Kai H. Christensen

Observation-based evaluation of surface wave effects on currents and trajectory forecasts

Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.

Evaluating Langmuir turbulence parameterizations in the ocean surface boundary layer

It is expected that surface gravity waves play an important role in the dynamics of the ocean surface boundary layer (OSBL), quantified with the turbulent Langmuir number ( La=u*/us0, where u* and us0 are the friction velocity and surface Stokes drift, respectively). However, simultaneous measurements of the OSBL dynamics along with accurate measurements of the wave and atmospheric forcing are lacking. Measurements of the turbulent dissipation rate ϵ were collected using the Air-Sea Interaction Profiler (ASIP), a freely rising microstructure profiler. Two definitions for the OSBL depth are used: the mixed layer derived from measurements of density (hρ), and the mixing layer (hϵ) determined from direct measurements of ϵ. When surface buoyancy forces are relatively small, ϵ∝La−2 only near the surface with no dependency on La at mid-depths of the OSBL when using hρ as the turbulent length scale. However, if hϵ is used then the dependence of ϵ with La−2 is more uniform throughout the OSBL. For relatively high destabilizing surface buoyancy forces, ϵ is proportional to the ratio of the OSBL depth against the Langmuir stability length LL. During destabilizing conditions, the mixed and mixing layer depths are nearly identical, but we have relatively few measurements under these conditions, rather than any physical implications. Observations of epsilon are compared with the OSBL regime diagram of Belcher et al. (2012) and are generally within an order of magnitude, but there is an improved agreement if hϵ is used as the turbulent length scale rather than hρ.

Measurement and modeling of oil slick transport

Transport characteristics of oil slicks are reported from a controlled release experiment conducted in the North Sea in June 2015, during which mineral oil emulsions of different volumetric oil fractions and a look-alike biogenic oil were released and allowed to develop naturally. The experiment used the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) to track slick location, size, and shape for ∼8 hours following release. Wind conditions during the exercise were at the high end of the range considered suitable for radar-based slick detection, but the slicks were easily detectable in all images acquired by the low noise, L-band imaging radar. The measurements are used to constrain the entrainment length and representative droplet radii for oil elements in simulations generated using the OpenOil advanced oil drift model. Simultaneously released drifters provide near-surface current estimates for the single biogenic release and one emulsion release, and are used to test model sensitivity to upper ocean currents and mixing. Results of the modeling reveal a distinct difference between the transport of the biogenic oil and the mineral oil emulsion, in particular in the vertical direction, with faster and deeper entrainment of significantly smaller droplets of the biogenic oil. The difference in depth profiles for the two types of oils is substantial, with most of the biogenic oil residing below depths of 10 m, compared to the majority of the emulsion remaining above 10 m depth. This difference was key to fitting the observed evolution of the two different types of slicks. This article is protected by copyright. All rights reserved.

A Quasi-Eulerian, Quasi-Lagrangian View of Surface-Wave-Induced Flow in the Ocean

Abstract In this study the influence of surface waves on the mean flow in an ocean of arbitrary depth is examined. The wave-induced forcing on the mean flow is obtained by integrating the Eulerian equations for mass and momentum balance from the bottom to an undulating material surface within the water column. By using the mean position of the material surface as the vertical coordinate, the authors obtain the depth dependence of the mean flow and the wave-induced forcing. Substitution of the vertical coordinate makes the model Lagrangian in the vertical direction. The model is Eulerian in the horizontal direction, allowing one to model the effects of a spatially nonuniform wave field or varying depth in a straightforward way.

Drift and deformation of oil slicks due to surface waves

We present a theoretical model for the wave-induced drift and horizontal deformation of an oil slick. The waves and the mean flow are coupled through the influence of the mean flow on the concentration of slick material, which in turn determines the damping rate of the waves and hence the transfer of momentum from the waves to the mean flow. We also briefly discuss a simplified version of the model that can be used when remote sensing data are available. With this simpler model the wave-induced forcing of the mean flow is obtained directly from observations of the wave field, hence knowledge of any specific slick properties is not required.

