What happens with the Ekman current under constant wind?

<p>The work examines the Ekman current  response to a steady<br>wind within the Stokes-Ekman paradigm. Under constant wind<br>in the classical Ekman model there is a single attractor<br>corresponding to the Ekman (1905)steady solution. It is<br>known that the account of wind waves  strongly affects the<br>Ekman current dynamics via the Stokes drift, which is<br>described by the Stokes-Ekman  model. Waves continue to<br>evolve even under constant wind, which makes  steady<br>solutions of the Stokes-Ekman equation impossible. Since<br>the dynamics of the Ekman response in the presence of<br>evolving wave field have not been considered,  the basic<br>questions on how  the Ekman current evolves and,<br>especially, whether it grows or decays at large times,<br>remain open.</p><p>Here by employing the known self-similar laws of wave<br>field evolution and  solving analytically the<br>the Stokes-Ekman equation we  find and analyse<br>evolution of the Ekman current. We show that the system has<br>a single time dependent attractor which can be described<br>asymptotically. The large time asymptotics of the Ekman<br>current is found to be determined by the regime of wave<br>field evolution:  for the regimes typical of young waves<br> the Ekman current grows with time to infinity, in contrast, for<br>`old waves'  the Ekman current asymptotically decays.</p><p> </p>

Schrödinger evolution of superoscillations with $$\delta $$- and $$\delta '$$-potentials

In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space $$A_1(\mathbb {C})$$ A 1 ( C ) . Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under $$\delta $$ δ - and $$\delta '$$ δ ′ -potentials.