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1. A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

   https://doi.org/10.1175/JPO-D-22-0191.1  

   Choi, Jang-Geun; Pringle, James; Lippmann, Thomas (October 2023, Journal of Physical Oceanography)

   Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS²forS< 1 and is in better agreement with numerical simulations. 

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2. Transport and emergent stratification in the equilibrated Eady model: the vortex-gas scaling regime

   https://doi.org/10.1017/jfm.2022.501  

   Gallet, Basile; Miquel, Benjamin; Hadjerci, Gabriel; Burns, Keaton J.; Flierl, Glenn R.; Ferrari, Raffaele (October 2022, Journal of Fluid Mechanics)

   We numerically and theoretically investigate the Boussinesq Eady model, where a rapidly rotating density-stratified layer of fluid is subject to a meridional temperature gradient in thermal wind balance with a uniform vertically sheared zonal flow. Through a suite of numerical simulations, we show that the transport properties of the resulting turbulent flow are governed by quasigeostrophic (QG) dynamics in the rapidly rotating strongly stratified regime. The ‘vortex gas’ scaling predictions put forward in the context of the two-layer QG model carry over to this fully three-dimensional system: the functional dependence of the meridional flux on the control parameters is the same, the two adjustable parameters entering the theory taking slightly different values. In line with the QG prediction, the meridional heat flux is depth-independent. The vertical heat flux is such that turbulence transports buoyancy along isopycnals, except in narrow layers near the top and bottom boundaries, the thickness of which decreases as the diffusivities go to zero. The emergent (re)stratification is set by a simple balance between the vertical heat flux and diffusion along the vertical direction. Overall, this study demonstrates how the vortex-gas scaling theory can be adapted to quantitatively predict the magnitude and vertical structure of the meridional and vertical heat fluxes, and of the emergent stratification, without additional fitting parameters. 

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3. Fueling limits in a cylindrical viscosity-limited reactor

   https://doi.org/10.1063/5.0101271  

   Rubin, T.; Kolmes, E. J.; Ochs, I. E.; Mlodik, M. E.; Fisch, N. J. (August 2022, Physics of Plasmas)

   Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. The threshold for this effect occurs at ρi≳0.1R. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number M≲2 is investigated. The limitation is found to be at moderate Mach numbers. 

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4. Dynamics and Thermodynamics of the Mean Transpolar Drift and Ice Thickness in the Arctic Ocean

   https://doi.org/10.1175/JCLI-D-19-0252.1  

   Spall, Michael A. (November 2019, Journal of Climate)

   Abstract A theory for the mean ice thickness and the Transpolar Drift in the Arctic Ocean is developed. Asymptotic expansions of the ice momentum and thickness equations are used to derive analytic expressions for the leading-order ice thickness and velocity fields subject to wind stress forcing and heat loss to the atmosphere. The theory is most appropriate for the eastern and central Arctic, but not for the region of the Beaufort Gyre subject to anticyclonic wind stress curl. The scale analysis reveals two distinct regimes: a thin ice regime in the eastern Arctic and a thick ice regime in the western Arctic. In the eastern Arctic, the ice drift is controlled by a balance between wind and ocean drag, while the ice thickness is controlled by heat loss to the atmosphere. In contrast, in the western Arctic, the ice thickness is determined by a balance between wind and internal ice stress, while the drift is indirectly controlled by heat loss to the atmosphere. The southward flow toward Fram Strait is forced by the across-wind gradient in ice thickness. The basic predictions for ice thickness, heat loss, ice volume, and ice export from the theory compare well with an idealized, coupled ocean–ice numerical model over a wide range of parameter space. The theory indicates that increasing atmospheric temperatures or wind speed result in a decrease in maximum ice thickness and ice volume. Increasing temperatures also result in a decrease in heat loss to the atmosphere and ice export through Fram Strait, while increasing winds drive increased heat loss and ice export. 

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5. A simple vortex-loop-based model for unsteady rotating wings

   https://doi.org/10.1017/jfm.2019.735  

   Chowdhury, Juhi; Ringuette, Matthew J. (December 2019, Journal of Fluid Mechanics)

   An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack. 

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