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Internal waves drive ocean mixing and enhance the transport of heat, momentum and other tracers in shelf seas. We collected observations of mixing over a 30‐day period from three cross‐shore moorings placed on the 330, 200 and 150 m isobaths on the offshore side of a pelagic ridge on the Australian North West Shelf. The region is forced by energetic surface and internal tides, exhibits non‐linear internal waves, experiences flow‐topography interactions, and is subject to episodic intense wind events. This complex forcing drove energetic diapycnal mixing at all sites. We identified five dominant internal wave forcing categories: mode‐1 waves at low‐frequency (time scales from double the buoyancy period to 4 hr), mode‐1 waves at high‐frequency (HF) (time scales between the buoyancy period and double the buoyancy period), mode‐2 waves, internal bores, and internal hydraulic jumps. Overall, just 15% of mixing events accounted for 90% of the total observed heat flux over the record. Mixing during internal wave events accounted for as much as 50% of the total heat flux in some locations. Of the internal wave categories, HF mode‐1 waves were the most significant contributors to the total heat flux at all sites (∼20%). On the other hand, internal bores made significant contributions to mixing only at the 200 and 150 m moorings; they made no contribution to mixing at the 330 m mooring. At the shallowest mooring, the different internal wave categories all made similar contributions to the total flux, indicating an increasingly complicated relationship between the evolving internal wavefield and the mixing. Plain Language Summary: Internal waves propagate along the density gradients found beneath the ocean's surface layer, analogous to surface waves propagating along the sharp density gradient where air and water meet. These waves play an important role in the distribution of nutrients, heat, contaminants, and other tracers in the ocean, especially in coastal regions where the waves break. The density structure of the ocean, the tidal and wind forcing, and the seabed features result in many different types of internal waves, each of which travel and break differently. In this work, we examine the mixing caused by different types of internal waves as they travel up and over a subsurface ridge on the Australian North West Shelf. We found that most of the significant mixing resulted from relatively rare events, which often occurred during internal wave forcing events. The magnitude of mixing increased in shallower waters due to internal waves breaking and causing energetic turbulent flows. However, the wave types that were the most significant for mixing changed depending on the location on the shelf and the depth. High‐frequency internal waves were generally the most significant contributor to mixing. Internal bores, a class of waves moving upslope near the seabed, did dominate the total ocean mixing near‐bottom at some locations. Key Points: Energetic but short‐lived nonlinear internal wave events drove most of the vertical turbulent heat flux over the month‐long recordInternal wave events evolved over relatively short time scales and relatively short spatial scalesEnergetic internal wave events contribute significantly to mixing in shelf seas [ABSTRACT FROM AUTHOR]

We describe a framework for the simultaneous estimation of model parameters in a partial differential equation using sparse observations. Markov Chain Monte Carlo sampling is used in a Bayesian framework to estimate posterior probability distributions for each parameter. We describe the necessary components of this approach and its broad potential for application in models of unsteady processes. The framework is applied to three case studies, of increasing complexity, from the field of cohesive sediment transport. We demonstrate that the framework can be used to recover posterior distributions for all parameters of interest and the results agree well with independent estimates (where available). We also demonstrate how the framework can be used to compare different model parameterizations and provide information on the covariance between model parameters. Plain Language Summary: We describe a framework for the simultaneous estimation of multiple unobserved parameters by combining observations of a tracer with a numerical model. This framework uses Bayesian inference techniques established in statistical literature to estimate the unobserved parameters of interest used in the model with uncertainty quantification. We explain the key components of this framework in simple terms to encourage its use for analyzing other unsteady processes and performing quantitative inference on parameters that are difficult or impossible to measure directly. We then demonstrate the framework's efficacy by applying it to three case studies from the field of cohesive sediment transport that all use the transport equation (advection‐diffusion). Inferred parameter values show good agreement with independent estimates, where available. Key Points: Probabilistic framework to estimate unobserved erosion model parameters using sparse measurements collected above the seabedGeneral approach can be updated with any model parameterization and quantitatively comparedThe framework is applicable to many similar data sets with both unsteady or quasi‐steady forcing and response [ABSTRACT FROM AUTHOR]

