Insight into the origin of hummocky cross-stratification (HCS): the role of internal waves (IWs)

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1 Insight into the origin of hummocky cross-stratification (HCS): the role of internal waves (IWs) Journal: Terra Nova Manuscript ID: Draft Wiley - Manuscript type: Review Article Date Submitted by the Author: n/a Complete List of Authors: Morsilli, Michele; Università di Ferrara, Scienze della Terra Pomar, Luis; Universitat de les Illes Balears, Ciencies de la Terra Keywords: Hummocky cross-stratification, Internal waves, sedimentary structures, gravity waves, internalites

2 Page 1 of 40 For Review Only Insight into the origin of hummocky cross-stratification (HCS): the role of internal waves (IWs) Michele Morsilli* & Luis Pomar** * Dipartimento di Scienze della Terra, Università di Ferrara, Via G. Saragat 1, Ferrara, Italy ** Departament de Ciencies de la Terra, Universitat de les Illes Balears, Ctra. Valldemossa km 7.5, Palma de Mallorca, Spain Corresponding author: Michele Morsilli Dipartimento di Scienze della Terra, Università di Ferrara, Via G. Saragat 1, Ferrara, Italy. Tel ; Fax ; mrh@unife.it Running head: Hummocky cross-stratification formed by internal waves Abstract Hummocky cross-stratification (HCS) is considered diagnostic of surface storm activity at the shoreface-offshore transition. However, the origin of HCS is still debated. Laboratory experiments have not yet reproduced it nor direct observations on the continental shelves exist. Most hydrodynamic interpretations invoke pure-oscillatory flows, unidirectionaldominated combined flows and oscillatory-dominated flows, but all them share the assumption of HCS to reflect the combined action of surface storm waves and related currents. Within this context of uncertainties internal waves (IWs), gravity waves propagating along the pycnocline, provide an alternative mechanism to explain the origin of HCS. IWs breaking

3 Page 2 of 40 on the shelf create episodic high-turbulence events and induce upslope- and downslope currents as well as oscillatory flows, at the depth where the pycnocline intersects the sea floor. In this scenario, both the oscillatory- and the unidirectional components needed for HCS to form are not necessarily linked to surface storms, but can occur at various depth in relation to the position of the pycnoclines. Introduction Since its definition by Harms et al. (1975), hummocky cross-stratification (HCS) has always been considered as a diagnostic feature of surface-storm waves (SSWs) on the shelf. Nevertheless, the origin of HCS is still debated and the required hydrodynamic processes still controversial (see Quin, 2011, for a recent review). Moreover, HCS has never been observed unequivocally in recent sediments nor its formation in natural environments (Swift et al., 1983; Amos et al., 1996; Li and Amos, 1999) and only smaller structures with similar characteristics have been produced in laboratory experiments (Allen, 1997; Southard et al., 1990; Myrow and Southard, 1991, 1996; Dumas et al., 2005; Dumas and Arnott, 2006). Consensus exists in HCS to be a diagnostic structure of the shoreface-offshore transition zone and it is commonly used as criterion for the occurrence of surface storm events (Harms et al., 1975; Barron, 1989), being characteristic in tempestite beds (Dott and Bourgeois, 1982; Walker et al., 1983; Myrow, 2005). Nevertheless, HCS and HCS-like structures have also been recognized in other depositional environments, from lacustrine to deep-water successions, regardless of age and sediment composition (Dott and Bourgeois, 1982; Duke, 1985; Leckie, 1988; Cheel and Leckie, 1993; Dumas and Arnott, 2006; Mulder et al., 2009; Quin, 2011). Despite the spectrum of environments where HCS has been recognized, this structure is often used as diagnostic of surface storm waves and thus may bias the interpretation. Nevertheless,

