A wave averaged energy equation: comment on "Global Estimates of Wind Energy Input to Subinertial Motions in the Ekman-Stokes Layer" by Bin Liu, Kejian Wu and Changlong Guan

In a recent paper, Liu et al. (2007) formulate an expression for how surface gravity waves modify the Ekman layer energy budget. They then diagnose the effect in the world oceans using available data. This comment addresses the formulation of the energy equation that is fundamental to their stud

Tidally induced mean flow over bathymetric features: a contemporary challenge for high-resolution wide-area models

Huthnance [Estuarine CoastalMar. Sci. 1973, 1, 89–99] is reviewed, whereby an oscillating tide over bathymetric features induces a mean flow generally along isobaths. The effect is a superposition of Coriolis and frictional processes. These are discussed with the intention of elucidating the processes for a more general readership. Induced velocities of order several cm/s are expected around the UK shelf seas. The effect is dynamically significant over bathymetric scales of order a few kilometres and has previously been of most interest to dynamicists studying processes on this scale. However, with the increase in computing power, appropriate scales can be simulated in shelf-wide regional models and in next generation operationalmodels. It is demonstrated that this small-scale effect is likely to be important for shelf-wide regionalmodels and that a spatial resolution of at least 1.8km is recommended for shelf sea simulations

Features of near-inertial motions observed on the northern South China Sea shelf during the passage of two typhoons

Features of near-inertial motions on the shelf (60 m deep) of the northern South China Sea were observed under the passage of two typhoons during the summer of 2009. There are two peaks in spectra at both sub-inertial and super-inertial frequencies. The super-inertial energy maximizes near the surface, while the sub-inertial energy maximizes at a deeper layer of 15 m. The sub-inertial shift of frequency is induced by the negative background vorticity. The super-inertial shift is probably attributed to the near-inertial wave propagating from higher latitudes. The near-inertial currents exhibit a two-layer pattern being separated at mid-depth (25–30 m), with the phase in the upper layer being nearly opposite to that in the lower layer. The vertical propagation of phase implies that the near-inertial energy is not dominantly downward. The upward flux of the near-inertial energy is more evident at the surface layer (<17 m). There exist two boundaries at 17 and 40 m, where the near-inertial energy is reflected upward and downward. The near-inertial motion is intermittent and can reach a peak of as much as 30 cm/s. The passage of Typhoon Nangka generates an intensive near-inertial event, but Typhoon Linfa does not. This difference is attributed to the relative mooring locations, which is on the right hand side of Nangka’s path (leading to a wind pattern rotating clockwise with time) and is on the left hand side of Linfa’s path (leading to a wind pattern rotating anti-clockwise with time)

Leaky slope waves and sea level: unusual consequences of the beta-effect along western boundaries with bottom topography and dissipation

Coastal Trapped Waves (CTWs) carry the ocean’s response to changes in forcing along boundaries, and are important mechanisms in the context of coastal sea level and the meridional overturning circulation. Motivated by the western boundary response to high latitude and open ocean variability, we investigate how the latitude dependence of the Coriolis parameter (β-effect), bottom topography, and bottom friction, modify the evolution of western boundary CTWs and sea level using a linear, barotropic model. For annual and longer period waves, the boundary response is characterized by modified Shelf Waves and a new class of leaky Slope Waves that propagate alongshore, typically at an order slower than Shelf Waves, and radiate short Rossby waves into the interior. Energy is not only transmitted equatorward along the slope, but also eastward into the interior, leading to the dissipation of energy locally and offshore. The β-effect and friction result in Shelf and Slope Waves that decay alongshore in the direction of the equator, decreasing the extent to which high latitude variability affects lower latitudes, and increasing the penetration of open ocean variability onto the shelf - narrower continental shelves and larger friction coefficients increase this penetration. The theory is compared against observations of sea level along the North American east coast and qualitatively reproduces the southward displacement and amplitude attenuation of coastal sea level relative to the open ocean. The implications are that the β-effect, topography, and friction are important in determining where along the coast sea level variability hot spots occur

Idealised modelling of offshore-forced sea level hot spots and boundary waves along the North American East Coast

Hot spots of sea level variability along the North American East Coast have been shown to shift in latitude repeatedly over the past 95 years and connections with a number of forcing phenomena, including the North Atlantic Oscillation (NAO) and Atlantic Meridional Overturning Circulation (AMOC), have been suggested. Using a barotropic 1/12° NEMO model of the North American East Coast (to represent the upper ocean and a homogeneous shelf), we investigate the coastal sea level response to remote sea surface height (SSH) variability along the upper continental slope. Hilbert transform Complex EOF analysis is used to investigate the responses to interannual changes in the strength of the mean winds and an idealised NAO. Variability in the mean winds produces in-phase coastal sea level variability along the entire coastline and is driven by a SSH anomaly in the subpolar gyre. Variability due to the NAO forcing is in phase along the coast south of Cape Hatteras. Interannual coastal sea level variability at a given latitude is found to be driven by off-shore SSH anomalies originating many degrees of latitude (100s km) further north, and linear barotropic trapped wave theory is used to explain the mechanism. A comparison of the results from an analytical model with those from the numerical model is used to suggest that the boundary wave mechanism is also relevant for understanding the coastal response to interior sea level change over longer time periods. Nonlinear effects are found not to significantly modify the character of the linear solution

The perturbation method - A novel large-eddy simulation technique to model realistic turbulence: Application to tidal flow

