Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

Estimates of wind power and radiative near-inertial internal wave flux

Ocean Dynamics - Energy transfer mechanisms between the atmosphere and the deep ocean have been studied for many years. Their importance to the ocean’s energy balance and possible...     

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Seasonal variations in internal wave energy in a Scottish sea loch

Near-continuous observations of an internal wave field were made over a period of 13 months at a location in Inchmarnock Water at the northern end of the Clyde Sea. This paper sets out to determine the seasonal form of the energy density of the internal wave field at this location based on the hypothesis that it varies smoothly throughout the year, being greater in summer than in winter. The mooring was maintained between June 1999 and July 2000 in 150-m water with seven deployments. Estimates of kinetic and potential energy density were derived from Acoustic Doppler Current Profiler (ADCP) and vertical temperature profiles respectively. Both were shown to vary on time scales less than 1 month with median values of mean kinetic energy (KE) density0.5 J m^–3 and for mean potential energy (PE) density0.01 J m^–3. The energy of the internal wave field was found to be continuous and without a clear seasonal form. Further, it was also always non-zero with intermittent peaks of much higher energy. In the late autumn the system experienced complete vertical overturning driven by local convective processes destroying the thermocline and causing a reduction in the overall KE density.Responsible Editor: Jens KappeubergOrginally presented as a poster at PECS 2002, Hamburg Germany     

On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions

The importance of using a non-hydrostatic model to compute tidally induced mixing and flow in the region of a sill is examined using idealized topography representing the sill at the entrance to Loch Etive. This site is chosen since detailed measurements were recently made there. Calculations are performed with and without the inclusion of non-hydrostatic dynamics using a vertical slice model for a range of sill widths corresponding to typical sill regions. Initial non-hydrostatic calculations showed that the model could reproduce the observed flow characteristics in the region. However, when calculations were performed using the model in hydrostatic form, the significant artificial convective mixing that occurred in order to remove density inversions led to excessively high vertical mixing. This influenced the computed temperature field and the intensity of the current jet that separated from the sill on its lee side. In addition it affected the magnitude and spatial characteristics of the lee waves generated on the lee side of the sill. Calculations with a range of sill widths, showed that as the sill width decreased the difference between the solution computed with the non-hydrostatic and hydrostatic model increased.     

Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

Magnetic topologies in the solar corona due to four discrete photospheric flux regions

Many dynamic phenomena in the solar corona are driven by the complex and ever-changing magnetic field. It is helpful, in trying to model these phenomena, to understand the structure of the magnetic field, i.e. the magnetic topology. We study here the topological structure of the coronal magnetic field arising from four discrete photospheric flux patches, for which we find that seven distinct, topologically stable states are possible; the changes between these are caused by six types of bifurcation. Two bifurcation diagrams are produced, showing how the changes occur as the relative positions and strengths of the flux patches are varied. A method for extending the analysis to higher numbers of sources is discussed.     

On the energy flux of Hide waves

Summary There are two ways to define the energy flux for Hide waves, one from its equations of motion and the other by multiplying its mean energy density by group velocity and these lead to different results FollowingLonguet-Higgins we point out that this is due to certain arbitrariness in the definition of the energy flux and that their difference is just a solenoidal vector.Dedicated to the memory of Dr.V. A. Wynne, 1945–1972.     

The influence of neap–spring tidal variation and wave energy on sediment flux in salt marsh tidal creeks

Sediment flux in marsh tidal creeks is commonly used to gauge sediment supply to marshes. We conducted a field investigation of temporal variability in sediment flux in tidal creeks in the accreting tidal marsh at China Camp State Park adjacent to northern San Francisco Bay. Suspended‐sediment concentration (SSC), velocity and depth were measured near the mouths of two tidal creeks during three 6‐ to 10‐week deployments: two in winter and one in summer. Currents, wave properties and SSC were measured in the adjacent shallows. All deployments spanned the largest spring tides of the season. Results show that tidally averaged suspended‐sediment flux (SSF) in the tidal creeks varied from slightly landward to strongly bayward with increasing tidal energy. SSF was negative (bayward) for tidal cycles with maximum water surface elevation above the marsh plain. Export during the largest spring tides dominated the cumulative SSF for each deployment. During ebb tides following the highest tides, velocities exceeded 1 m s^?1 in the narrow tidal creeks, resulting in negative tidally averaged water flux, and mobilizing sediment from the creek banks or bed. Storm surge also produced negative SSF. Tidally averaged SSF was positive in wavy conditions with moderate tides. Spring tide sediment export at the creek mouth was about twice that at a station 130 m further up the tidal creek. The negative tidally averaged water flux near the creek mouth during spring tides indicates that in the lower marsh some of the water flooding directly across the bay–marsh interface drains through the tidal creeks, and suggests that this interface may be a pathway for sediment supply to the lower marsh as well. Copyright © 2018 John Wiley & Sons, Ltd.     