4 Page 3 of 40 For Review Only and as already pointed out by Lamb et al. (2008), despite the advances in the recognition of deposits related to the flow wax and van, either related to hyperpycnal- or wave-modified turbiditic flows (e.g.: Kneller and Branny, 1995; Myrow and Southard, 1996; Myrow et al., 2002; Mulder et al., 2003; Mutti et al., 2003; Wright and Friedrichs, 2006), much remains unknown about cross-shelf sediment transport and the origin of eventitic sandy-beds in the sedimentary record. In this context of uncertainties, internal waves (IWs) are an alternative mechanism to generate HCS and HCS-like structures both in open marine and in lacustrine settings. In this scenario, the oscillatory-related part of the HCS structure is not necessary linked to the surface storm wave, but it depends on the bathymetry at which the pycnocline intersect the sea floor. Hummocky cross stratification First described by Campbell (1966) as truncated wave-ripples laminae and latter defined as HCS by Harms et al. (1975, page 87), HCS consist of low-angle (generally < 10, up to 15 ), curved to undulating laminae that are concave- (swales) and convex upward (hummock), commonly formed by silt to fine sand grains. Above an erosional base, laminae are broadly sub-parallel, thin over hummocks and thicken into intervening swales, and are isotropic in three dimensions forming sets usually up to 20-cm thick (Fig. 1). Hummocks are typically m high and spaced from one- to few metres apart (Harms et al., 1975; Harms, 1979; Dott and Bourgeois, 1982; Walker et al., 1983; Cheel and Leckie, 1993; Dumas and Arnott, 2006). Thickness of the HCS bed varies from few centimetres to m (average cm), whereas individual laminae vary from about 1 mm to 1-2 cm in thickness (Dott and Bourgeois, 1982).

5 Page 4 of 40 Swaley cross-stratification (SCS) consists of a series of superimposed concave upward shallow scours, about m wide and a few tens of cm deep, that generally occurs above HCS (Leckie and Walker, 1982, p. 143). The diagnostic features are antiformal hummocks and synformal swales (Dott and Bourgeois, 1982). Anisotropic HCS are characterized by low-angle cross-strata sets that have a preferred unimodal dip direction (Arnott and Southard, 1990; Cheel and Leckie, 1993). Dott and Bourgeois (1982) also suggested the existence of different order surfaces (Fig. 2) and a sequence of sedimentary structures: overlaying a first-order scoured base (with sole marks) the hummocky zone contains several second-order truncation surfaces; above it, a zone with flat laminae and a zone with well-oriented ripples do commonly occur. This bed type commonly lies and is overlain by mudstone or siltstone, frequently burrowed, or is amalgamated with other hummocky beds. Sole marks frequently occur at the base of the beds in discrete HCS overlying mud intervals (Leckie and Krystinik, 1989). Cheel (1991) found that in plan view, particle a-axes, despite variable, are mostly oriented normal to the sole marks and parallel to the associated ripple crests. Macrofossils associated to HCS may also have a preferred long-axis alignment, parallel to elongate crests of hummocks (Handford, 1986). Fig. 1 & 2 Thicker sandstone beds preferentially occur in proximal settings, where amalgamated HCS predominate, and grade into discrete HCS interbedded with fines toward distal position (Dott and Bourgeois, 1982; Dumas and Arnott, 2006; Cheel and Leckie, 1993). Downdip, a decrease in grain size, sandstone-shale ratio and steepness of scour at the base of the sandstone beds also commonly occur, as well as an increase of the thickness of the basal parallel-laminated

6 Page 5 of 40 For Review Only interval (see Fig. 2), in the abundance of symmetrical or eventually asymmetrical ripples, and in bioturbation at the top of the HCS beds. Environment, hydrodynamics and depth estimation for HCS Although HCS is mostly recognized at the transition between nearshore- and outer-shelf facies (e.g.: Duke, 1985) and most commonly between the lower shoreface and the offshore facies (Harms et al., 1975) it has also been reported in other depositional environments like lacustrine, estuarine, intertidal flat and pelagic settings, as well as in turbidites (Table 1). The abundance of HCS in shelf settings, however, might be related to the greatest preservation potential between fair weather- and storm-wave base (e.g.: Dott and Bourgeois, 1982; Dumas and Arnott, 2006), an to the availability of granular sediments (silt to fine sand) that can be transported downdip through various transport mechanisms such as storm induced currents, hyperpycnal flows and turbiditic currents. Table 1 Harms et al. (1975) were the first to interpret the hydrodynamic conditions required for HCS to form and suggested they were the result of strong surges of varied directions, generated by relatively large storm waves on a rough sea. Latter, Dott and Bourgeois (1982) proposed HCS to form by unusual waves beyond the fair-weather breaker zone and evidenced the need of having a first transport process to deliver sand to the offshore (e.g.: flooding rivers or scour on the bottom by wave-surge and wind-driven currents) in which suspension was a predominant component of the flow, as reflected by the efficient sorting of sand; when the

