Manhar R. Dhanak

Large-eddy simulations of the wind-induced turbulent Ekman layer

At urbulent Ekman layer created by a steady wind near the water surface is investigated using the numerical method of large-eddy simulations. The classical case of a flow unaffected by density stratification and surface waves is revisited to understand the internal structure of the flow and implications of the traditional assumptions of constant effective viscosity and the ‘f -plane’ approximation. A series of numerical experiments reveals that the Ekman solution needs correcting even in this case. The examination of the effective viscosity hypothesis confirms its validity but shows that the viscosity varies strongly with depth. It increases in the subsurface layer of thickness about 1/4 the turbulent length scale and decreases below this level. A Bessel function solution is proposed that corresponds to the approximate effective viscosity profile and matches with the LES results. Strong flow dependence on the latitude and wind direction is detected and explained by the effects of redistribution of turbulent kinetic energy between the velocity components and modification of the vertical transfer of turbulent momentum. In this paper, we consider the classical problem of a turbulent flow generated near the ocean surface by a steady wind stress in the presence of Earth’s rotation. Interest in this flow goes back to Ekman’s landmark work published in 1905. (An interesting historical review of Fridtjof Nansen’s polar expedition and other events preceding Ekman’s paper is given by Walker (1991).) Ekman assumed a balance between the Coriolis force, viscous friction and the pressure gradient, adopted the approximation of constant vertical eddy viscosity Az ,a ndderived a solution now known as the ‘Ekman spiral’. In the case of a steady wind in the x-direction, the steady-state Ekman velocity profile in the open ocean is (for the northern hemisphere) u = V0 cos π + π D z

On reduction of turbulent wall friction through spanwise wall oscillations

A model for turbulent skin friction, proposed by Orlandi & Jimenez, involving consideration of quasi-streamwise vortices in the cross-stream plane, is used to study the effect on the skin friction of oscillating the surface beneath the boundary layer in the spanwise direction. Using an exact solution of the Navier-Stokes equations, it is shown that the interaction between evolving, axially stretched, streamwise vortices and a modified Stokes layer on the oscillating surface beneath, leads to reduction in the skin friction, the Reynolds stress and the rate of production of kinetic energy, consistent with predictions based on experiments and direct numerical simulations

An Assessment of the Hydrokinetic Energy Resource of the Florida Current

Available ocean model and physically measured data from the Florida Current are analyzed to provide a detailed assessment of the hydrokinetic energy resource of the Florida Current, in support of harnessing a portion of it using ocean energy conversion devices. It has been estimated that approximately 25 GW of hydrokinetic power is available in the Florida Current. Fluctuations in this energy resource are described. Based on the analysis, realistic parameters governing where hydrokinetic energy extraction devices-turbines-may be ideally installed are discussed. An energy resource assessment methodology that has been developed is described. It can be used as a design tool for implementation of arrays of ocean energy extraction devices.

An AUV survey in the littoral zone: small-scale subsurface variability accompanying synoptic observations of surface currents

A survey of small-scale subsurface variability within the synoptic observational field of an ocean surface current radar (OSCR) using an autonomous underwater vehicle (AUV) is described. The survey involved observation of a developing upper mixed layer in a littoral zone off southeast Florida, on the edge of a strong Florida current during the summer of 1999. Complimentary in situ observations from a bottom-mounted acoustic Doppler current profiler (ADCP), conductivity-temperature (CT) chain arrays, atmospheric measurements from a surface buoy, and CTD and ADCP observations from a surface ship provided the background to the survey. The AUV, the Ocean Explorer, equipped with a CTD, downward and upward looking ADCPs, and a small-scale turbulence package, was used to conduct a continuous 12-h survey of small-to-fine-scale variability within a few grid cells of the surface current radar field. The vehicle repeatedly sampled the same grid in a set pattern at a fixed mid-water depth. Maps of developing spatial distribution of current, salinity, temperature, and rate of dissipation have been developed using the AUV-based observations. The observed features in the current field compare well with the OSCR and the bottom-mounted ADCP measurements.