Turbulence in the ocean dominates the vertical movement of heat and salt, as well as chemical and biological particulates. The modelling of turbulence is therefore essential to forecast the strength of the biological pump, for example, in which CO2 is drawn out of the atmosphere and trapped in the deep ocean. Obtaining observations of turbulence is an expensive process and the modelling of turbulence still remains an open problem. Using state-of-the-art 3D hydrodynamic models, such as Large-Eddy Simulation and Direct Numerical Simulation, to understand turbulence driven by mean flow is a popular method. However in this approach, the turbulence creates its own mean flow contribution which, in some applications, results in an undesirable divergence from the prescribed mean flow. Here, the perturbation method is introduced. This technique ensures zero divergence to the prescribed mean flow. Results reveal the high level of accuracy this approach has in replicating the observed turbulent field when using ADCP mean current data to prescribe the model mean flow. It is envisaged that the user-friendly nature of this method will enable non-specialists to derive turbulence data when turbulence profilers are not a tractable resource. This modelling approach also sets a rigid framework for the testing of turbulence closure schemes

Modelling Large-Scale CO2 Leakages in the North Sea

A three dimensional hydrodynamic model with a coupled carbonate speciation sub-model is used to simulate large additions of CO2 into the North Sea, representing leakages at potential carbon sequestration sites. A range of leakage scenarios are conducted at two distinct release sites, allowing an analysis of the seasonal, inter-annual and spatial variability of impacts to the marine ecosystem. Seasonally stratified regions are shown to be more vulnerable to CO2 release during the summer as the added CO2 remains trapped beneath the thermocline, preventing outgasing to the atmosphere. On average, CO2 injected into the northern North Sea is shown to reside within the water column twice as long as an equivalent addition in the southern North Sea before reaching the atmosphere. Short-term leakages of 5000 tonnes CO2 over a single day result in substantial acidification at the release sites (up to -1.92 pH units), with significant perturbations (greater than 0.1 pH units) generally confined to a 10 km radius. Long-term CO2 leakages sustained for a year may result in extensive plumes of acidified seawater, carried by major advective pathways. Whilst such scenarios could be harmful to marine biota over confined spatial scales, continued unmitigated CO2 emissions from fossil fuels are predicted to result in greater and more long-lived perturbations to the carbonate system over the next few decades

The effect of uncertain river forcing on the thermohaline properties of the North West European Shelf Seas

Modeling studies and observations show that the thermohaline properties of the North West European Shelf Seas (NWESS) are sensitive to surface wind and heat flux forcing, as well as river outflows that transport fresh water from land to the ocean. In previous studies, it was assumed that the variability of the thermohaline properties in response to river outflow could be adequately sampled with a high-resolution, submesoscale permitting, long-term (i.e., 30-year) deterministic hindcast. In this study, we assume that the statistical distribution of the river forcing, rather than the time series of forcing itself, is adequately constrained by a 28-year history (1991 to 2018) of river forcing created specifically for our domain. In this way, we created an ensemble of 10 lower-resolution ( 7-km), short-term (i.e., 2.5 years) hindcast models that are forced with randomly perturbed river outflows and an ensemble of surface fluxes from the 10-member ECMWF ERA5 reanalysis (the ‘Test’ ensemble) as well with a companion ensemble that is forced with the ERA5 surface forcing fluxes but unperturbed river outflows (the ‘Base’ ensemble) for the June 2016 through December 2018 time period. In both ensembles, the modeled evolution of 25-hour averaged (to partially filter out tides) temperature and salinity is realistic with peaks in summer for sea surface temperature and in winter for salinity, and annual amplitudes that are comparable to those found in other studies of the NWESS. The increased mean and standard deviation of the sea surface and bottom salinity in the Test ensemble are partly an artifact of the assumption that the errors in river forcing have a log-normal distribution that mimics the episodic nature of river outflow with a positive mean and an asymmetrical shape with a long tail towards large values. For surface density, the standard deviation in the Test ensemble was below 0.5 kg/m3, covering an areal extent larger than that for the Base ensemble throughout the year. The annual cycle of the areal extent of density in that range had a peak in summer and minima in winter, in phase with that of the river outflow forcing. Overall, the effect of uncertain river forcing on the thermohaline properties in this study is small. In order to understand the true impact of river forcings, better temporal and spatial observations of river outflow are needed

Evolution of oceanic near surface stratification in response to an autumn storm

Understanding the processes that control the evolution of the ocean surface boundary layer (OSBL) is a prerequisite for obtaining accurate simulations of air-sea fluxes of heat and trace gases. Observations of the rate of dissipation of turbulent kinetic energy (ɛ), temperature, salinity, current structure and wave-field over a period of 9.5 days in the NE Atlantic during the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS), are presented. The focus of this study is a storm which passed over the observational area during this period. The profiles of ɛ in the OSBL are consistent with profiles from large eddy simulation (LES) of Langmuir turbulence. In the transition layer (TL), at the base of the OSBL, ɛ was found to vary periodically at the local inertial frequency. A simple bulk model of the OSBL and a parametrisation of shear driven turbulence in the TL are developed. The parametrisation of ɛ is based on assumptions about the momentum balance of the OSBL and shear across the TL. The predicted rate of deepening, heat budget and the inertial currents in the OSBL were in good agreement with the observations, as is the agreement between the observed value of ɛ and that predicted using the parametrisation. A previous study reported spikes of elevated dissipation related to enhanced wind-shear alignment at the base of the OSBL after this storm. The spikes in dissipation are not predicted by this new parametrisation, implying that they are not an important source of dissipation during the storm

Reply to “Comments on ‘Langmuir Turbulence and Surface Heating in the Ocean Surface Boundary Layer’”

The differences between the conclusions of Noh and Choi and of Pearson et al., which are largely a result of defining different length scales based on different quantities, are discussed. This study shows that the layer over which Langmuir turbulence mixes (nominally hTKE) under a stabilizing surface buoyancy flux should be scaled by a combination of the Langmuir stability length LL and initial/nocturnal boundary layer depth h0 rather than by the Zilitinkevich length