7 Page 6 of 40 wave energy decreases, fallout from suspension begins, and the falling grains encounter a zone of intense oscillatory sheet flow, which molded the beds in hummocks and swales. Dott and Bourgeois (1982) also suggested each lamina to represent deposition from a single wave or wave train. The hypothesis that one set of HCS is created in one event (Greenwood and Sherman 1986; Van de Meene et al., 1996; Amos et al., 1996) seems to also be supported by some boxcores recovered along the Dutch coast in the North Sea (Passchier and Kleinhans, 2005), of course with the doubt if they are true HCS instead of 3D large ripples, not clearly identifiable in boxcores. Allen (1985) and Allen and Pound (1985) considered HCS bedforms as polygenetic in origin but not necessarily related to storm waves. Cheel and Leckie (1993) retained HCS to be a bucket term that embodies similar stratification styles, which may be generated by a variety of processes or combinations of processes. In any case, most authors agree on the importance of SSWs in forming isotropic HCS as well as the occurrence of unidirectional currents responsible of the emplacement of sand. Anisotropic HCS, however, is interpreted to be the product of a combined flow with an effective unidirectional component that causes the bedform migration. Thus the variety of HCS appears to represent a continuum of flow types, from purely oscillatory- to combined flow, additionally controlled by the rate of bed aggradation (Nøttvedt and Kreisa, 1987; Cheel and Leckie, 1993; Dumas and Arnott, 2006). In fact, many authors pointed out the difficulty in explaining the deposition of thick beds containing isotropic HCS; this fact requires transport and rapid deposition of a large volume of sand, presumably with a predominant unidirectional-flow component, and reworking during deposition of the suspended sediment load by complex oscillatory flow or oscillationdominated combined flow during the rapid deceleration of the unidirectional flow (Myrow and Southard, 1996). In fact, the existence of graded shelf sandstones with HCS implies the suspension of large amount of nearshore sediments to generate density currents and to carry

8 Page 7 of 40 For Review Only them downdip for long distances (Myrow et al., 2002). In a classical tempestite sequence (Fig. 3), deposition starts with a plane-parallel interval thought to indicate an upper-plane bed in a supercritical flow regime- after the erosional scour formation indicative of turbulent flow (Dott and Bourgeois, 1982, Walker et al., 1983). In this context, it is likely that also conditions for antidune formation cannot be excluded. Laminae are mostly parallel to the erosional base with thickening in the swaley and thinning toward the hummock. At the top of the sandy bed, symmetrical ripples frequently occur (Fig. 3). Leckie and Krystinik (1989) also describe asymmetrical ripples migrating offshore at the top of tempestite beds with HCS. Fig. 3 For medium sand in a depth of 10 m, minimum near-bottom velocities required to produce plane beds would be on the order of 50 cm/sec (Bourgeois, 1980). High suspended-sediment concentration would also be required in order to produce laminae that repeat (parallel) the hummock and- swale topography as deposition proceeds. Southard et al. (1990), based in experiments, suggested some HCS to be generated during sediment fallout from strong purely oscillatory flows at moderate to long oscillation periods. Conditions needed for HCS to form are thought to require, in a first phase, a high Reynolds number (turbulent flow) and Froude number >> 1 with erosion, transport and sediment supply (De Celles and Cavazza, 1992). Recent experiments (Dumas et al., 2005; Dumas and Arnott, 2006) indicate that hummocks can be generated under moderate to high oscillatory velocities (> 50 cm/s) and low unidirectional velocities (less than 10 cm/s). Dumas et al. (2005) experimentally generated some HCS-like structures by aggrading large 3D ripples, and suggested HCS to be generated by migrating hummocky bedforms under either purely