The effects of freestream pressure gradient on a corner boundary layer

The incompressible boundary layer in the corner formed by two intersecting perpendicular semi-infinite planes is investigated; the freestream flow, aligned with the corner, is of the form x*n,x* representing the streamwise distance from the leading edge. Similarity-type asymptotic solutions for large Reynolds numbers are derived and it is found that solutions do not exist for all values of the parameter n, and that for values of n where solutions do exist, non-uniqueness is a common feature; previous theoretical work has focused almost exclusively on the Blasius–type far field, corresponding to one of the

Dynamics-aware target following for an autonomous surface vehicle operating under COLREGs in civilian traffic

n=0

An Autonomous Ocean Turbulence Measurement Platform

solutions. One corollary of the study is that in the case of a boundary–layer flow over a flat plate with a distant bounding wall (or other crossflow irregularity) and zero streamwise pressure gradient, in addition to the distant flow taking the form of the Blasius similarity solution, a second similarity solution also exists, exhibiting a sizeable jet-like crossflow velocity component. The present work may help partly explain some of the difficulties reported in observing corner similarity–type flows experimentally. The question of asymmetrical solutions is also alluded to. A study is also made regarding the nature of the linear local stabilityof the corner flow, and this indicates that the flow becomes more stable with increasing positive values of n, and less stable with increasing negative values of n. Further, the critical Reynolds number for the local flow increases with increasing distance from the corner.

Non-similarity solutions to the corner boundary-layer equations (and the effects of wall transpiration)

We present a model-predictive trajectory planning algorithm for following a target boat by an autonomous unmanned surface vehicle (USV) in an environment with static obstacle regions and civilian boats. The planner developed in this work is capable of making a balanced trade-off among the following, possibly conflicting criteria: the risk of losing the target boat, trajectory length, risk of collision with obstacles, violation of the Coast Guard Collision Regulations (COLREGs), also known as “rules of the road”, and execution of avoidance maneuvers against vessels that do not follow the rules. The planner addresses these criteria by combining a search for a dynamically feasible trajectory to a suitable pose behind the target boat in 4D state space, forming a time-extended lattice, and reactive planning that tracks this trajectory using control actions that respect the USV dynamics and are compliant with COLREGs. The reactive part of the planner represents a generalization of the velocity obstacles paradigm by computing obstacles in the control space using a system-identified, dynamic model of the USV as well as worst-case and probabilistic predictive motion models of other vessels. We present simulation and experimental results using an autonomous unmanned surface vehicle platform and a human-driven vessel to demonstrate that the planner is capable of fulfilling the above mentioned criteria.

Experimental Evaluation of Approach Behavior for Autonomous Surface Vehicles

Abstract The use of a small autonomous underwater vehicle (AUV) as a platform for making in situ flow measurements in the ocean environment is described. Two high-wavenumber shear probes and a dynamic Pitot tube, housed in a pressure vessel mounted on the nose of the AUV, allow measurements, in the dissipation range, of all three components of velocity. Microstructure temperature and possible body vibrations are monitored using auxiliary local probes. A conductivity–temperature–depth package, an acoustic Doppler current profiler, and a Marsh–McBirney current meter on board allow measurement of mean background conditions. Gathered data are stored on an onboard computer. The AUV can survey 7–11-km regions at a speed of 1.5–2 m s−1, its motion being uncoupled from that of any surface mother ship. The vehicle has relatively low manufacture and operational costs and can potentially operate in stormy conditions. The small-scale measurements allow the determination of estimates of in situ energy dissipation rate...

On the instability of flow in a streamwise corner

The incompressible boundary layer in the corner formed by two intersecting, semiinfinite planes is investigated, when the free-stream flow, aligned with the corner, is taken to be of the form U∞F(x), x representing the non-dimensional streamwise distance from the leading edge. In Dhanak & Duck similarity solutions for F(x) = x n were considered, and it was found that solutions exist for only a range of values of n, whilst for ∞ > n > -0.018, approximately, two solutions exist. We extend the work of Dhanak & Duck to the case of non-90° corner angles and allow for streamwise development of solutions. In addition, the effect of transpiration at the walls of the corner is investigated. The governing equations are of boundary-layer type and as such are parabolic in nature. Crucially, although the leading-order pressure term is known a priori, the third-order pressure term is not, but this is nonetheless present in the leading-order governing equations, together with the transverse and crossflow viscous terms. Particular attention is paid to flows which develop spatially from similarity solutions. It turns out that two scenarios are possible. In some cases the problem may be treated in the usual parabolic sense, with standard numerical marching procedures being entirely appropriate