Overlapping boundary layers in coastal oceans

Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e. surface and bottom boundary layers, separated by an interior stratification. The overlapping boundary layers evolve through three phases, i.e. a rapid deepening, an oscillatory equilibrium and a prompt merger, separated by two transitions. Before the merger, internal waves are observed in the stratified layer, and they are excited mainly by Langmuir turbulence in the surface boundary layer. These waves induce a clear modulation on the bottom-generated turbulence, facilitating the interaction between the surface and bottom boundary layers. After the merger, the Langmuir circulations originally confined to the surface layer are found to grow in size and extend down to the sea bottom (even though the surface waves do not feel the bottom), reminiscent of the well-organized Langmuir supercells. These full-depth Langmuir circulations promote the vertical mixing and enhance the bottom shear, leading to a significant enhancement of turbulence levels in the vertical column.

Diapycnal motion, diffusion, and stretching of tracers in the ocean

Small-scale mixing drives the diabatic upwelling that closes the abyssal ocean overturning circulation. Measurements of in-situ turbulence reveal that mixing is bottom-enhanced over rough topography, implying downwelling in the interior and stronger upwelling in a sloping bottom boundary layer. However, in-situ mixing estimates are indirect and the inferred vertical velocities have not yet been confirmed. Purposeful releases of inert tracers, and their subsequent spreading, have been used to independently infer turbulent diffusivities; however, these Tracer Release Experiments (TREs) provide estimates in excess of in-situ ones. In an attempt to reconcile these differences, Ruan and Ferrari (2021) derived exact buoyancy moment diagnostics, which we here apply to quasi-realistic simulations. We show in a numerical simulation that tracer-averaged diapycnal motion is directly driven by the tracer-averaged buoyancy velocity, a convolution of the asymmetric upwelling/downwelling dipole. Diapycnal spreading, however, involves both the expected contribution from the tracer-averaged in-situ diffusion and an additional non-linear diapycnal stretching term. These diapycnal stretching effects, caused by correlations between buoyancy and the buoyancy velocity, can either enhance or reduce tracer spreading. Diapycnal stretching in the stratified interior is compensated by diapycnal contraction near the bottom; for simulations of the Brazil Basin Tracer Release Experiment these nearly cancel by coincidence. By contrast, a numerical tracer released near the bottom experiences leading-order stretching that varies in time. These results suggest mixing estimates from TREs are not unambiguous, especially near topography, and that more attention should be paid towards the evolution of tracers' first moments.

The Influence of a Suspended Cage Aquaculture Farm on the Hydrodynamic Environment in a Semienclosed Bay, SE China

Hydrodynamic responses of the aquaculture farm structures have been increasingly studied because of their importance in informing the aquaculture carrying capacity and ecological sustainability. The hydrodynamical effect of the suspended cage farm on flow structures and vertical mixing in the Sansha Bay, SE China, is examined using observational data of two comparative stations inside and outside the cage farm. The results show that current velocities are relatively uniform in the vertical except a bottom boundary layer outside the cage farm. Within the cage farm, the surface boundary layer produced by the cage-induced friction is obvious with current velocities decreasing upward, combining the classic bottom boundary layer to form a “double-drag layers” structure in the water column. The cage-induced drag decreases with water depth in the surface boundary layer with a maximum thickness of 3/4 the water column, and the current velocities can be reduced by 54%. The cage-induced friction can also significantly hinder the horizontal water exchange in the farm. Periodic stratification phenomena exist at both stations under the influence of lateral circulation. However, the subsurface (5–10 m below the sea surface) water column below the cage facilities is well-mixed as indicated by the vertical density profile, where the velocity shear (10–3 m–2) is about 10 times higher than that of the subsurface layer outside the cage farm. Therefore, we speculate that the well-mixing of the subsurface water column results from the local turbulence induced by the velocity shear, which in turn is produced by the friction of cage structures.

The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom boundary, the Cauchy conditions are specified, meanwhile, the second of them has a discontinuity of the first kind at one point. The smooth boundary condition, which has the first and the second order derivatives, is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved and the conditions are established under which a piecewise-smooth solution exists. The problem with matcing conditions is considered.

Seasonal change in heat flux at the water-bottom sediment boundary in a small lake

Heat exchange with bottom sediments is the main component of the thermal regime of ice-covered shallow lakes of the temperate zone, which explains the importance of its study and parameterization for inclusion in numerical models. Circulations arising in ice-covered lakes due to heat exchange with bottom sediments, and existing for several months, can make a significant contribution to the transport of dissolved and suspended particles along the water column. The aim of this work was to study the seasonal variability of the heat flux at the waterbottom boundary in a shallow lake during the under-ice period, including the period of spring under-ice convection. Based on the analysis of data from high-frequency (minute) long-term measurements of water temperature in the bottom area of a small lake in the temperate zone, a wide range of variability of the heat flux across the water-bottom boundary during the winter from minute to daily fluctuations was established. The role of the spring under-ice heating in the change in the heat flow at the water-bottom boundary is shown. It is shown that shallow areas of the lake bottom, falling into the zone of influence of spring subglacial convection, can accumulate heat already at the end of the ice period. The comparison of temperature fluctuations in the deep-water part of the lake and tin he area with depths close to the average is carried out. It is shown that the spectrum of temperature fluctuations has similar periods, however, in time, sharp temperature jumps in different areas of the lake do not coincide.

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.