Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that removes the need for any commonly used approximations. This is accomplished by augmenting the state vector of the prognostic variables with the Lagrangian drifter coordinates at assimilation. It is shown that this method is best formulated using the ensemble Kalman filter, resulting in an algorithm that is essentially transparent for assimilating Lagrangian data. The method is tested using a set of twin experiments on the shallow-water system of equations for an unsteady double-gyre flow configuration. Numerical simulations show that this method is capable of correcting the flow even if the assimilation time interval is of the order of the Lagrangian autocorrelation time scale (TL) of the flow. These results clearly demonstrate the benefits of this method over other techniques that require assimilation times of 20%–50% of TL, a direct consequence of the approximations introduced in assimilating their Lagrangian data. Detailed parametric studies show that this method is particularly effective if the classical ideas of localization developed for the ensemble Kalman filter are extended to the Lagrangian formulation used here. The method that has been developed, therefore, provides an approach that allows one to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.

We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment. DOI: 10.1103/PhysRevLett.118.144503 Rogue waves are rare events of exceptional height that may surge without warnings [1][2][3][4]. This peculiar phenomenon is ubiquitous. It has been observed in different contexts such as gravity and capillary waves [5][6][7][8][9][10], optical fibers [11][12][13][14][15][16][17][18][19], superfluid helium [20], and plasmas [21,22]. Because of their universal and potentially detrimental nature, there is a pressing need to understand their physics in order to predict and control them.The generating mechanisms can be disparate [23]. These include the spatiotemporal linear focusing of wave energy [24,25], the focusing due to bathymetry and currents (see, e.g., [26][27][28]), and the self-focusing that results from the Benjamin-Feir instability [29]. The latter is described by exact breather solutions of the nonlinear Schrödinger (NLS) equation [30], which are coherent structures that oscillate in space and/or time. Interestingly enough, breathers can also exist embedded in random waves [31]. Provided that the ratio of the dominant wave steepness to the spectral bandwidth is Oð1Þ and propagation is unidirectional, large amplitude structures can occur often enough to originate strong deviations from Gaussian statistics [6,15,[31][32][33]. Therefore, breathers have been considered in various fields of physics as a plausible prototype of rogue waves.Such solutions have been reproduced experimentally in wave tanks using prescribed boundary conditions at the wave maker [8]. Indeed, the standard form of the NLS equation describes the nonlinear dynamics of a preexisting (initial) wave field, which propagates without gaining or losing energy. This framework, however, is not transferable in a straightforward manner to systems driven by external forcing. The most obvious example of such a context is the ocean, where the oscillatory motion of the water surface is generated by the forcing of local wind (the resulting wave field is generally known as wind sea). Waves then grow with fetch and/or time until a quasistationary condition is reached, i.e., a fully developed sea [34]. Experimental work in wave tanks where waves are generated only by winds have been reported in the past;...

We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings.

We study the relaxation of a two-dimensional (2D) ultracold Bose gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large-scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Poisson-Boltzmann equation. The results allow us to characterize the spectral energy condensate in a 2D quantum fluid that bears striking similarity to similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum