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Register a new userDo small swimmers mix the ocean?
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Added by
Alexander Leshansky
Publication date
2010
fields
Physics
and research's language is
English
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In this communication we address some hydrodynamic aspects of recently revisited drift mechanism of biogenic mixing in the ocean (Katija and Dabiri, Nature vol. 460, pp. 624-626, 2009). The relevance of the locomotion gait at various spatial scales with respect to the drift is discussed. A hydrodynamic scenario of the drift based on unsteady inertial propulsion, typical for most small marine organisms, is proposed. We estimate its effectiveness by taking into account interaction of a swimmer with the turbulent marine environment. Simple scaling arguments are derived to estimate the comparative role of drift-powered mixing with respect to the turbulence. The analysis indicates substantial biomixing effected by relatively small but numerous drifters, such as krill or jellyfish.
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We present a model describing evolution of the small-scale Navier-Stokes turbulence due to its stochastic distortions by much larger turbulent scales. This study is motivated by numerical findings (laval, 2001) that such interactions of separated scales play important role in turbulence intermittency. We introduce description of turbulence in terms of the moments of the k-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko, 2003). Working with the $k$-space moments allows to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the 2D turbulence shows that the energy cascade is scale invariant and Gaussian whereas the enstrophy cascade is intermittent. In 3D, we show that the statistics of turbulence wavepackets deviates from gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centered at its origin and having one large, one neutral and one small axes with the velocity field pointing parallel to the smallest axis.
In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal. The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic therma
A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.
Marine microorganisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies is that the time series of environmental cues in non-linear flow is complex, and that it depends on the decisions taken by the organism. One way of determining and evaluating optimal strategies is reinforcement learning. In a proof-of-principle study, Colabrese et al. [Phys. Rev. Lett. (2017)] used this method to find out how a micro-swimmer in a vortex flow can navigate towards the surface as quickly as possible, given a fixed swimming speed. The swimmer measured its instantaneous swimming direction and the local flow vorticity in the laboratory frame, and reacted to these cues by swimming either left, right, up, or down. However, usually a motile microorganism measures the local flow rather than global information, and it can only react in relation to the local flow, because in general it cannot access global information (such as up or down in the laboratory frame). Here we analyse optimal strategies with local signals and actions that do not refer to the laboratory frame. We demonstrate that symmetry-breaking is required in order to learn vertical migration in a meaningful way. Using reinforcement learning we analyse the emerging strategies for different sets of environmental cues that microorganisms are known to measure.
Early research in aerodynamics and biological propulsion was dramatically advanced by the analytical solutions of Theodorsen, von K{a}rm{a}n, Wu and others. While these classical solutions apply only to isolated swimmers, the flow interactions between multiple swimmers are relevant to many practical applications, including the schooling and flocking of animal collectives. In this work, we derive a class of solutions that describe the hydrodynamic interactions between an arbitrary number of swimmers in a two-dimensional inviscid fluid. Our approach is rooted in multiply-connected complex analysis and exploits several recent results. Specifically, the transcendental (Schottky-Klein) prime function serves as the basic building block to construct the appropriate conformal maps and leading-edge-suction functions, which allows us to solve the modified Schwarz problem that arises. As such, our solutions generalize classical thin aerofoil theory, specifically Wus waving-plate analysis, to the case of multiple swimmers. For the case of a pair of interacting swimmers, we develop an efficient numerical implementation that allows rapid computations of the forces on each swimmer. We investigate flow-mediated equilibria and find excellent agreement between our new solutions and previously reported experimental results. Our solutions recover and unify disparate results in the literature, thereby opening the door for future studies into the interactions between multiple swimmers.
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