that drifter-based divergence and vorticity are close to true model values, except when drifters get aligned into long and narrow filaments. Drifter-based vertical velocity is close to true values in the model at 1 m but differs from the true model values at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths, and partially due to having drifters at only 4 depths. Overall, multi-level drifters provided useful information about the 3D flow structure.&lt;/p&gt;

Deep Eastern Boundary Currents: idealized models and dynamics

Concentrated poleward flows along eastern boundaries between two and four kilometers depth in the southeast Pacific, Atlantic, and Indian Oceans have been observed, and appear in data-assimilation products and regional model simulations at sufficiently high horizontal resolution, but their dynamics are still not well understood. We study the local dynamics of these Deep Eastern Boundary Currents (DEBCs) using idealized GCM simulations and use a conceptual vorticity model for the DEBCs, to gain additional insights into the dynamics. Over most of the zonal width of the DEBCs, the vorticity balance is between meridional advection of planetary vorticity and vortex stretching, which is an interior-like vorticity balance. Over a thinner layer very close to the eastern boundary, a balance between vorticity tendencies due to friction and stretching that rapidly decay away from the boundary is found. Over the part of the DEBC that is governed by an interior-like vorticity balance, vertical stretching is driven by both the topography and temperature diffusion, while in the thinner boundary layer, it is driven instead by parameterized horizontal temperature mixing. The topographic driving acts via a cross-isobath flow that leads to stretching and thus to vorticity forcing for the concentrated DEBCs.

On the Vorticity Balance over Steep Slopes: Kuroshio Intrusions Northeast of Taiwan

The circulation of the Kuroshio northeast of Taiwan is characterized by a large anticyclonic loop of surface intrusion and strong upwelling at the shelfbreak. To study the mechanisms of Kuroshio intrusions, the vorticity balance is examined using a high-resolution nested numerical model. In the 2D depth-averaged vorticity equation, the advection of geostrophic potential vorticity (APV) term and the joint effect of baroclinicity and relief (JEBAR) term are dominant. On the other hand, in the 2D depth-integrated vorticity equation, the main balance is between nonlinear advection and bottom pressure torque. It is shown that JEBAR and APV tend to compensate, and their difference is comparable to bottom pressure torque. Perhaps most significantly, a general framework is provided for examination of vorticity balance over steep slopes through a full 3D depth-dependent vorticity equation. The 3D analysis reveals a well-defined bottom boundary layer over the shelfbreak, about 40 m deep and capped by the vertical velocity maximum. In the upper frictionless layer from the surface to about 100 m, the primary balance is between nonlinear advection and horizontal divergence. In the lower frictional layer, viscous stress is balanced by nonlinear advection and horizontal divergence. The bottom pressure torque, which corresponds to the depth-integrated viscous effect, is a proxy for viscous stress divergence at the bottom. The importance of nonlinear advection is further demonstrated in a sensitivity experiment by removing advective terms from momentum equations. Without nonlinear advection, the bottom pressure torque becomes trivial, the boundary layer vanishes, and the on-shelf intrusion is considerably weakened.

Barotropic vorticity balance of the North Atlantic subpolar gyre in an eddy-resolving model

The circulation in the North Atlantic subpolar gyre is complex and strongly influenced by the topography. The gyre dynamics are traditionally understood as the result of a topographic Sverdrup balance, which corresponds to a first-order balance between the planetary vorticity advection, the bottom pressure torque, and the wind stress curl. However, these dynamics have been studied mostly with non-eddy-resolving models and a crude representation of the bottom topography. Here we revisit the barotropic vorticity balance of the North Atlantic subpolar gyre using a new eddy-resolving simulation (with a grid space of ≈2 km) with topography-following vertical coordinates to better represent the mesoscale turbulence and flow–topography interactions. Our findings highlight that, locally, there is a first-order balance between the bottom pressure torque and the nonlinear terms, albeit with a high degree of cancellation between them. However, balances integrated over different regions of the gyre – shelf, slope, and interior – still highlight the important role played by nonlinearities and bottom drag curls. In particular, the Sverdrup balance cannot describe the dynamics in the interior of the gyre. The main sources of cyclonic vorticity are nonlinear terms due to eddies generated along eastern boundary currents and time-mean nonlinear terms in the northwest corner. Our results suggest that a good representation of the mesoscale activity and a good positioning of mean currents are two important conditions for a better representation of the circulation in the North Atlantic subpolar gyre.

The global dominance of the Atlantic circulation, seen through boundary pressures.

&lt;p&gt;The rapid propagation of boundary waves (or, equivalently, the strong influence of topography on vorticity balance) ensures that bottom pressure along the global continental slope reflects large scale ocean processes, making it possible to see through the fog of the mesoscale, which obscures many observable quantities. This fact is exploited in systems to monitor the Atlantic Meridional Overturning Circulation (AMOC). Here, we use diagnostics from an ocean model with realistic mesoscale variability to demonstrate two things. First: boundary pressures form an efficient method of monitoring AMOC variability. Second: pressures are remarkably constant along isobaths around the global continental slope, varying by less than 5 cm sea-level-equivalent over vast distances below the directly wind-driven circulation. In the latter context, the AMOC stands out as a clear exception, leading to a link between the AMOC and differences in the hydrography of entire ocean basins.&lt;/p&gt;

Energy Transfers Between Balanced and Unbalanced Motions in Geophysical Flows

&lt;p&gt;Geophysical flows such as the atmosphere and the ocean are characterized by rotation and stratification, which together give rise to two dominant motions: the slow balanced and the fast unbalanced motions. The interaction between the balanced and unbalanced motions and the energy transfers between them impact the energy and momentum cycle of the flow, and is therefore crucial to understand the underlying energetics of the atmosphere and the ocean. Balanced motions, for instance mesoscale eddies, can transfer their energy to unbalanced motions, such as internal gravity waves, by spontaneous loss of balance amongst other processes. The exact mechanism of wave generation, however, remain less understood and is hindered to an extent by the challenge of separating the flow field into balanced and unbalanced motions.&lt;/p&gt;&lt;p&gt;This separation is achieved using two different balancing procedures in an identical model setup and assess the differences in the obtained balanced state and the resultant energy transfer to unbalanced motions. The first procedure we implement is a non-linear initialisation procedure based on Machenhauer (1977) but extended to higher orders in Rossby number. The second procedure implemented is the optimal potential vorticity balance to achieve the balanced state. The results show that the numerics of the model affect the obtained balanced state from the two procedures, and thus the residual signal which we interpret as the unbalanced motions, i.e. internal gravity waves.&amp;#160; A further complication is the presence of slaved modes, which appear along the unbalanced motions but are tied to the balanced motions, for which we need to extend the separation to higher orders in Rossby number. Further, we assess the energy transfers between balanced and unbalanced motions in experiments with different Rossby numbers and for different orders in Rossby number. We find that it is crucial to consider the effect of the numerics in models and make a suitable choice of the balancing procedure, as well as diagnose the unbalanced motions at higher orders to precisely detect the unbalanced wave signal.&lt;/p&gt;