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Register a new userConfronting Grand Challenges in Environmental Fluid Mechanics
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Environmental fluid mechanics underlies a wealth of natural, industrial and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of grand challenge problems that need to be tackled, ranging from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing, to applied studies of pollution transport in the ocean, atmosphere and urban environments. A workshop was organized in the Les Houches School of Physics in France in January 2019 with the objective of gathering leading figures in the field to produce a road map for the scientific community. Five subject areas were addressed: multiphase flow, stratified flow, ocean transport, atmospheric and urban transport, and weather and climate prediction. This article summarizes the discussions and outcomes of the meeting, with the intent of providing a resource for the community going forward.
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We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable scales of fluid motion, due to unresolvable, small, rapid scales of fluid motion.
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a coarse-grained field on a grid cannot properly resolve regions of saturation---in which condensation occurs---that are smaller than the grid boxes. Thus, in the absence of a parameterization scheme, either the grid box must become saturated or condensation will be underestimated. On the other hand, in a stochastic Lagrangian model of moisture transport, trajectories of parcels tagged with humidity variables are tracked and small-scale moisture variability can be retained; however, explicitly implementing such a scheme in a global model would be computationally prohibitive. One way to introduce subgrid-scale saturation into an Eulerian model is to assume the humidity within a grid box has a probability distribution. To close the problem, this distribution is conventionally determined by relating the required subgrid-scale properties of the flow to the grid-scale properties using a turbulence closure. Here, instead, we determine an assumed probability distribution by using the statistical moments from a stochastic Lagrangian version of the system. The stochastic system is governed by a Fokker--Planck equation and we use that, rather than explicitly following the moisture parcels, to determine the parameters of the assumed distribution. We are thus able to parameterize subgrid-scale condensation in an Eulerian model in a computationally efficient and theoretically well-founded way. In two idealized advection--condensation problems we show that a coarse Eulerian model with the subgrid parameterization is well able to mimic its Lagrangian counterpart.
In this study the influence of stratification on surface tidal elevations in a two-layer analytical model is examined. The model assumes linearized, non-rotating, shallow-water dynamics in one dimension with astronomical forcing and allows for arbitrary topography. Using a natural modal separation, both large scale (barotropic) and small scale (baroclinic) components of the surface tidal elevation are shown to be comparably affected by stratification. It is also shown that the topography and basin boundaries affect the sensitivity of the barotropic surface tide to stratification significantly. This paper, therefore, provides a framework to understand how the presence of stratification impacts barotropic as well as baroclinic tides, and how climatic perturbations to oceanic stratification contribute to secular variations in tides. Results from a realistic-domain global numerical two-layer tide model are briefly examined and found to be qualitatively consistent with the analytical model results.
A framework is introduced to compare moist `potential temperatures. The equivalent potential temperature, $theta_e,$ the liquid water potential temperature, $theta_ell,$ and the entropy potential temperature, $theta_s$ are all shown to be potential temperatures in the sense that they measure the temperature moist-air, in some specified state, must have to have the same entropy as the air-parcel that they characterize. They only differ in the choice of reference state composition: $theta_ell$ describes the temperature a condensate-free state, $theta_e$ a vapor-free state, and $theta_s$ a water-free state would require to have the same entropy as the given state. Although in this sense $theta_e,$ $theta_ell,$ and $theta_s$ are all different flavors of the same thing, only $theta_ell$ satisfies the stricter definition of a `potential temperature, as corresponding to a reference temperature accessible by an isentropic and closed transformation of a system in equilibrium; only $theta_e$ approximately measures the ability of moist-air to do work; and only $theta_s$ measures air-parcel entropy. None mix linearly, but all do so approximately, and all reduce to the dry potential temperature, $theta$ in the limit as the water mass fraction goes to zero. As is well known, $theta$ does mix linearly and inherits all the favorable (entropic, enthalpic, and potential temperature) properties of its various -- but descriptively less rich -- moist counterparts. All, involve quite complex expressions, but admit relatively simple and useful approximations. Of the three moist `potential temperatures, $theta_s$ is the least familiar, but the most well mixed in the broader tropics, a property that merits further study as a basis for constraining mixing processes.
We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone to patch formation using the concept of Finite-Time Compressibility (FTC, a generalisation of the notion of time series of divergence). The LCSs are evaluated using the Finite Time Lyapunov Exponent (FTLE) method. The test area is the Gulf of Finland (GoF) in the Baltic Sea. A basin-wide spatial average of backward FTLE is calculated for the GoF for the first time. This measure of the mixing strength displays a clear seasonal pattern. The evaluated backward FTLE features are linked with potential patch formation regions with high FTC levels. It is shown that areas hosting frequent upwelling or downwelling have consistently stronger than average mixing intensity. The combination of both methods, FTC and LCS, has the potential of being a powerful tool to identify the formation of patches of pollution at the sea surface.
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