9 Page 8 of 40 oscillatory flow (Uo; cm/s) or oscillatory-dominant combined flow (Uu;12 cm/s) 1. A further increase in Uu generates anisotropic stratification due to downstream migration of bedforms to become asymmetric. According to these authors, hummocky bed forms are better developed in finer sediment (0.14 mm or 0.11 mm; unscaled variables) and under longer wave period (10.5 s or 9.4 s, unscaled variables), implying HCS to be preferentially generated during high-energy storm events where fine sediment (very fine to fine sand) is available in large, deep, and unsheltered bodies of water where long-period waves can propagate. Another important parameter is the wavelength of HCS, interpreted to be a function of the orbital diameters of storm-induced oscillatory currents near the sea floor (Ito et al., 2001). These authors suggested a direct relationship between HCS wavelength and bed thickness and inverse relationship between wavelength and paleo-water depth. Recently, Quin (2011) suggested isotropic HCS in shelf environments to be generated by high-energy combined flows, which develop inherent instabilities. Although the origin of the invoked instabilities is unclear, they could form in response to shear generated within storm flow boundary layers or as a result of Kelvin-Helmholtz type instabilities associated with density flows (such as hyperpycnal currents). Quin (2011) concludes that the prevalence of HCS in the shelf may indicate an interaction between density flows and surface gravity waves (SSWs), but there is still persisting uncertainty regarding the process that generates HCS. Paleodepth estimations of HCS are also highly variable (Table 2). Harms (1979) suggested that HCS might form at water depths of 5 to 30 m, from an estimation of the relative position of facies in the geologic record. Seguret et al. (2001) inferred the maximum paleodepth to range between 50 and 80 m, based on the modern bathymetry of the ocean wave influence on the continental shelf. McCave (1985) estimated HCS to occur at a maximum depth of ) Uo: orbital wave velocity; Uu: velocity of unidirectional flow added to the oscillatory flow.

10 Page 9 of 40 For Review Only m on the basis of the theoretical combined effects of surface storm waves and their induced bottom orbital velocities. But, as pointed out by Immenhauser (2009, p. 129), when this structure is viewed in a critical manner, the bathymetric significance is just a relative depth indicator for the neritic domain. Table 2 Internal waves Internal waves (IWs) are waves that propagate along a pycnocline, the interface between two different density fluids in oceans and lakes. IWs are gravity waves and are as common as waves at the sea surface, and perhaps even more, and vary widely in amplitude, period, speed and depth (Munk, 1981, Global Ocean Associates, 2002; Thorpe, 2005). IWs amplitude can range from few centimeters to more than 100 meters and have much lower frequencies than surface waves because the smaller density differences (Apel, 2002). Internal waves arise from perturbations of the hydrostatic equilibrium, where balance is maintained between the force of gravity and the buoyant restoring force. IWs are commonly excited by storms, wind-stress fluctuations, interaction of tidal currents with topography, tsunamis, turbiditic flows, and other processes that are still poorly documented (Staquet and Sommeria, 2002; Santek and Winguth, 2007). Internal waves are typically the most energetic high-frequency events in the coastal ocean, displacing water parcels by up to 100 m and generating strong currents (both upslope and downslope) and turbulence (Moum et al., 2003; Nash and Moum, 2005)

11 Page 10 of 40 The depth of the pycnocline is highly variable and it depends on the amount of mixing. In modern icehouse conditions, under thermohaline circulation, it mostly depends on the temperature gradient and strongly changes with latitude and season. A permanent thermocline is typically strongest at low latitudes where it can be as deep as m and tend to be minimal at high latitudes. At mid latitudes, seasonal thermoclines develop in the upper 100 m during spring and summer, and disappear during fall and winter when wind systems strengthen. Large internal solitary waves (or solitons) occur as solitary wave packets (sensu Apel, 2002) are widespread and ubiquitous wherever water currents and stratification occur in the neighborhood of irregular topography (Munk, 1981; Global Ocean Associates, 2002). They particularly occur near regions with abrupt bathymetry changes (e.g.: shelf edges, seamounts, sills, and submarine canyons) where the bathymetry forces the pycnocline to oscillate with the frequency of the tidal wave (Santek and Winguth, 2007). These conditions frequently happen during the warm months, when a shallow thermocline develops. Where horizontal currents impinge on undersea ridges or mountains, internal waves are generated and internal wave energy flows away from this generation area (Farmer and Armi, 1999; Holloway and Merrifield, 2003; Wolansky et al., 2004) Internal waves and solitons propagating along the shallow-water pycnocline mostly dissipate over the continental shelf regions of the World oceans, where they are especially common (e.g.: Wolanski et al., 2004; Quaresma et al., 2007; Lim et al., 2010). Internal waves propagating along the deeper permanent pycnocline commonly have tidal frequencies and are ubiquitous in submarine canyons and continental slopes (e.g.: Cacchione et al., 2002) On the shelf, the impact of IWs is usually strongest in the midshelf region (depth of the pycnocline) and weaker in shallow water, in contrast to SSWs whose impact is strongest near

