## 1 Introduction

[2] Barrier coasts, covering about 10% of the world's coastline [*Glaeser*, 1978; *Stutz and Pilkey*, 2011], are densely populated areas subject to the potentially conflicting interests of economy, coastal safety, and ecology. They usually display a chain of barrier islands, separated by tidal inlets that connect a back-barrier basin to a sea or ocean [*De Swart and Zimmerman*, 2009]. Observations from mesotidal barrier coasts, e.g., the Wadden Sea [*Wolff*, 1986; *Oost and De Boer*, 1994] (see Figures 1a and 1b), Georgia Bight [*Hayes*, 1979, 1994; *Fitzgerald*, 1996], and Long Island [*Fitzgerald*, 1996], show that barrier island length generally decreases for increasing tidal range. Barrier island length is also observed to decrease for increasing lagoon area [*Stutz and Pilkey*, 2011; *Davis and Hayes*, 1984]. To reproduce and explain these relationships, we combine an empirical relationship for inlet dynamics with process-based modeling of the water motion.

[3] There are various empirical relationships describing tidal inlets [*LeConte*, 1905; *O'Brien*, 1931; *Escoffier*, 1940; *Bruun and Gerritsen*, 1959]. Recently, process-based support for these concepts has been provided by complex simulation models applied to single inlet systems [*Tung et al.*, 2009; *Nahon et al.*, 2012]. In this contribution, we use the stability concept by *Escoffier* [1940]. Based on a balance between wave-driven import and tide-driven export of sediment, he proposed an equilibrium condition *U*=*U*_{eq} for the ebb-tidal flow velocity amplitude *U* in the inlet (Figure 1c). If *U*>*U*_{eq}, the inlet erodes, if *U*<*U*_{eq}, it accretes, where *U*_{eq} is the equilibrium velocity. To determine the tidal flow velocity in the inlet, *Escoffier* [1940] applied a simple lumped-parameter model which assumes a spatially uniform surface elevation in the basin. The resulting closure curve (Figure 1c) displays one unstable and one stable equilibrium value of the inlet's cross-sectional area *A* (or no equilibrium at all if *U*<*U*_{eq}).

[4] Extending Escoffier's approach to two or more inlets draining a single basin, assuming a spatially uniform surface elevation, has shown that all systems are unstable [e.g., *Van de Kreeke*, 1990a, 1990b]. This implies that one inlet will remain open, whereas all other inlets close. As suggested by *Escoffier* [1977], accounting for spatial variations in the basin's surface level may lead to stable equilibria with more than one inlet open. For double inlet systems, this was recently confirmed using models in which these spatial variations were included either explicitly [*Van de Kreeke et al.*, 2008; *Brouwer et al.*, 2012b; *De Swart and Volp*, 2012] or parametrically [*Brouwer et al.*, 2012a].

[5] So far, there have been no model studies that explain the existence of stable barrier coasts with more than one inlet open, let alone the observed relationships in inlet spacing. To tackle this problem, we develop an exploratory morphodynamic model that simulates the dynamics of mesotidal barrier coasts with initially an arbitrary number of tidal inlets, while explicitly accounting for spatial variations in the tide levels in the back-barrier lagoon and in the ocean (section 2). The model results reveal the existence of stable equilibrium states with more than one inlet open, and the number of inlets depends on the tidal range and basin width (section 3). Both aspects of these results are then qualitatively explained from the physical mechanisms (section 4.1) and embedded in the observational literature (section 4.2). Finally, we present the conclusions (section 5).