The Flow in Periciliary Layer in Human Lungs with Navier-Stokes-Brinkman Equations

In the human respiratory tract, air breathed in is often contaminated with strange particles such as dust and chemical spray, which may cause people respiratory diseases. However, the human body has an innate immune system that helps to trap the debris by secreting mucus to catch the foreign particles, which are removed from the body by the movement of tiny hairs lining on the surface of the epithelial cells in the immune system. The layer containing the tiny hairs or cilia is called Periciliary Layer (PCL). In this research, we find the velocity of the fluid in the PCL moved by a ciliary beating by using the Navier-Stokes-Brinkman equations. We apply the Galerkin finite element method to determine numerical solutions. For the steady linear case of the equation, the numerical result is in good agreement with an exact solution. Including the time derivative and nonlinear terms, we show that the velocity of the liquid is affected by the velocity of the solid, which follows the physical meaning of the fluid flow. The result can be applied as a bottom boundary condition of the mucous layer to be able to find the velocity of mucus in the human lungs.

Bathymetric Data Requirements for Operational Coastal Erosion Forecasting Using XBeach

There is an increasing interest in the broad-scale implementation of coastal erosion early warning systems (EWS) with the goal of enhancing community preparedness to extreme coastal storm wave events. These emerging systems typically rely on process-based models to predict the storm-induced morphological change. A key challenge with incorporating these models in EWSs is the need for up-to-date nearshore and surf zone bathymetry data, which is difficult to measure routinely, but potentially important for accurate erosion forecasting. This study evaluates the degree to which up-to-date bathymetry is required for accurate coastal erosion predictions using the morphodynamic model XBeach and, subsequently, whether a range of “representative” and/or “synthetic” bathymetries can be used for the bottom boundary, when a survey of the immediate pre-storm bathymetry is not available. Twelve storm events at two contrasting sites were modelled using six different bathymetry scenarios, including the expected “best case” bathymetry surveyed immediately pre-storm. These results indicate that alternative bathymetries can be used to obtain sub-aerial erosion predictions that are similar (and in some cases better) than those resulting from the use of an immediately pre-storm surveyed bathymetry, provided that rigorous model calibration is undertaken prior. This generalized finding is attributed to specific parametrizations in the XBeach model structure that are optimized during the calibration process to match the particular bottom boundary condition used. This study provides practical guidance for the selection of suitable nearshore bathymetry for use in operational coastal erosion EWSs.

Increasing the depth of a Land Surface Model. Part I: Impacts on the subsurface thermal regime and energy storage

The representation of the thermal and hydrological states in Land Surface Models is important for a realistic simulation of land-atmosphere coupling processes. The available evidence indicates that the simulation of subsurface thermodynamics in Earth System Models is inaccurate due to a zero-heat-flux bottom boundary condition being imposed too close to the surface. In order to assess the influence of soil model depth on the simulated terrestrial energy and subsurface thermal state, sensitivity experiments have been carried out in piControl, historical and RCP scenarios. A deeper bottom boundary condition placement has been introduced into the JSBACH land surface model by enlarging the vertical stratification from 5 to 12 layers, thereby expanding its depth from 9.83 to 1416.84 m. The model takes several hundred years to reach an equilibrium state in stand-alone piControl simulations. A depth of 100 m is necessary, and 300 m recommendable, to handle the warming trends in historical and scenario simulations. Using a deep bottom boundary, warming of the soil column is reduced by 0.5 to 1.5 K in scenario simulations over most land areas, with the largest changes occurring in northern high latitudes, consistent with polar amplification. Energy storage is 3 to 5 times larger in the deep than in the shallow model and increases progressively with additional soil layers until the model depth reaches about 200 m. While the contents of Part I focus on the sensitivity of subsurface thermodynamics to enlarging the space for energy, Part II (Steinert et al. 2021) addresses the sensitivity to changing the space for water and improving hydrological and phase-change interactions.

Skills and limitations of the adiabatic omega equation: how effective is it to retrieve oceanic vertical circulation at meso and submesoscale ?

The quasi-geostrophic and the generalized omega equations are the most widely used methods to reconstruct vertical velocity (w) from in-situ data. As observational networks with much higher spatial and temporal resolutions are being designed, the question rises of identifying the approximations and scales at which an accurate estimation of w through the omega equation can be achieved and what are the critical scales and observables needed. In this paper we test different adiabatic omega reconstructions of w over several regions representative of main oceanic regimes of the global ocean in a fully eddy-resolving numerical simulation with a 1=60o horizontal resolution. We find that the best reconstructions are observed in conditions characterized by energetic turbulence and/or weak stratification where near-surface frontal processes are felt deep into the ocean interior. The quasi-geostrophic omega equation gives satisfactory results for scales larger than ~ 10 km horizontally while the improvements using a generalized formulation are substantial only in conditions where frontal turbulent processes are important (providing improvements with satisfactory reconstruction skill down to ~ 5 km in scale). The main sources of uncertainties that could be identified are related to processes responsible for ocean thermal wind imbalance (TWI), which is particularly difficult to account for (especially in observation-based studies) and to the deep flow which is generally improperly accounted for in omega reconstructions through the bottom boundary condition. Nevertheless, the reconstruction of mesoscale vertical velocities may be sufficient to estimate vertical fluxes of oceanic properties in many cases of practical interest.

