Tom P. Rippeth

The Vertical Structure of Turbulent Dissipation in Shelf Seas

Abstract The free-fall FLY profiler has been used to determine the variation in energy dissipation ϵ in the water column over a tidal cycle at mixed and stratified sites in the Irish Sea. It was found that ϵ exhibits a strong M4 variation with a pronounced phase lag that increases with height above the bed. In mixed conditions this M4 signal, which extends throughout the water column, is reasonably well reproduced by turbulent closure models of the vertical exchange. In the summer stratified situation, the M4, signal in ϵ is confined to about 40 m above the seabed with phase delays of more than 4 h relative to the seabed. The lowest levels of dissipation (∼10−5 W m−3), measured in the pycnocline, are significantly above the system noise level and much higher than predicted by a model using the Mellor-Yamada level 2 closure scheme (MY2.0). However, when allowance is made for the diffusion of TKE, the model (MY2.2) simulates the depth-time distribution of dissipation in the stratified case satisfactorily if...

Comparing the performance of the Mellor‐Yamada and the κ‐ε two‐equation turbulence models

The aim of this paper is to systematically compare κ-e and Mellor-Yamada two-equation turbulence models. Both models include prognostic equations for turbulent kinetic energy and a length scale related parameter which are used to calculate eddy viscosities and vertical diffusivities. The results from laboratory experiments, using mixed and stratified flows, are simulated in order to systematically compare and calibrate the models. It is shown that the Monin-Obukhov similarity theory is well represented in both models. The models are used to simulate stratified tidal flow in the Irish Sea, and the results show that the κ-e models generally predict a larger phase lag between currents and turbulent dissipation, in the bottom boundary layer, than the Mellor-Yamada models. The comparison between the model results and field measurements, of the rate of dissipation of turbulent kinetic energy, shows that both models require modification through the inclusion of an internal wave parameterization in order that they are able to correctly predict the observed levels of turbulent dissipation. As the main result, it is shown that the choice of the stability functions, which are used as proportionality factors for calculating the eddy viscosity and diffusivity, has a stronger influence on the performance of the turbulence model than does the choice of length scale related equation.

The Cycle of Turbulent Dissipation in the Presence of Tidal Straining

In regions of large horizontal density gradient, tidal straining acts to produce a periodic component of stratification that interacts with turbulent mixing to control water column structure and flow. A 25-h series of measurements of the rate of dissipation of turbulent kinetic energy ( e) in the Liverpool Bay region of freshwater influence (ROFI) have revealed the form of this interaction and indicate substantial differences from regions where horizontal gradients are weak. In the ROFI system there is a pronounced difference between flood and ebb regimes. During the ebb the water column stratifies and strong dissipation is confined to the lower half of the water column. By contrast, during the flood, stratification is eroded with complete vertical mixing occurring at high water and high values of dissipation (3 mW m23) extending throughout the water column. The cycle of dissipation is therefore predominantly semidiurnal in the upper layers whereas, near the bottom boundary, the principal variation is at the M4 frequency as observed in regions of horizontal uniformity. Toward the end of the flood phase of the cycle, tidal straining produces instabilities in the water column that release additional energy for convective mixing. Confirmation of increased vertical motions throughout the water column during the late flood and at high water is provided by measurements of vertical velocity and the error velocity from a bottom-mounted acoustic Doppler current profiler.

Reynolds Stress and Turbulent Energy Production in a Tidal Channel

Abstract A high-frequency (1.2 MHz) acoustic Doppler current profiler (ADCP) moored on the seabed has been used to observe the mean and turbulent flow components in a narrow tidally energetic channel over six tidal cycles at neap and spring tides. The Reynolds stress has been estimated from the difference in variance between the along-beam velocities of opposing acoustic beams with a correction for the sampling scheme and bin size. Shear stress was found to vary regularly with the predominantly semidiurnal tidal flow with the stresses on the spring ebb flow (up to 4.5 Pa) being generally greater than on the flood flow (<2 Pa) when the currents are weaker. The vertical structure approximated to linear stress profiles decreasing from maximum values near the bed to almost zero stresses just below the surface. The variation in the bed stress was well represented by a quadratic drag law, based on the depth-mean current, with an estimated drag coefficient of 2.6 ± 0.2 × 10−3. The production of turbulent kinetic...

Impact of nonlinear waves on the dissipation of internal tidal energy at a shelf break

The vertical and temporal structure of the dissipation of turbulent kinetic energy within the internal tide at a location 5 km shoreward of the shelf break on the Malin Shelf has been determined using a combination of the free-falling light yo-yo profiler and acoustic doppler current profilers. Two distinct internal wave regimes were encountered: period I in which large-amplitude high-frequency nonlinear internal waves (NIWs) occurred (around neap tides) and period II in which the internal wave spectral continuum was not dominated by any particular frequency band (around spring tides). Empirical orthogonal function analysis shows that for the low-frequency waves, 76% of the variance was described by mode 1, rising to 95% for the high-frequency waves. During period I the dissipation and vertical mixing were characterized by the NIWs, and 70% of the dissipation occurred in the bottom boundary layer. During period II the depth-integrated dissipation was more evenly distributed throughout the tidal cycle, whereas vertical mixing was greatly enhanced during a single hour long episode of elevated thermocline dissipation coincident with weakened stratification. During both periods I and II ∼30% of the total measured dissipation occurred within the thermocline when averaged over 12.4 hours; the remainder occurred within the bottom boundary layer(BBL). Tidal average values for depth-integrated dissipation and vertical eddy diffusivity for period I (II) were 1.1×10−2 W m−2 (4.0×10−2 W m−2) and 5 cm2 s−1 (12 cm2 s−1), respectively. Decay rates and internal damping are discussed, and vertical heat fluxes are estimated. Observed dissipation rates are compared with a simple model for BBL dissipation.

