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.

Nonlinear Wave Transformation in Coastal Zone: Free and Bound Waves

The nonlinear transformation of waves in the coastal zone over the sloping bottom is considered on the base of field, laboratory, and numerical experiments by methods of spectral and wavelet analyses. The nonlinearity leads to substantial changes of wave shape during its propagation to the shore. Since these changes occur rapidly, the wave movement is non-periodical in space, and the application of linear theory concepts of wavenumber or wavelength results in some paradoxical phenomena. When analyzing the spatial evolution of waves in the frequency domain, the effect of periodic energy exchange and changes in the phase shift between the first and second wave harmonics are observed. When considering the wavenumber domain, the free and bound waves of both the first and second harmonics with constant in space amplitudes appear, and all spatial fluctuations of the wave parameters are caused by interference of these four harmonics. Practically important consequences such as the wave energy spatial fluctuations and of anomalous dispersion of the second harmonic are shown and discussed.

Instability Assessment of Hanging Wall Rocks during Underground Mining of Iron Ores

The paper presents the study of the deformation processes development in unstable rocks of the hanging wall during mining a thick steeply dipping ore deposit in the example of the Yuzhno-Belozerskyi deposit. In the studied field, there are problems of stability of hanging wall rocks, represented by low-resistant shale rocks that do not withstand significant outcrops in time. A decrease in stability is manifested in the form of failure of the hanging wall rocks into the stope. Based on a detailed study of the ore deposit geological structure and the performance of the stopes mining, according to the survey data, an area of the deposit has been identified where the ore failure and dilution reach 4%–8% with a maximum value of 12%. This also makes it possible to determine the most important averaged source data for performing physical modeling on equivalent materials. It has been determined that the deformation value of the hanging wall rocks with subsequent failure into the stope and ore mass deformation in the sloping bottom change exponentially with an increase in the depth of the stope location, and the dynamics of increasing rock deformations in the hanging wall is noticeably higher than in the sloping bottom of the stope. This reduces the quality of the mined ore and increases the probability of rock failure area propagation to the hanging wall drifts with their subsequent destruction. The results of physical modeling are characterised by acceptable reliability and are confirmed by a high similarity with the actual data on ore dilution with broken rocks during the stopes development. It has been found that during the formation of a steeply dipping outcrop of stopes with an area of 1200 m2, unstable rocks of the hanging wall are prone to failure of significant volumes. For successful mining and achieving stope element stability, it is recommended to optimise its parameters, the height, width and the value of a steeply dipping outcrop, as well as to preserve the ore pillar in the hanging wall until the ore is broken and drawn from the rest of the stope.

A Validated Study of a Modified Shallow Water Model for Strong Cyclonic Motions and Their Structures in a Rotating Tank

A joint theoretical and numerical study was carried out to investigate the fluid dynamical aspect of the motion of a vortex generated in a rotating tank with a sloping bottom. This study aims at understanding the evolution of strong cyclonic motions on a β-plane in the Northern Hemisphere. The strong cyclonic vortices were characterized by four nondimensional parameters which were derived through a scale analysis of the depth variations of fluid. By simplifying the model flow field and the prototype flow field, respectively, through the conservation of potential vorticity, two sets of dynamic similarity conditions are derived. This study proposed a sophisticated modified shallow water model (MSWM) to investigate the flow features of such strong vortices. A detailed numerical calculation adopted by multidimensional positive definite advection transport algorithm (MPDATA) was carried out to validate those effects considered in the MSWM model, including sloping bottom, parabolic free surface deformation, and viscous dissipation. Close agreements were found between the experimental and numerical results, including the streamlines patterns and the vortex trajectory. Comprehensive simulations for strong cyclonic vortices over different sloping bottoms were investigated to understand the impact of planetary β effect on vortex. The results calculated by MSWM demonstrate a variety of flow features of interactions between the primary vortex and induced secondary Rossby wave wakes that were essential and prominent in environmental geophysical flows.

Numerical investigation on motion responses of a floating hemisphere over a sloping bottom

In the last several decades, some numerical approaches have been proposed to deal with 3D wave-body interaction problems in sloping bottom environment. Most of them either adopt the finite depth Green function or add numerical damping terms into the free surface condition to treat far field radiation condition, which certainly give rise to numerical errors. The hybrid model [1] adopting the consistent coupled-mode system for incident wave propagation problem combining with the three-dimensional bottom-dependent Green function to treat the diffraction and radiation problem is a complete formulation, as the latter function appropriately characterise the far field radiation wave pattern over a smoothly sloping bottom. However, this model has not been validated after its publication. In this connection, comparisons with Computational Fluid Dynamic (CFD) results are presented to verify its accuracy. Application of this hybrid model is also performed to investigate the effects on the floating hemisphere by the sloping bottom.

Immersion of grains in a liquid along an inclined plane

Grain material delivered from combine harvesters to post-harvest processing points is a mixture of grain, weed and harmful impurities. Toxic ergot sclerotia are among the harmful impurities. Modern grain cleaning machines do not provide the separation of toxic ergot from grain material in one technological process. This is due to the closeness of the most toxic of ergot sclerotia and the of the grain. Ergot sclerotia are less dense than grain. Then the release of ergot from grain in one technological process is possible in an aqueous solution of salt. To develop a device for cleaning grain material by density in a liquid, practical experiments were carried out to supply grains of winter rye varieties Falenskaya 4 with a moisture content of 14% to an inclined plate placed in water. This plate mimicked the sloping bottom of an ergot seed separator. The statistical results of the experiments are presented by the distributions of the proportion of immersion of winter rye grains in water (ρzh = 1000 kg/m3) over the surface of the inclined plate from the angle α of its inclination to the horizon. It has been established that 100% immersion of the grains in water occurs at an angle of inclination of the plate of 60°. When developing a machine for the extraction of ergot from rye grain, the angle of inclination of the bath bottom must be taken at least 65° to the horizon for guaranteed immersion of grains in an aqueous solution of salt.

EFFECT OF THE DENSITY OF INUNDATION WATER ON TSUNAMI RUN-UP

Aiming for the advancement of historical and/or prospective tsunami scale evaluations, and focusing on the tsunami run-up, series solutions to the tip position a(t), velocity U (=da/dt) and acceleration d2a/dt2 in the tip region of inundation flow (unsteady flow) with sediment over a uniformly sloping bottom under the condition that the friction factor K is not linked to the density of inundation water, and analytical solutions to a(t), U(t), d2a/dt2, the maximum run-up distance a_m and height Rm under the condition that K is linked to density are derived, and effects of density on them and run-up process are theoretically examined. It is indicated that (1) in the run-up analysis (including numerical simulation) of tsunami with sediment under the condition of a constant K, even if a_m and Rm can be predicted accurately, there is a possibility of evaluating the run-up duration time inaccurately and vice versa, and (2) linking K to density is necessary to solve this matter. An expression for the relationship between K and is also presented. Moreover, it is verified that the derived series and analytical solutions are useful to discuss the effects of density on the run-up of tsunami with sediment through a comparison between the experimental and theoretical maximum run-up distances.