The Arrested Ekman Layer Escapes! Ventilation of the BBL by Internal Swash.

<p>Moored data from the northern Deepwater Gulf of Mexico in the vicinity of DeepWater Horizon are presented.  Subinertial flows of O(0.1-0.2 m/s) are in the sense of Kelvin wave propagation and support a downwelling Ekman layer with reduced near boundary stratification.  The moored data document cross-slope and vertical buoyancy fluxes dominated by a frequency band that includes diurnal and inertial frequencies and extend to about an order of magnitude larger than inertial.  We refer to this frequency band as internal swash and the region of reduced stratification at the bottom boundary exhibiting these fluxes as the internal swash zone.  Vertical fluxes of cross-slope momentum associated with internal swash band frequencies are large, of similar order of magnitude as the drag associated with the viscous no-flow bottom boundary condition on the cross-slope subcentral current.  Typical mixing efficiencies of (Γ ~ 0.2) are found in association with elevated mixing O(100 times background) one-to-two hundred meters above the bottom. This enhanced turbulence appears in conjunction with near-inertial frequency motions that may be dynamically coupled to the mean flow.  </p><p> </p>

Gradient of the Cost Function Via the Adjoint Method for Underwater Acoustic Inversion

The acoustic propagation problem in the ocean is modeled via the wide angle parabolic equation with a Neumann to Dirichlet map bottom boundary condition. An environment consisting of the water column, a sediment layer and the semi-infinite sub-bottom region is considered. The derivatives of a new cost function with respect to the unknown environmental parameters are calculated analytically via the adjoint operator and incorporated numerically in an inversion scheme. Full geoacoustic inversion for eight bottom parameters is performed successfully, using experimental field data from the Yellow Shark experiment, for the first time according to the authors’ knowledge. Adjoint inversion for the water SSP, using the EOFs, is also presented and validated with simulated data.

Sheared free-surface flow over three-dimensional obstructions of finite amplitude

When shallow water flows over uneven bathymetry, the water surface is modulated. This type of problem has been revisited numerous times since it was first studied by Lord Kelvin in 1886. Our study analytically examines currents whose unperturbed velocity profile $U(z)$ follows a power law $z^{q}$, flowing over a three-dimensional uneven bed. This particular form of $U$, which can model a miscellany of realistic flows, allows explicit analytical solutions. Arbitrary bed shapes can readily be imposed via Fourier’s theorem provided their steepness is moderate. Three-dimensional vorticity–bathymetry interaction effects are evident when the flow makes an oblique angle with a sinusoidally corrugated bed. Streamlines are found to twist and the fluid particle drift is redirected away from the direction of the unperturbed current. Furthermore, a perturbation technique is developed which satisfies the bottom boundary condition to arbitrary order also for large-amplitude obstructions which penetrate well into the current profile. This introduces higher-order harmonics of the bathymetry amplitude. States of resonance for first- and higher-order harmonics are readily calculated. Although the method is theoretically restricted to bathymetries of moderate inclination, a wide variety of steeper obstructions are satisfactorily represented by the method, even provoking occurrences of recirculation. All expressions are analytically explicit and sequential fast Fourier transformations ensure quick and easy computation for arbitrary three-dimensional bathymetries. A method for separating near and far fields ensures computational convergence under the appropriate radiation condition.

A Nonlinear Coupled-Mode Model for Waves Propagating in Vertically Sheared Currents in Variable Bathymetry—Collinear Waves and Currents

A novel coupled-mode model is developed for the wave–current–seabed interaction problem, with application in wave scattering by non-homogeneous, sheared currents over general bottom topography. The formulation is based on a velocity representation defined by a series of local vertical modes containing the propagating and evanescent modes, able to accurately treat the continuity condition and the bottom boundary condition on sloping parts of the seabed. Using the above representation in Euler equations, a coupled system of differential equations on the horizontal plane is derived, with respect to the unknown horizontal velocity modal amplitudes. In the case of small-amplitude waves, a linearized version of the above coupled-mode system is obtained, and the dispersion characteristics are studied for various interesting cases of wave–seabed–current interaction. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system is reduced to a one-equation, non-linear model, generalizing Boussinesq models. The analytical structure of the present coupled-mode system facilitates extensions to treat non-linear effects and further applications concerning wave scattering by inhomogeneous currents in coastal regions with general 3D bottom topography.