A prescriptive model of stratification induced by freshwater runoff

Abstract Stratification induced by freshwater buoyancy input constitutes a key determinant of the environment both in estuaries and adjacent regions of freshwater influence (ROFIs). Predicting the development and breakdown of estuarine stratification is inherently more difficult than the prediction of thermal stratification because the buoyancy input is localized at the lateral boundaries rather than being uniformly distributed over the surface. The primary processes responsible for controlling water column stability have been identified in a previous paper (Simpson et al. , 1990 Estuaries 12 , 125–132) as (i) the estuarine circulation driven by horizontal density gradients, (ii) stirring by tidal and wind stresses and (iii) straining of the density field by tidal shear. These processes are incorporated in a prescriptive model of the time evolution of stratification which utilizes analytical solutions for the tidal and density current profiles, specifies the mixing in terms of energy conditions previously used in the heating-stirring models and assumes a horizontal density gradient which is invariant with depth. The behaviour of this simple model is described and compared with recent time series observations of the variability of stratification in a tidally energetic ROFI which indicate the presence of strong semi-diurnal and semi-monthly cycles in water column stability. The model reproduces the main qualitative features of the observations but is restricted as a predictive tool by the constant density gradient assumption and the omission of the interaction between the tidal- and density-driven flows. The inclusion of this latter interaction, which occurs via the frictional stresses and the control of eddy viscosity by stratification and the turbulent energy intensity, requires a dynamically active model which specifies the feedback processes in terms of an appropriate closure scheme.

Mixing in seasonally stratified shelf seas : a shifting paradigm

Although continental shelf seas make up a relatively small fraction (ca 7%) of the world oceans surface, they are thought to contribute significantly (20–50% of the total) to the open-ocean carbon dioxide storage through processes collectively known as the shelf sea pump. The global significance of these processes is determined by the vertical mixing, which drives the net CO2 drawdown (which can occur only in stratified water). In this paper, we focus on identifying the processes that are responsible for mixing across the thermocline in seasonally stratified shelf seas. We present evidence that shear instability and internal wave breaking are largely responsible for thermocline mixing, a clear development from the first-order paradigm for the water column structure in continental shelf seas. The levels of dissipation observed are quantitatively consistent with the observed dissipation rates of the internal tide and near-inertial oscillations. It is perhaps because these processes make such a small contribution to the total energy dissipated in shelf seas that they are not well represented in current state-of-the-art numerical models of continental shelf seas. The results thus present a clear challenge to oceanographic models.

Vertical mixing at intermediate depths in the Arctic boundary current

Microstructure and hydrographic observations, during September 2007 in the boundary current on the East Siberian continental slope, document upper ocean stratification and along-stream water mass changes. A thin warm surface layer overrides a shallow halocline characterized by a ~40-m thick temperature minimum layer beginning at ~30 m depth. Below the halocline, well-defined thermohaline diffusive staircases extended downwards to warm Atlantic Water intrusions found at 200-800 m depth. Observed turbulent eddy kinetic energy dissipations are extremely low (epsilon <10^-6 W m^-3), such that double diffusive convection dominates the vertical mixing in the upper-ocean. The diffusive convection heat fluxes F^dc_H ~1 W m^-2, are an order of magnitude too small to account for the observed along-stream cooling of the boundary current. Our results implicate circulation patterns and the influence of shelf waters in the evolution of the boundary current waters.

Microstructure of turbulence in the northern North Sea: a comparative study of observations and model simulations

Dissipation rate measurements in the northern North Sea from two independent observations are compared with various numerical models. The turbulence was characterised by tidal forcing in the bottom boundary layer and atmospheric forcing in the surface boundary layer. The observations were carried out by using free-falling profilers equipped with shear probes and fast CTD sensors. The models are based on Reynolds averaging and range from simple one-equation models to two-equation models with algebraic second-moment closures. Several error measures are applied for comparison of observations and model results. It is shown that the differences between the two observations are significantly larger than the equivalent measures between the model results. This is caused by the stochastic character of turbulent microstructure in connection with under-sampling, but also by the distance between the two observational sites, the movements of the vessels, instrument errors and so forth. The models on the other hand, although closed on different levels, are all based on the same assumptions and driven by the same external forcing, thus showing only relatively small differences between each other.

An investigation of internal mixing in a seasonally stratified shelf sea

The shelf sea seasonal thermocline is a critical interface within the marine environment, separating the euphotic zone from nutrient-rich deep water. Fluxes across the thermocline therefore represent a key biogeochemical pathway. In this paper we quantify the rate of mixing across the seasonal thermocline for a location in the Celtic Sea and investigate the processes responsible for driving thermocline fluxes. Profiles of the rate of dissipation of turbulent kinetic energy (e) show enhanced dissipation within the thermocline region (similar to 6 x 10(-5) W m(-3)). The diffusivity implied by these measurements is similar to 0.5 cm(2) s(-1), similar to previous shelf sea studies, and is sufficient to explain the observed warming of the deep water, suggesting that vertical mixing is the dominant control on water column structure. Two potential sources of mixing energy are identified, the internal tide and near-inertial waves. The mechanism of energy transfer from the candidate ! mixing mechanisms to turbulence is not clear. Thermocline dissipation rates were found to have no Richardson number dependence, but scaled positively with N-2 and S-2, in agreement with a previous turbulence parameterization. Application of this model to our data does a good job of capturing the mean characteristics of the observed heating flux across the thermocline, although none of the short-term fluctuations in mixing were reproduced