12 Page 11 of 40 For Review Only the sea surface and decreases with depth (Thorpe, 2005; Butman et al., 2006; Quaresma et al., 2007). The possible impact of IWs in inducing the hydrodynamic conditions required for isotropic HCS to form has been largely disregarded in the literature, except for a few and very short hints. For example, Woodrow (1983) stated, but only in the abstract, that the formation of internal waves, that moved along the pycnocline and shoaled, broke and reworked sediment, leaving a record of relatively thick sandstones, some with hummocky cross-bedding (sic). Also Allen (1997, page 337) suggested the unsteady component for HCS to form might be provided by wind waves, internal waves or Kelvin-Helmholtz instabilities, whereas the steady flow might result from a turbiditic underflow, a geostrophic flow or a littoral current. Refraction on the shelf strongly orients the packet crests along isobaths and retards their speed of advance (Emery and Gunnerson, 1973; Apel, 2002). Breaking of IWs on sloping sea bottom creates episodic high-turbulence events (Southard and Cacchione, 1972; Ribbe and Holloway, 2001; Apel, 2002; Fringer and Street, 2003; Bogucki et al., 2005; Thorpe, 2005; Bourgault et al., 2008; Legg and Klymak, 2008; Boegman and Ivey, 2009; Lim et al., 2010), and remobilize the sediment from the depth at which the pycnocline intersects the sea floor (Thorpe, 2005). Worth to mention that in all the above reported examples (see Table 2), depth estimations are only based on the oscillatory effect of SSWs and no one has suggested or considered the IWs as a potential mechanism to generate oscillatory flows. In this scenario the precise paleodepth cannot be calculated, because the oscillatory flow induced by IWs is linked to the pycnocline depth, not to the position of the sea level neither to the amplitude of the storm waves. And the depth of the pycnocline is more variable than the storm wave base and can vary through time, even in a short time interval (30-40 years, Capotondi et al., 2005).

13 Page 12 of 40 Discussion The hydrodynamic characteristics of IWs are consistent and fully compatible with the hydrodynamic conditions required by HCS to form rather than SSWs, which have a more limited spectrum in terms of min/max wave amplitude, period, frequency and height. IWs meet the required conditions postulated by Dott and Bourgeois (1982) in terms of: a) bathymetric position (inner-shelf to lower shoreface transition), b) evidence for large waves, and c) their relative event frequency. IWs also fit with the depositional model proposed by Duke et al. (1991) who stated that hummocky storm beds were: a) affected by waves oriented roughly parallel to shore, b) flat-laminated intervals were deposited under oscillatorydominant combined flows with a relatively weak seaward current component near the bed, and c) the hummocky intervals were formed under waning, purely oscillatory flows, or very strongly oscillatory-dominant combined flows, during-late or post-storm conditions and produced by swell waves. Based on laboratory experiments (e.g.: Wallace and Wilkinson, 1988; Southard and Cacchione, 1972), direct observations on modern oceans (e.g.: Emery and Gunnerson, 1973; Haury et al., 1979; Noble and Xu, 2003; Hosegood et al., 2004; Butman et al., 2006; Quaresma et al., 2007) and numerical models (e.g.: Fringer and Street, 2003; Venayagamoorthy and Fringer, 2005, 2006, 2007; Barad, 2006; Michallet and Ivey, 1999; Aghsaae et al., 2010), the processes associated to the break of IWs on a sloping surface (Fig. 4) can be summarized as follow: 1) Breaking of IWs on a sloping surface creates a zone of high turbulence and suspension of sediment; the disruption of orbital trajectory creates a mass transport and induces an up-slope unidirectional current that transports updip water and sediment in suspension and, eventually, rip-up clasts (swash, run-up movement). The

