Estonian Journal of Earth Sciences, 2017, 66, 4, 238–255 https://doi.org/10.3176/earth.2017.20 The impact of seasonal changes in stratification on the dynamics of internal waves in the Sea of Okhotsk Oxana E. Kurkinaa, Tatyana G. Talipovaa,b, Tarmo Soomerec,d, Andrey A. Kurkina and Artem V. Rybina a Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 603950 Nizhny Novgorod, Russia b Institute of Applied Physics, 603950 Nizhny Novgorod, Russia c Department of Cybernetics, School of Science, Tallinn University of Technology, 12618 Tallinn, Estonia; [email protected] d Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn, Estonia Received 26 June 2017, accepted 7 August 2017, available online 28 November 2017 Abstract. The properties and dynamics of internal waves in the ocean crucially depend on the vertical structure of water masses. We present detailed analysis of the impact of spatial and seasonal variations in the density-driven stratification in the Sea of Okhotsk on the properties of the classic kinematic and nonlinear parameters of internal waves in this water body. The resulting maps of the phase speed of long internal waves and coefficients at various terms of the underlying Gardner’s equation make it possible to rapidly determine the main properties of internal solitary waves in the region and to choose an adequate set of parameters of the relevant numerical models. It is shown that the phase speed of long internal waves almost does not depend on the particular season. The coefficient at the quadratic term of the underlying evolution equation is predominantly negative in summer and winter and therefore internal solitons usually have negative polarity. Numerical simulations of the formation of internal solitons and solibores indicate that seasonal variations in the coefficient at the cubic term of Gardner’s equation lead to substantial variations in the shape of solibores. Key words: internal waves, stratification, internal solitons, Gardner’s equation, Sea of Okhotsk. INTRODUCTION Moum 2011). The presence of internal waves modifies the local field of water density and thus impacts the Internal waves are an intrinsic constituent of dynamics propagation regimes of acoustic waves through the of all stratified water bodies, having a particular role water masses (Warn-Varnas et al. 2009; Rutenko 2010). in the functioning of the entire ecosystem of seas and The main source of energy of internal waves in the oceans. They provide massive transport of energy over open ocean and in most of shelf seas is the tidal motion. large distances from their generation region to remote The parameters of internal waves generated, for example, and partially sheltered areas under favourable conditions. via the interaction of a tidal wave and bathymetry sub- Locally, they substantially contribute to the mixing of stantially depend on the vertical structure of water density water masses and resuspension and transport of bottom (local stratification) and the properties of currents in the sediment (Stastna & Lamb 2008; Reeder et al. 2011; wave generation and propagation area. While the field Bourgault et al. 2014). In this way internal waves greatly of currents often varies rapidly, changes in the stratifi- impact the distribution of nutrients, often markedly cation are usually slow but often extensive on a seasonal relocate patches of plankton in the water column and scale (Holloway et al. 1997). The intricacy of the entire thus play a crucial role in the formation of the biological phenomenon of internal waves and complexity of their productivity of seas and oceans (Vázquez et al. 2009; generation and impact have initiated many studies into Pan et al. 2012). their dynamics. These studies are largely targeted to the The propagation and breaking of internal waves is understanding of this phenomenon in shelf seas that often associated with the excitation of strong currents have large resources of oil and gas such as the South that serve as a major danger to deep-water engineering China Sea (Ramp et al. 2010; Liu et al. 2013; Alford et structures (Osborne 2010; Song et al. 2011; Stober & al. 2015; Xu et al. 2016). © 2017 Authors. This is an Open Access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International Licence (http://creativecommons.org/licenses/by/4.0). 