Wave to wave and wave to zonal mean flow kinetic energy exchanges during contrasting monsoon years

Fourier analysis of the monthly mean northern hemispheric geopotential heights for the levels 700 mb and 300 mb are undertaken for the months of April through to August. The wave to wave and wave to zonal mean flow kinetic energy interactions are computed for specified latitude bands of the northern hemisphere during the pre-monsoon period (April to May) and monsoon period (June through to August) for bad monsoon years (1972, 1974, 1979) and for years of good monsoon rainfall over India (1967, 1973, 1977). Planetary scale waves (waves 1 to 4) are the major kinetic energy source in the upper atmosphere during the monsoon months. Waves 1 and 2 in particular are a greater source of kinetic energy to other waves via both wave to wave interactions as well as wave to zonal mean flow interactions in good monsoon years than in bad monsoon years. The zonal mean flow shows significantly larger gains in the kinetic energy with a strengthening of zonal westerlies in good monsoon years than in bad monsoon years.     

Turbulent kinetic energy and sediment resuspension due to wave groups

Wave-induced sediment resuspension in nearshore regions has been observed occurring in an event-like manner and associated with the passage of wave groups. This paper describes field measurements of turbulent velocities obtained simultaneously with suspended sediment concentration and water surface elevation from Floreat Beach, Perth, Western Australia. The data were used to study the relationship between turbulent kinetic energy (TKE) on suspension events caused by wave groups and the intermittent nature of bottom turbulence production and sediment suspension. The field measurements showed the high TKE events occurred under wave crests, and sometimes under wave toughs, when the wave heights were increasing during the passage of a wave group; the TKE decreased after the maximum wave in the wave group had passed over the measurement location. High suspended sediment concentrations (ssc) and the intermittent high TKE events were not related rather the higher ssc events were associated with a secondary peak in the surface elevation, close to the maxima in the offshore velocity, and “burst” events in the Reynolds stress.     

Bioturbation on a south‐east Australian hillslope: estimating contributions to soil flux

The contribution of bioturbation to downslope soil transport is significant in many situations, particularly in the context of soil formation, erosion and creep. This study explored the direct flux of soil caused by Aphaenogaster ant mounding, vertebrate scraping and tree‐throw on a wildfire‐affected hillslope in south‐east Australia. This included the development of methods previously applied to Californian gopher bioturbation, and an evaluation of methods for estimating the volume of soil displaced by tree‐throw events. All three bioturbation types resulted in a net downslope flux, but any influence of hillslope angle on flux rates appeared to be overshadowed by environmental controls over the spatial extent of bioturbation. As a result, the highest flux rates occurred on the footslope and lower slope. The overall contribution of vertebrate scraping (57.0 ± 89.4 g m^?1 yr^?1) exceeded that of ant mounding (36.4 ± 66.0 g m^?1 yr^?1), although mean rates were subject to considerable uncertainty. Tree‐throw events, which individually cause major disturbance, were limited in their importance by their scarcity relative to faunalturbation. However, tree‐throw might be the dominant mechanism of biotic soil flux on the mid‐slope provided that it occurs at a frequency of at least 2–3 events ha^?1 yr^?1. Although direct biotic soil flux appears to be geomorphologically significant on this hillslope, such transport processes are probably subordinate to other impacts of bioturbation at this site such as the enhancement of infiltration following wildfire. Copyright © 2011 John Wiley & Sons, Ltd.     

The energy and energy flux of planetary waves in an ocean of variable depth

Abstract

In a recent paper, Buchwald (1972a) has shown that besides the kinetic energy and gravitational potential energy usually associated with planetary waves in an ocean of uniform depth it is useful to define also a “spin energy”, associated with the rotation.

The present paper is basically an extension of Buchwald's result to a uniformly rotating β-plane ocean of variable depth. As in the previous work, energy conservation equations are derived and the separate energies shown to be independently conserved over the total volume of the ocean. The time-averaged energies are further shown to be propagated in the direction of the group velocity and to satisfy the equipartition rule.

Unlike Buchwald, however, we need not consider the boundary conditions in order to achieve these results. Furthermore, the use of a more realistic ocean configuration admits the possibility of a multiply connected region in the present of mean currents.

Finally, there is a physical explanation for the appearance of a spin energy in a rotating system.     

Improvements to the statistical theoretical model for wave breaking based on the ratio of breaking wave kinetic and potential energy

An improvement was proposed for the statistical theory of breaking entrainment depth and surface whitecap coverage of real sea waves in this study. The ratio of the kinetic and potential energy was estimated on a theoretical level, and optimal constants were determined to improve the statistical theory model for wave breaking. We also performed a sensitivity test to the model constants. A comparison between the model and in situ observations indicated that the level of agreement was better than has been achieved in previous studies.     

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.