Modulational instability in periodic quadratic nonlinear materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.Comment: 4 pages, 7 figures corrected minor misprint

Advection and diffusion in random media: implications for sea surface temperature anomalies

The book presents the foundations of the theory of turbulent transport within the context of stochastic partial differential equations. It serves to establish a firm connection between rigorous and non-rigorous results concerning turbulent diffusion. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: stochastic advection-diffusion (transport) equation. There is no attempt made to derive universal statistics for turbulent flow. Instead emphasis is placed on a statistical description of a passive scalar (tracer) under given velocity statistics. An application concerning transport of sea surface temperature anomalies reconciles the developed theory and a highly practical issue of modern physical oceanography by using the newly designed inversion techniques which take advantage of powerful maximum likelihood and autoregressive estimators. Audience: Graduate students and researchers in mathematics, fluid dynamics, and physical oceanography

Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

This paper is concerned with the analysis of the long-term regular time series of current velocity and conductivity, temperature, and depth (CTD) profiles, measured with the moored autonomous profiler Aqualog over the upper part of the continental slope at a fixed geographical location in the Northeastern Black Sea. This study focuses on the fine structure of the density profiles to show that the fine-structure Cox number (C) is a power function of the Richardson number (Ri). A similar inverse power relationship with the same exponent was found earlier for the coefficient of vertical turbulent mass exchange (Kρ) and Ri. Based on those results, the analysis indicated a statistically significant correlation between C and Kρ, which suggests that the estimations of Kρ could be conducted from the CTD data only

Laboratory Study of Turbulent Mass Exchange in a Stratified Fluid

In this study, a laboratory experiment was conducted to investigate quantitatively turbulent exchange between two quasi-homogeneous layers of equal thickness and different density (salinity), as well as the fine structure of the density transition zone (interface) between the layers. The fluid was continuously stirred by a system of horizontally oscillating vertical rods, piercing through both layers and producing vertically homogeneous turbulent impact in a two-layered fluid. In every experimental run, the stirring process was carried out continuously from certain initial state up to the complete mixing of the layers. The buoyancy flux between the layers was estimated using the data on time changes of the salinity in both upper and lower layers. The fine structure of density interface was measured by vertically profiling conductivity microprobe. The results were presented in a dimensionless form and analyzed depending on two dimensionless parameters as follows: the Richardson number, Ri, and Reynolds number, Re. It was found that if Ri>Ri∗Re where Ri∗ is the critical Richardson number, the interface exists in “sharpening” mode and in “eroding” (diffusive) mode if RiRi∗Re. The maximum mixing efficiency was achieved at critical Richardson number, when the density interface was in a transition state between the sharpening and diffusive modes

Automated Tethered Profiler for Hydrophysical and Bio-Optical Measurements in the Black Sea Carbon Observational Site

Special Issue Technological Oceanography.-- 17 pages, 13 figurese.g., daily thermocline, variation in solar irradiance, thermohaline convection, and intermittent mixing. These processes should be regularly observed with sufficient time resolution at fixed geographical locations. This study provides a brief overview of the carbon observational site in the Northeastern Black Sea. The focus is on the design of a new tethered profiler Winchi for the inner continental shelf part of the site. The profiler hull and two outriggers comprise an open trimaran platform that is positively buoyant and tends to maintain a horizontal position in the water. The lower end of the winch wire is secured to the bottom anchor. By unwinding/winding the wire, the profiler ascends/descends while measuring the depth profiles of marine environment parameters ranging from the seafloor to air–sea interface. After surfacing, the profiler determines its location using the Global Positioning System (GPS) and transmits data to (and from) a server on land through the Global System for Mobile Communications (GSM). Initial field tests with the Winchi profiler at the Northeastern Black Sea shelf exhibited promising results. We report these early tests to demonstrate the use of WinchiThe research and development of the new tethered profiler Winchi was carried out within the framework of the assignment of the Ministry of Science and Higher Education of Russia No 0128-2021-0018 and supported in part by the Russian Fund for Basic Research via grant No 19-05-00459With the institutional support of the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000928-S)Peer reviewe

Combinatorial distance geometry in normed spaces

We survey problems and results from combinatorial geometry in normed spaces, concentrating on problems that involve distances. These include various properties of unit-distance graphs, minimum-distance graphs, diameter graphs, as well as minimum spanning trees and Steiner minimum trees. In particular, we discuss translative kissing (or Hadwiger) numbers, equilateral sets, and the Borsuk problem in normed spaces. We show how to use the angular measure of Peter Brass to prove various statements about Hadwiger and blocking numbers of convex bodies in the plane, including some new results. We also include some new results on thin cones and their application to distinct distances and other combinatorial problems for normed spaces