14 Page 13 of 40 For Review Only IWs run-up is commonly much more longer than the run-up induced by SSWs. Thorpe and Lemmin (1999) evidenced that the internal-wave surf zone has some, but possibly not all, the characteristics of the conventional surface-wave surf zone, with waves steepening as they approach the slope at oblique angles; fronts form during the upslope phase of the motion, and the return flow may become unstable, leading to small advecting billows. 2) The backwash or return flow that follows the swash is much more efficient in downslope sediment transport, both as bedload and in suspension. The inclination of the sea-bottom also favors the acceleration of the return flow and increases the potential creation of density flows (e.g.: hyperpycnal flow). During this phase, flow becomes turbulent and supercritical and can erode the substrate, creating scour surfaces (sole marks). Southard and Cacchione (1972) have shown individual vortex to produce ridges and furrows. These erosional features created by IWs during break and during the backwash are represented, in our view, by the sole-mark structures found at the base of many HCS. The planar laminations of upper flow regime above the basal erosion surface in HCS (see lower part of the tempestite bed in Fig. 3) is suggested to form when the swash current starts to loss their and deposits the bedload sediments Recent measurements in the Chinese Sea (Xu et al., 2011) have shown the local Froude number to reach a maximum value and the flow to become supercritical during the passage of an ISW near the main thermocline with the Froude number decreasing gradually upward and downward whilst before and after the passage of the ISW, the local Froude number was less than 1 and the flow was subcritical in the entire water column. This supports the possibility that some upper-flow structures can be created directly from the action of the IWs. Another important difference between SSWs and IWs is related to the period; longer period for IWs prevents the backwash flow to be

15 Page 14 of 40 hindered by the next coming wave and, consequently, the return flow can travel downdip for a longer distance. 3) Downdip of the breaker, the energy of IWs progressively decreases and, consequently, the induced unidirectional currents wane and the oscillatory-flow component of the IWs become dominant in re-shaping the sediments deposited in the previous phases and, eventually, still supplied from the remaining currents. The oscillatory flow has a strong shear component that is sufficient to resuspend the sediments and to create the internal truncation surfaces of the HCS. On the other hand less energy pulsations during the waning phase generating the conditions to create the deposition of wavy single laminae both of the classical hummocky and/or swaley. It can also be suggested deposition of the single laminae that conform the hummocky and swaley cross stratification to be the response to the successive pulses of energy induced by the passage of an IWs train. 4) The amplitude and wavelength of single HCS bedform can be related to the same parameters of the IWs, scaled in relation to the effective internal wave base, with the Froude number decreasing gradually upward and downward. fig. 4 The characteristic shape of isotropic HCS is, apparently, difficult to conciliate with the shoreward propagation of IWs, with crests parallel to the shoreline. While sole marks and the lower part of the classical tempestite beds can be easily explained with the unidirectional currents induced by breaking IWs (swash and backwash). The periclinalic dips orientation of

16 Page 15 of 40 For Review Only laminae that create the classical bumped structure in the isotropic HCS, requires of further considerations. A relatively simple explanation would be to consider some interference (reflection-refraction) between distinct trains of solitons or with sea-bottom irregularities along the shelf (e.g.: canyons, banks, or islands; Prasad and Rajasekhar, 2011). Interference mechanism, or secondary internal waves (e.g.: Vlasenko and Alpers, 2005) created by IWs approaching an obstacle on the sea floor, may also easily explain the tridimensional shape of isotropic HCS. The shape of IWs crest is not linear but arcuate due to the interaction and refraction of IWs on a shoaling the shelf (Wunsch, 1969). This leads to also consider, for a shallow pycnocline, the interference between IWs and SSWs; in this case the angle of the surface-waves crest can be highly variable respect to the shoreline, while the IWs remain parallel. In fact, a possible interference mechanism has already been proposed for some Tithonian-Neocomian rocks of India, where HCS developed from storm wave interference with ebb-tide currents (Bose et al., 1988). In this case nearly asymmetrical HCS are consistent with the direction of ebb-tidal cross-stratification, suggesting offshore sand transport by superposition of waves on an ebb-tidal current. Resonance effect between IWs and bottom layer currents can be very important in amplifying the sediment transport on the sea floor (e.g.: Shrira et al., 2000). Standing waves can also influence the shaping of HCS (Emery, 1956; Allen, 1982; Staquet and Sommeria, 2002; Boegman and Ivey, 2009; Rodeborn et al., 2011). As well known from surface gravity waves, when the angle of incidence is 0 (wave crest parallel to the shoreline) the two waves interact to form standing waves (Bridge and Demicco 2008, p.219). In fact, a standing wave is formed by the superposition of two waves of the same frequency propagating in opposite directions. If the waves of the two trains have the same period and height, the water-surface ranges within an envelope in which stationary nodes alternate with antinodes (Allen, 1982). Resonance amplifies the displacement at the nodes and occurs when

