George S. Triantafyllou

Wake mechanics for thrust generation in oscillating foils

Foils oscillating transversely to an oncoming uniform flow produce, under certain conditions, thrust. It is shown through experimental data from flapping foils and data from fish observation that thrust develops through the formation of a reverse von Karman street whose preferred Strouhal number is between 0.25 and 0.35, and that optimal foil efficiency is achieved within this Strouhal range.

THREE-DIMENSIONAL DYNAMICS AND TRANSITION TO TURBULENCE IN THE WAKE OF BLUFF OBJECTS

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments. Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

Frequency selection and asymptotic states in laminar wakes

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately. It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

Active vorticity control in a shear flow using a flapping foil

It is shown experimentally that free shear flows can be substantially altered through direct control of the large coherent vortices present in the flow. First, flow-visualization experiments are conducted in Kalliroscope fluid at Reynolds number 550. A foil is placed in the wake of a D-section cylinder, sufficiently far behind the cylinder so that it does not interfere with the vortex formation process. The foil performs a heaving and pitching oscillation at a frequency close to the Strouhal frequency of the cylinder, while cylinder and foil also move forward at constant speed. By varying the phase of the foil oscillation, three basic interaction modes are identified

Efficient Foil Propulsion Through Vortex Control

We investigate the problem of a heaving and pitching hydrofoil in an inflow that consists of a uniform velocity field and a staggered array of vortices. The foil can exploit the energy in such a Karman vortex street for efficient propulsion of animals or submarines. Through a two-dimensional inviscid analysis, we find that the phase between foil motion and the arrival of inflow vortices is a critical parameter. Everything else being equal, the highest efficiency is seen when this phase is such that the foil moves in close proximity to the oncoming vortices. Different modes of vortex interaction in the wake results from a variation in this phase, and we show that the flow downstream of the foil is related to the foil input power.

On the formation of vortex streets behind stationary cylinders

The formation of vortex streets behind stationary cylinders is found to be caused by an absolute instability in the wake immediately behind the cylinder. The inviscid Orr–Sommerfeld equation is used together with measured profiles at Reynolds numbers of ( a ) Re = 56 when the absolute instability provides a Strouhal number of 0.13; and ( b ) Re = 140000 providing a Strouhal number of 0.21, both in agreement with experimental values. At the subcritical Re = 34 the instability is of the convective type; i.e. the disturbance decays, being convected away once the external disturbance is removed, in agreement with experimental observations. Finally, the instability of the mode which causes a symmetric array of vortices is shown to be always of the convective type.

A New Approximate Solution of the Optimal Nonlinear Filter for Data Assimilation in Meteorology and Oceanography

This paper introduces a new approximate solution of the optimal nonlinear filter suitable for nonlinear oceanic and atmospheric data assimilation problems. The method is based on a local linearization in a low-rank kernel representation of the states probability density function. In the resulting low-rank kernel particle Kalman (LRKPK) filter, the standard (weight type) particle filter correction is complemented by a Kalman-type correction for each particle using the covariance matrix of the kernel mixture. The LRKPK filters solution is then obtained as the weighted average of several low-rank square root Kalman filters operating in parallel. The Kalman-type correction reduces the risk of ensemble degeneracy, which enables the filter to efficiently operate with fewer particles than the particle filter. Combined with the low-rank approximation, it allows the implementation of the LRKPK filter with high-dimensional oceanic and atmospheric systems. The new filter is described and its relevance demonstrated through applications with the simple Lorenz model and a realistic configuration of the Princeton Ocean Model (POM) in the Mediterranean Sea.

Modelling the spatial and temporal variability of the Cretan Sea ecosystem

Abstract The ecosystem function of the oligotrophic Cretan Sea is explored through the development and application of a 3D ecological model. The simulation system comprises of two on-line coupled submodels: the 3D Princeton Ocean Model (POM) and the 1D European Regional Seas Ecosystem Model (ERSEM) adapted to the Cretan Sea. For the tuning and initialisation of the ecosystem parameters, the 1D version of the biogeochemical model is used. After a model spin up period of 10 years to reach a quasi-steady state, the results from an annual simulation are presented. A cost function is used as validation method for the comparison of model results with field data. The estimated annual primary and bacteria production are found to be in the range of the reported values. Simulation results are in good agreement with in situ data illustrating the role of the physical processes in determining the evolution and variability of the ecosystem.

A singular evolutive interpolated Kalman filter for efficient data assimilation in a 3-D complex physical-biogeochemical model of the Cretan Sea

A singular evolutive interpolated Kalman (SEIK) filter is used to assimilate pseudo-observations via twin simulation experiments in a complex three-dimensional coupled physical–biogeochemical model of the Cretan Sea. The simulation system comprises two on-line coupled sub-models: the three-dimensional Princeton Model and the European Regional Seas Ecosystem Model (ERSEM). In the SEIK filter, the estimation error is represented by an ensemble of state vectors, which are drawn randomly at every filtering step. In the twin experiments performed the predictions of the coupled model were corrected every 2 days using synthetic measurements extracted from a model reference run according to a network of 23 stations in the Cretan Sea. The filter is shown to be very efficient, with the assimilation results exhibiting a continuous decrease of the estimation error during the experimental period. D 2003 Elsevier Science B.V. All rights reserved.

Interaction of two‐dimensional separated flows with a free surface at low Froude numbers

It is shown that the low Froude number wake of floating two‐dimensional objects is convectively unstable. This is shown to be true for bluff objects, like a circular cylinder, and for streamlined objects, like a thin airfoil. As a result, the wake behind a floating object remains steady, even at high Reynolds numbers, characterized by a long region of recirculating flow. It is concluded that the presence of the free surface has a stabilizing effect at low Froude numbers, suppressing the unsteadiness of the wake. The structure of the dispersion relation, shows that, at low Froude numbers, a short wavelength interaction between the wake instability and ambient waves is possible in the form of a spatially growing response.