We present 15 days of both mean and turbulent field observations bottom mixing‐layer at a gently sloping 250 m deep continental shelf site, energized by tides and nonlinear internal waves (NLIWs). The tidal frequency forcing was due to the combined effects of the barotropic tide and a mode‐1 internal tide (IT), while the NLIWs were predominantly mode‐1 waves of depression. The bottom mixing‐layer thickness varied at both semidiurnal and sub‐tidal ∼O(10)d frequencies, with an average thickness of around 10 m. Compression and expansion of the mixing‐layer by both the IT and NLIWs affected the mean velocity profiles in the mixing‐layer, while the phasing between the barotropic and baroclinic flows led to an asymmetry in mean velocity profiles between periods of rising and falling isotherms. With the exception of periods of flow reversal, the turbulent kinetic energy balance and turbulent stress observations were consistent with the existence of an inertial‐sublayer with thickness of approximately 10%–15% of the mixing‐layer thickness (∼1 m), even beneath NLIWs. In the outer portion of the mixing‐layer—that is, above the inertial‐sublayer—NLIWs modulated the local turbulence spectra. We discuss the observations in the context of a predictive model for mixing‐layer thickness. The analysis suggests that the high‐frequency variability in mixing‐layer thickness was dominated by internal wave pumping, though strength of the ambient stratification and the frequency of the forcing were important controls on the time‐averaged (sub‐tidal) variation. Plain Language Summary: The bottom boundary layer (BBL) is the portion of an ocean flow that "feels" the presence of the seabed. Oceanic bottom boundary layer dynamics are globally significant as they control many important physical, biological, and chemical transport processes in the ocean, and furthermore, most man‐made sub‐sea structures are located within this relatively thin layer. We present 15 days of detailed observations of a near well‐mixed BBL at a 250 m deep continental shelf site, where the ocean flow was characterized by strong tides and large internal waves. The boundary layer thickness varied at tidal and sub‐tidal frequencies, and was ∼10 m thick on average. In the lowermost 1 m of this layer, the flow conformed to conventional boundary layer dynamics as observed in the lowest layers of the atmosphere, for example. More than 1 m above the bed, however, the overlying internal waves modified both the nature of the turbulent flow and the time‐averaged properties of the bottom mixing‐layer. We also discuss a simple empirical model to estimate the layer thickness. Key Points: A full spring‐neap cycle of mean and turbulent observations within a tide and internal wave driven bottom mixing‐layer (BML) are presentedInfluenced by stratification and unsteady flow above, BML thickness varied at semidiurnal and sub‐tidal ∼O(10)d timescalesTurbulence observations consistent with an inertial sublayer whose thickness was ∼10%–15% of the total BML thickness (∼1 m) [ABSTRACT FROM AUTHOR]

While it has been recognized for some time that large amplitude non‐linear internal waves (NLIW) can mobilize and transport sediment, quantitative observations of this process are rare. Rarer still are accompanying estimates of suspended sediment mass concentration (SSC) during the passage of NLIW. Here, we present high resolution observations of NLIW and the SSC response within the bottom boundary layer. The observations were made in 250 m of water in a mildly sloping region of the Browse Basin on Australia's Northwest Shelf. We compare two independent but direct calibration methods, and employ Bayesian methods to estimate the uncertainty in SSC. During a large NLIW event, the peak mean SSC estimate at 0.49 m above the sea bed was 161 mg L−1, with a maximum time‐rate‐of‐change of 0.14 mg L−1 s−1. The unsteady boundary layer forcing under NLIW resulted in a variable time‐height dependent relationship between bed stress and SSC with increasing height above the sea bed. Suspended sediment was restricted to the bottom mixing layer, with sharp vertical gradients of up to 40 mg L−1 m−1 observed at the edge of the layer. The observations presented here are intended to offer guidance to numerical sediment modelers about likely SSC under strong NLIW. Plain Language Summary: Internal waves are waves that travel along layers of different density within the ocean. They can travel through the ocean and have the potential to generate strong currents as they move into shallow water on the continental shelf. This process can lift and transport local sea bed sediment if the near‐bed currents are strong enough. This process is short‐lived, unpredictable, and generally occurs in deeper waters, making high quality observations rare. We present detailed observations of ocean currents and the sediment response during the passage of several large internal waves. The observations were captured on the Northwest Shelf of Australia in 250 m depth for two months in 2017. We used a range of instruments to measure the properties of sediment in the water. These data sets were converted to estimates of suspended sediment mass concentration by calibration. The observed near‐bed currents created by internal waves resulted in significant sediment transport, which was trapped in a region close to the sea bed due to density layers. Key Points: Calibrated observations of sediment mobilization and transport on the continental shelf under barotropic and baroclinic forcingSediment response to bed stress was unsteady, resulting in a variable time lag with height above the sea bedSuspended sediment concentration dropped sharply coincident with a bottom mixing layer pycnocline [ABSTRACT FROM AUTHOR]