238 O. E. Kurkina et al.: Dynamics of internal waves in the Sea of Okhotsk The options of analytical studies of internal waves In spite of severe climate and a location at are limited and the use of the relevant exact solutions comparatively high latitudes, the Sea of Okhotsk has for practical purposes is fairly complicated. For this a highly productive ecosystem and large fish stock. reason the use of numerical simulations of different Extensive reserves of gas and oil below the seabed properties of internal waves (e.g., the evaluation of make this basin an attractive location for various velocities of water parcels excited by the internal wave engineering activities. The fastest development occurs motion and associated impact on the underwater parts of in the nearshore of Sakhalin. While it is usually assumed engineering structures) is rapidly increasing (Kurkina & that harsh ice conditions, frequent storm winds and severe Talipova 2011; Si et al. 2012; Vlasenko & Stashchuk seas create the greatest danger to the drilling rigs and 2015; Kurkina et al. 2016). Such simulations of internal other constructions in the Arctic region (Petterssen 2011), waves of the lowest mode often rely on the classic the situation in the Sea of Okhotsk is even more weakly nonlinear models of the family of Korteweg– complicated because of the frequent presence of highly de Vries equations. A natural extension of this family energetic internal waves. There exist only a few contact towards taking into account the impact of spatially measurements of such structures in the shelf region of inhomogeneous stratification patterns leads to so-called the Sea of Okhotsk. The existing records indicate that Gardner’s equation (Holloway et al. 1997; Grimshaw et internal waves in this basin may have the appearance al. 2004, 2010; Talipova et al. 2014, 2015). of internal solitons with an amplitude of 5–15 m and The coefficients of this equation at a particular length of 200–400 m (Nagovitsyn & Pelinovsky 1988; location depend on the properties of stratification in this Nagovitsyn et al. 1991). However, numerous signatures location. A reliable implementation of models of this of single internal waves and various wave packets are type thus requires an adequate representation of the evident in satellite photos (Jackson 2004) in many horizontal variability in stratification along the wave regions of the Sea of Okhotsk, including the above- propagation direction. The relevant information is mentioned nearshore of Sakhalin. Similarly to the commonly extracted either from in situ measurements or situation in many other parts of the World Ocean, trains in a generalized form from contemporary hydrophysical of internal waves have often a shape of localized wave data bases and atlases such as the World Ocean Atlas or packets whereas their leading waves are often the largest Generalized Digital Environmental Model. These sources ones. As these trains frequently resemble combinations usually contain gridded monthly average vertical profiles of internal solitary waves and undular bores, we shall of salinity and temperature, from which one can derive call such trains solibores in what follows. The main the required vertical density profiles. This approach source of energy of internal waves is the barotropic tide. has been used for the analysis of the properties of Its motion gives rise to high-amplitude internal waves coefficients of Gardner’s equation and associated regimes once in every 12.4 h. This feature leads to a highly of the propagation of internal waves in many regions of periodic propagation pattern of internal waves in the Sea the World Ocean such as the Mediterranean Sea and the of Okhotsk. Black Sea (Ivanov et al. 1993; Kurkina et al. 2017а), In this paper we aim at the clarification of spatial several parts of the Arctic seas (Poloukhin et al. 2003; distributions of the basic parameters that govern the Polukhin et al. 2004), the Baltic Sea (Talipova et al. propagation regime and the resulting seasonal variations 1998; Kurkina et al. 2011) and the South China Sea in the main properties of internal waves in the Sea of (Grimshaw et al. 2010; Liao et al. 2014; Kurkina et al. Okhotsk. We employ a somewhat simplified approach 2017b). in order to derive estimates of limiting values of The Sea of Okhotsk (Zonn & Kostianoy 2009) is internal wave properties. For this purpose it is to a a marginal sea on the eastern shelf of the Eurasian first approximation acceptable to exclude the effect of continent (Fig. 1). Its several features are similar to the Earthʼs rotation and to avoid the calculation of the those of the Baltic Sea. It is separated from the western exact location of the internal wave generation from Pacific Ocean by the Kamchatka Peninsula in the east internal tides. and by the chain of Kuril Islands in the southeast. The These distributions reflect not only the geographic islands of Hokkaido and Sakhalin separate this water variability of the bathymetry and water masses of this body from the Sea of Japan. Its area (1 583 000 km2) basin but also mirror strong seasonal variations in the and mean depth (851 m) are much larger than the atmospheric and hydrographic features in the region. surface area and depth of the Baltic Sea. A voluminous These parameters are crucial for both detailed simulations discharge of the Amur River into the Sea of Okhotsk and express estimates of hydrodynamic loads to various results in the rise of the freezing point of the sea and in engineering structures in the study area.