17 Page 16 of 40 the period of the basin is similar to the period of the force producing the standing wave. The presence of lateral boundaries in the natural water bodies creates the condition for reflection of both surface and internal waves. Thus the returning waves must be superposed with the initial wave train. Under certain conditions, the reflected and progressive waves match in such a way that the waves appear to stand still and create the so-called standing waves. An important effect of the reflection of the internal waves related to the existence of boundaries in the natural systems, as well as in laboratory experiments, is the creation of harmonics and mixing (Rodenborn et al., 2011). These authors demonstrate that some values of the topographic slope give the most intense generation of second harmonic waves in the reflection process. In a domain with a sloping boundary, rays exponentially approach a closed circuit an attractor after several reflections; a wave attractor is a part of the domain where almost all the wave-induced energy is concentrated. The corresponding standing waves have a fractal structure along the attractor. Maas et al. (1997) experimentally observed the existence of such a wave attractor. A strong-wave steepness is obtained along the attractor, producing some turbulence and could have applications for mixing in closed oceanic basins or lakes and also on the sediment resuspension and deposition. The origin of hummocks and swales in classical isotropic HCS in relation to the internal standing waves action can be summarized as follows. Production of internal standing waves is not a rare event if we consider that IWs are generally refracted along continental shelf and this orients them preferentially in updip direction (Wunsch, 1969). When standing internal waves form, they may also interact with the sediment. The mass-transport beneath standing waves occurs as a series of cell-like circulations with boundaries at a spacing of one-quarter the wavelength of the surface or internal waves (Allen, 1982; Ng 2004). In 3D, standing waves can have the same geometry of vibrations that forms, for example, in a drum and, at scale of natural systems, mimic the topography in plan view of fossil HCS, such as the well-

18 Page 17 of 40 For Review Only documented example, using ground penetrating radar, of an Upper Cretaceous lowershoreface succession in Utah (Lee et al., 2009). In fact, oscillation between node and antinode in a 3D view is quite similar in shape to the superficial shape of HCS and can explain how, in a prevalent oscillation mode, concave-convex lamina can form. Shear stress, due to the orbital velocity, can resuspend temporarily the fine sand and redistribute such sediment with the characteristic hummock and swale. Such movement, described for standing waves by Allen (1982, see his fig. 1.22), can also explain the thickness difference of the single lamina set between the swale and the hummock part of the structure. In the convex-up part (hummock), the sediments are less prone to accumulate than in the concave part (swale), in relation to the orbital velocity variation between the two parts. According to these hydrodynamic characteristics, internal standing waves related to the reflection of IWs against the continental shelf, can be a plausible mechanism for generating hummocky bedforms. If we consider the effect and the behavior of IWs in both modeled and observed in modern oceans (Inall et al., 2001; Storlazzi et al., 2003) and we combine together these factors i.e.: shape, amplitude, periods, breaker and eddies formation (boluses), upslope and downslope flows, changes in orbital parameters when approaching the bottom, 3D evolution in the breaking zone (Boegman and Ivey, 2009) the formation of HCS may plausibly be the result of such hydrodynamic behavior and the strong interaction with bottom sediments. Chou and Fringer (2010) developed a three-dimensional numerical model to simulate bed form dynamics in a turbulent boundary layer. Currently the code is being used to study turbulence mixing, sediment transport and sand ripple evolution in combined wavecurrent flows. Considering the 3D shape of some simulations (Venayagamoorthy and Fringer, 2007) and particularly in proximity of the breaking zone, isotropic HCS could be the result of the IWs alone, whereas anisotropic HCS could be the result of both the two different types of waves or only related to the SSWS.