Non‐linear internal waves (NLIW) are important to processes such as heat transfer, nutrient replenishment and sediment transport on continental shelves. Our unique field observations of shoaling NLIW of elevation revealed a variety of different wave shapes, varying from relatively symmetric waves, to waves with either steepened leading‐ or trailing‐faces; many had evidence of trapped cores. The wave shape was related to the position of maximum density overturns and diapycnal mixing. We observed both shear (where sheared currents overcome the stabilizing effects of stratification) and convective (where the local velocity exceeds the wave propagation speed) instabilities. The elevated diapycnal mixing (>10−3 m2s−1) and heat flux (>500 Wm−2) were predominantly local to the NLIW of elevation packets, and were transported onshore 10s kilometers with the wave packets. We demonstrate that wave steepness may be a useful bulk property for the parameterization of wave‐averaged diapycnal heat flux. Plain Language Summary: Predicting the distribution of constituents such as nutrients, heat, sediment and pollutants on the continental shelf is key to processes such as: the safe operation of offshore infrastructure; understanding the variation in primary productivity; the prediction of marine heat waves; and environmental impact assessments of new activities. Non‐linear internal waves, waves that travel within the stratified water column, are likely to have a significant impact on constituent transport; however, they are poorly understood. Here we present unique observations that quantify the properties of a class of these nonlinear internal waves, known as waves of elevation. These waves can break in a similar way to surface waves at the beach, leading to dramatic increases in turbulent mixing over horizontal length scales of 10s kilometers. We have used our observations to define the amount of vertical heat transport induced by the breaking waves as a function of wave steepness. The vertical heat transport can be used as a proxy to estimate the vertical nutrient transport. This study has made a step change in quantifying the impact of NLIW of elevation on vertical transport. Key Points: Nonlinear internal waves of elevation can form both convective and shear instabilities, resulting in enhanced diapycnal mixing and heat fluxBreaking continues as the nonlinear waves propagate onshore, influencing diapycnal mixing and vertical heat flux over 10s of kilometersThe elevated heat flux associated with the nonlinear internal waves of elevation increases with the wave steepness [ABSTRACT FROM AUTHOR]

We present a statistical method for reconstructing continuous background density profiles that embeds incomplete measurements and a physically intuitive density stratification model within a Bayesian hierarchal framework. A double hyperbolic tangent function is used as a parametric density stratification model that captures various pycnocline structures in the upper ocean and offers insight into several density profile characteristics (e.g., pycnocline depth). The posterior distribution is used to quantify uncertainty and is estimated using recent advances in Markov chain Monte Carlo sampling. Temporally evolving posterior distributions of density profile characteristics, isopycnal heights, and nonlinear ocean process models for internal gravity waves are presented as examples of how uncertainty propagates through models dependent on the density stratification. The results show 0.95 posterior interval widths that ranged from 2.5% to 4% of the expected values for the linear internal wave phase speed and 15%–40% for the nonlinear internal wave steepening parameter. The data, collected over a year from a through-the-column mooring, and code, implemented in the software package Stan, accompany the article. [ABSTRACT FROM AUTHOR]