Higher order schemes in time for the surface quasi-geostrophic system under location uncertainty

<p>In this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations. The LU framework, first introduced in [1], is based on the decomposition of the Lagrangian velocity into two components: a large-scale smooth component and a small-scale stochastic one. This decomposition leads to a stochastic transport operator, and one can, in turn, derive the stochastic LU version of every classical fluid-dynamics system.<span> </span></p><p>    SQG is a simple 2D oceanic model with one partial differential equation, which models the stochastic transport of the buoyancy, and an operator which relies the velocity and the buoyancy.</p><p><span>    </span>For this kinds of equations, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time: the first step is to consider Milstein scheme, which improves the strong convergence to the order 1. To do this, it is necessary to simulate or estimate the Lévy area [2].</p><p><span>    </span>We show with some numerical results how the Milstein scheme is able to capture some of the smaller structures of the dynamic even at a poor resolution.<span> </span></p><p><strong>References</strong></p><p>[1] E. Mémin. Fluid flow dynamics under location uncertainty. <em>Geophysical & Astrophysical Fluid Dynamics</em>, 108.2 (2014): 119-146.<span> </span></p><p>[2] J. Foster, T. Lyons and H. Oberhauser. An optimal polynomial approximation of Brownian motion. <em>SIAM Journal on Numerical Analysis</em> 58.3 (2020): 1393-1421.</p>

Improving the Accuracy of Hydrodynamic Model Predictions Using Lagrangian Calibration

While significant studies have been conducted in Intermittently Closed and Open Lakes and Lagoons (ICOLLs), very few have employed Lagrangian drifters. With recent attention on the use of GPS-tracked Lagrangian drifters to study the hydrodynamics of estuaries, there is a need to assess the potential for calibrating models using Lagrangian drifter data. Here, we calibrated and validated a hydrodynamic model in Currimundi Lake, Australia using both Eulerian and Lagrangian velocity field measurements in an open entrance condition. The results showed that there was a higher level of correlation (R2 = 0.94) between model output and observed velocity data for the Eulerian calibration compared to that of Lagrangian calibration (R2 = 0.56). This lack of correlation between model and Lagrangian data is a result of apparent difficulties in the use of Lagrangian data in Eulerian (fixed-mesh) hydrodynamic models. Furthermore, Eulerian and Lagrangian devices systematically observe different spatio-temporal scales in the flow with larger variability in the Lagrangian data. Despite these, the results show that Lagrangian calibration resulted in optimum Manning coefficients (n = 0.023) equivalent to those observed through Eulerian calibration. Therefore, Lagrangian data has the potential to be used in hydrodynamic model calibration in such aquatic systems.

Velocity and acceleration statistics in rapidly rotating Rayleigh–Bénard convection

Background rotation causes different flow structures and heat transfer efficiencies in Rayleigh–Bénard convection. Three main regimes are known: rotation unaffected, rotation affected and rotation dominated. It has been shown that the transition between rotation-unaffected and rotation-affected regimes is driven by the boundary layers. However, the physics behind the transition between rotation-affected and rotation-dominated regimes are still unresolved. In this study, we employ the experimentally obtained Lagrangian velocity and acceleration statistics of neutrally buoyant immersed particles to study the rotation-affected and rotation-dominated regimes and the transition between them. We have found that the transition to the rotation-dominated regime coincides with three phenomena; suppressed vertical motions, strong penetration of vortical plumes deep into the bulk and reduced interaction of vortical plumes with their surroundings. The first two phenomena are used as confirmations for the available hypotheses on the transition to the rotation-dominated regime while the last phenomenon is a new argument to describe the regime transition. These findings allow us to better understand the rotation-dominated regime and the transition to this regime.