**1. Introduction**

The nearshore environments of mild-sloped sandy beaches are often characterized by the presence of a variety of morphological features, as most common are sand bars. Typically, they are shore-parallel, crescentic or irregular shoals [1]. Sand bars are often found at depths less than 10 m and within or just seaward of the surf zone, whose width is influenced by variations in the incident wave climate. Over the years, many mechanisms have been proposed to explain bar formation [2], which eventually were placed into three main groups [3]: breakpoint-related mechanisms [4,5], infra-gravity wave-related mechanisms [6,7] and self-organizational mechanisms [8,9]. The presence of sand bars in the coastal zone is of significant importance for sandy beach morphodynamics since they act as a storage of sediments and as a natural protection by dissipating high wave energy during storms by breaking, thus limiting coastal erosion and flooding hazards [10,11]. These morphological features may exert a significant impact on the nearshore hydrodynamics due to their cross-shore and long-shore geometry and location [12,13]. Moreover, studying the sand bar dynamics allows identification of important physical processes that control coastal evolution, and thus enrich the understanding and knowledge about sediment transport in the coastal zone [14].

**Citation:** Andreeva, N.; Saprykina, Y.; Valchev, N.; Eftimova, P.; Kuznetsov, S. Influence of Wave Climate on Intra and Inter-Annual Nearshore Bar Dynamics for a Sandy Beach. *Geosciences* **2021**, *11*, 206. https://doi.org/10.3390/ geosciences11050206

Academic Editors: Jesus Martinez-Frias and Gianluigi Di Paola

Received: 16 February 2021 Accepted: 5 May 2021 Published: 8 May 2021

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Nearshore bathymetry varies on a spectrum of time scales ranging from inter-annual (longer than a year) to intra-annual (equal to or shorter than 1 year). Intra-annual time scales include the seasonal cycle and shorter fluctuations associated with passing storms and weak to calm wave conditions [1]. The strong seasonal variability of wind and wave climate drives sandy beaches to exhibit strong seasonal morphodynamic cycles [15]. They are associated with sediments being eroded from the foreshore during high waves, forming storm or winter beach profile [16] followed by recovery during lower energy conditions (swell or summer profile). Typically, these seasonal cycles in beach morphodynamics are reflected in the submerged beach profile with "sandbars building and migrating offshore during storm conditions, and deflating and migrating onshore during low-energy swell conditions" [15]. Cross-shore sand bar migration, resulting in beach profile changes is associated with "imbalance between the cross-shore sediment transport driven by wave non-linearities (orbital velocity skewness and asymmetry), undertow and the gravitational downslope effects" [17]. The offshore sandbar migration is attributed to breaking of large storm waves over the bar with a dominant offshore bed return flow-induced sediment transport. On the other hand, its slow onshore migration takes place in between storms due to a dominant onshore sand transport driven by wave non-linearities during weakly to non-breaking wave regimes across the bar [17,18]. Meanwhile, frequent changes in wave intensity may exert minor bar displacements reflecting its relative stability in the nearshore zone [19]. In the last decades the seasonal sandbar migration has been studied using in situ measurements and numerical modeling in [15,20–25]. Despite that, the nearshore morphological evolution on seasonal time scales is still poorly understood since field observations have been limited due to difficulties and expense of working in nearshore environments [15,23]. Over the years, nearshore morphodynamics on different coastal stretches along the Bulgarian Black Sea coast has been investigated via field measurements and numerical simulations. On inter-annual time scale in [26,27], on seasonal and monthly basis in [28,29], and due to individual storms in [30–35].

The inter-annual variability of sand bar migration has not been sufficiently studied due to lack of long-term continuous field observations in various coastal environments. At present, sand bar migration is much better investigated and understood at the mediumterm time spans, i.e., less than 10 years. It is reported that there are migration cycles (return periods) of about 3–4 years [11,36] and 2–5 years [37]. It is assumed that the decrease of the return period is associated with more energetic wave conditions [36]. According to an analysis of bathymetric data collected for 30 years on the Terschelling coast the long-term evolution of sand bars has characteristic stages: generation, seaward migration and decay, and this cycle has periods up to 10–20 years [38]. Investigations of long-term bar behavior based on nearshore profiles' measurements performed for nearly 30 years along the Holland coast have revealed strong alongshore bar variability [39]. Regions of homogeneous Large-Scale Coastal Behavior (LSCB-regions) controlled by different hydrodynamics, or sediment and morphological structure were selected. The length sizes of the LSCB-regions are from 5 km up to 42 km. The change between LSCB-regions occurs sharply at distances shorter than 2 km. Such alongshore variability also does not allow determination of clear patterns of long-term variability trends on barred shores. In the model proposed in [40] a short-term (months) dynamical processes in the coastal zone are used to predict medium-term bar displacements. The model reproduces well enough the seaward bar migration, but do not explain bar generation stage, because of the influence of wave climate on the medium-term bar migration and because the nearshore sediment transport is not completely understood.

The first study that has associated the sand bar migration with changes in the climatic indices (the North Atlantic Oscillation in particular) is [41]. They confirmed the existence of such connection based on 15-year time series of Argus video images on the evolution of the submerged profile in the Perranporth beach. In [42], on the example of the Black Sea, it was shown that coastal wave climate is rather heterogeneous and different parts of the coast can correlate in a different manner with variations in the climatic indices, i.e., having

different periods of long-term fluctuations. This can also cause heterogeneous variability in the bar's migration along the coast.

Thus, the primary objective of the study is to investigate inter- and intra-annual cross-shore outer bar migration and their dependence on the regional wave climate on the example of an open-coast non-tidal beach at the western Black Sea coast. Description of the study site is given in Section 2. Section 3 introduces data sets of beach profile field measurements (Section 3.1), numerically modeled wave forcing (Section 3.2) and their statistical processing. Results are discussed in Section 4. Section 4.1 presents examination of the intra-annual bar evolution on the grounds of variability of wave forcing and nonlinearity, storms and direction of wave incidence. Section 4.2 explores the inter-annual bar evolution and reveals main periods of its middle and long-term variability due to changes in the main climatic indices affecting the wave climate of the coastal region under consideration. The conclusions follow in Section 5.
