What happens with the Ekman current under constant wind?

2021 ◽  
Author(s):  
Victor Shrira ◽  
Rema Almelah
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Wind Waves ◽  
Time Dependent ◽  
Stokes Drift ◽  
Large Time Asymptotics ◽  
Time Asymptotics ◽  
Field Evolution ◽  
Self Similar ◽  
Ekman Current

<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>

Large-time evolution of statistical moments of wind–wave fields

2013 ◽  
Vol 726 ◽  
pp. 517-546 ◽  
Author(s):  
Sergei Y. Annenkov ◽  
Victor I. Shrira
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Random Wave ◽  
Wave Spectra ◽  
Large Time Asymptotics ◽  
Wave Fields ◽  
Weakly Nonlinear ◽  
Time Asymptotics ◽  
Random Wave Field ◽  
Skewness And Kurtosis

AbstractWe study the long-term evolution of weakly nonlinear random gravity water wave fields developing with and without wind forcing. The focus of the work is on deriving, from first principles, the evolution of the departure of the field statistics from Gaussianity. Higher-order statistical moments of elevation (skewness and kurtosis) are used as a measure of this departure. Non-Gaussianity of a weakly nonlinear random wave field has two components. The first is due to nonlinear wave–wave interactions. We refer to this component as ‘dynamic’, since it is linked to wave field evolution. The other component is due to bound harmonics. It is non-zero for every wave field with finite amplitude, contributes both to skewness and kurtosis of gravity water waves and can be determined entirely from the instantaneous spectrum of surface elevation. The key result of the work, supported both by direct numerical simulation (DNS) and by the analysis of simulated and experimental (JONSWAP) spectra, is that in generic situations of a broadband random wave field the dynamic contribution to kurtosis is small in absolute value, and negligibly small compared with the bound harmonics component. Therefore, the latter dominates, and both skewness and kurtosis can be obtained directly from the instantaneous wave spectra. Thus, the departure of evolving wave fields from Gaussianity can be obtained from evolving wave spectra, complementing the capability of forecasting spectra and capitalizing on the existing methodology. We find that both skewness and kurtosis are significant for typical oceanic waves; the non-zero positive kurtosis implies a tangible increase of freak wave probability. For random wave fields generated by steady or slowly varying wind and for swell the derived large-time asymptotics of skewness and kurtosis predict power law decay of the moments. The exponents of these laws are determined by the degree of homogeneity of the interaction coefficients. For all self-similar regimes the kurtosis decays twice as fast as the skewness. These formulae complement the known large-time asymptotics for spectral evolution prescribed by the Hasselmann equation. The results are verified by the DNS of random wave fields based on the Zakharov equation. The predicted asymptotic behaviour is shown to be very robust: it holds both for steady and gusty winds.

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

2019 ◽  
Vol 7 (3) ◽  
pp. 293-305 ◽  
Author(s):  
Yakir Aharonov ◽  
Jussi Behrndt ◽  
Fabrizio Colombo ◽  
Peter Schlosser
Keyword(s):  
Entire Function ◽  
Initial Data ◽  
Plane Wave ◽  
Large Time ◽  
Main Tool ◽  
Time Dependent ◽  
Convolution Operators ◽  
Compact Sets ◽  
Large Time Asymptotics ◽  
Time Asymptotics

AbstractIn 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.

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