19 Page 18 of 40 Another question still to be solved is the availability of fine sand sediments to form HCS in the loci influenced by the IWs action. This implies to explain the sand to be transported from the shoreface to the offshore area. Michallet and Ivey (1999) have shown an effective transport related to the IWs breaking zone and this can be relatively shallow if is associated to the seasonal pycnocline. In any case we cannot exclude other type of unidirectional currents (geostrophic current, hyperpycnal flow or turbiditic currents) in playing a role, or to be concomitant, in such sediment redistribution, even some which can necessarily be confined to the nearshore zone (Swift et al., 1983; Myrow et al., 2002; Wright and Friedrichs, 2006; Lamb et al., 2008, 2010; Lamb and Mohrig, 2009). In any case, and contrarily to SSWS, IWs are most efficient in resuspend and transport sediment in the middle- and outer shelf (Butmann et al., 2006). IWs and hyperpycnal flows can also be concomitant, and IWs can rework, rather than surface waves, the upper part of the hyperpycnal flow (Mutti et al., 2003). Conclusions The origin of hummocky cross stratification (HCS), a well-known sedimentary structure, is still unknown and debated. Despite these uncertainties HCS is commonly considered as a diagnostic structure of surface storm events, and indicative of the lower-shoreface- to offshore-transition zones. In this context of uncertainties, internal waves provide a plausible alternative mechanism. Our rationale can be summarized as follows: 1) IWs can form in any aquatic depositional environment as far as there is any stratified fluid. More frequently on the shelf associated to the seasonal pycnocline, they can also occur in lakes, in stratified fluids associated to turbidite flows and in deep-water settings. 2) On the shelf, the impact of IWs is usually strongest in midshelf region and weaker in shallow water, in contrast to SSWs the impact of which is strongest near the shoreline and

20 Page 19 of 40 For Review Only exponentially decreases with depth. IWs provide thus a mechanism for water motion at certain depth independent of SSWS. 3) The bathymetric position of the shallow seasonal pycnocline is variable but most commonly below the storm wave base. As discrete HCS beds tends to occur in more distal settings than amalgamated HCS, it is plausible to conclude amalgamated sandstones to occur below but near the IWs-breaker zone, whereas discrete HCS sandstone beds should form in a deeper zone, with predominant muddy background sedimentation. 4) IWs, and particularly solitons, occur as isolated wave trains in which the individual oscillations are rank-ordered by amplitude, wavelengths and crest lengths. The amplitude is largest in the frontal wave of the train and the smallest is at its rear. We suggest that the organization and hierarchy of internal laminae in HCS beds can be explained with this variations: the first pulse might be responsible of the origin of the scoured first-order bounding surfaces, whereas second- and third order surfaces might be attributed to the individual cycles within soliton packets. 5) Flow regime interpretations for HCS to form, although not yet fully understood, range from pure oscillatory flow, unidirectional-dominated combined flow or oscillatory-dominated combined flow. This variability seems also to be consistent with the variability of flow conditions associated to IWs and their induced flows. IWs provide both unidirectional (offshore directed) and oscillatory flow conditions. Moreover, interference and internal standing waves are plausible mechanisms to explain the 3D geometries seen in HCS bedforms. 6) Offshore-directed paleoflow direction indicated by sole marks, parting lineation and, locally, internal cross-laminae, as well as orientation of capping ripples with crests roughly parallel to regional are all them consistent with the bottom currents induced by breaking IWs.

21 Page 20 of 40 7) HCS and HCS-like sedimentary structures may reflect an array of hydrodynamic conditions, that they can form in various depositional environments. From these considerations above we suggest IWs to be the most plausible process for HCS and HCS-like structures to form. They satisfactorily explain HCS occurrence in different depositional environments, the wide range of their bathymetric position and the required flow regime. This scenario also suggests that HCS are not linked to the surface storm wave base but linked to the position of the pycnocline, although both surfaces might be concomitant. We propose that hummocky cross-stratification (HCS) and HCS-like sedimentary structures, can be regarded as a type of internalites formed by the action of internal waves alone or associated to other transport mechanisms (e.g.: hyperpycnal flows, turbiditic flows) that occur frequently along the continental shelf, in lacustrine environments, and also in deepwater settings. We suggest that laboratory experiments and mathematical simulations need to consider the IW parameters (amplitude, period, wavelength etc.) instead of SSW parameters and, eventually, the potential interactions between these two different types of waves. Acknowledgements: We acknowledge interaction and critical discussions with Pamela Hallock. Financial support was provided by Spanish CGL Research Project. References cited Allen, J.R.L., Sedimentary Structures, Their Character and Physical Basis. vol. 1, Elsevier, New York.

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