Transient and steady drift currents in waves damped by surfactants

In this paper we study the Lagrangian mean drift induced by spatially damped capillary-gravity waves on a surface covered by an elastic film. The analysis is developed with regard to a typical laboratory setup, and explicit solutions for both transient and steady horizontal drift velocities are given. We consider a situation where the film covers the entire surface and is prevented from drifting away, e.g., by a film barrier. The drift below an inextensible film resembles the drift under an ice cover, with a jetlike current in the wave propagation direction just below the surface. If the film is elastic the solution changes drastically. For certain values of the film elasticity parameter the mean flow is in the direction opposite to that of wave propagation in the upper part of the water column.

Note on Coriolis-Stokes force and energy

In this study, we consider the origin of the Coriolis-Stokes (CS) force in the wave-averaged momentum and energy equations and make a short analysis of possible energy input to the ocean circulation (i.e., Eulerian mean velocity) from the CS force. Essentially, we find that the CS force appears naturally when considering vertically integrated quantities and that the CS force will not provide any energy input into the system for this case. However, by including the “Hasselmann force”, we show some inconsistencies regarding the vertical structure of the CS force in the Eulerian framework and find that there is a distinct vertical structure of the energy input and that the net input strongly depends on whether the wave zone is included in the analysis or not. We therefore question the introduction of the “Hasselmann force” into the system of equations, as the CS force appears naturally in the vertically integrated equations or when Lagrangian vertical coordinates are used.

Stokes Drift in Internal Equatorial Kelvin Waves: Continuous Stratification versus Two-Layer Models

The Stokes drift in long internal equatorial Kelvin waves is investigated theoretically for an inviscid fluid of constant depth. While the Stokes drift in irrotational waves is positive everywhere in the fluid, that is, directed alongthe phase velocity, this is not always the case for internal Kelvin waves, which possess vorticity. For constant Brunt–V€€€ frequency, the Stokes drift in such waves is sinusoidal in the vertical with a negative value in the middle of the layer for the first baroclinic mode. For a pycnocline that is typical of the equatorial Pacific, this study finds for the first mode that the largest negative Stokes drift velocity occurs near the depth where the Brunt–V€€€ frequency has its maximum. Here, estimated drift values are found to be on thesame order ofmagnitudeas thoseobservedin thePacific Equatorial Undercurrent at the samelevel. In contrast,atwo-layermodelwithconstantdensityineachlayeryieldsapositiveStokesdriftinbothlayers.This contradicts the fact that, as shown in this paper, the vertically integrated Stokes drift (the Stokesflux) must be zero for arbitrary Brunt–V€€€ frequency.

Enhanced Turbulence Associated with the Diurnal Jet in the Ocean Surface Boundary Layer

AbstractDetailed observations of the diurnal jet, a surface intensification of the wind-driven current associated with the diurnal cycle of sea surface temperature (SST), were obtained during August and September 2012 in the subtropical Atlantic. A diurnal increase in SST of 0.2° to 0.5°C was observed, which corresponded to a diurnal jet of 0.15 m s−1. The increase in near-surface stratification limits the vertical diffusion of the wind stress, which in turn increases the near-surface shear. While the stratification decreased the turbulent dissipation rate e below the depth of the diurnal jet, there was an observed increase in e within the diurnal jet. The diurnal jet was observed to increase the near-surface shear by a factor of 5, which coincided with enhanced values of e. The diurnal evolution of the Richardson number, which is an indicator of shear instability, is less than 1, suggesting that shear instability may contribute to near-surface turbulence. While the increased stratification due to the diu...

Dispersive effects on wave-current interaction and vorticity transport in nearshore flows

Frequency dispersive effects on the interaction of waves and currents in a nearshore circulation system are analyzed. By means of both analytical and numerical calculations, we find that dispersive effects are important in the description of the correct amount of the wave forcing, represented, within the generalized-Lagrangian-mean-like approach, by the pseudomomentum p. They are particularly important when describing the flow using depth-averaged velocities. For some configurations, the depth-averaged current is forced not only by the nondispersive terms but also, with the same intensity, by the dispersive forcing terms. In such terms is included a vortex-force dispersive contribution, usually negligible in a small-wave amplitude approximation, which arises because of the presence of dissipative terms.